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					SPSS
tutorial for beginners



        a   c h i l l i b r e e z e   p u b l i c a t i o n
       a   c h i l l i b r e e z e      p u b l i c a t i o n




SPSS Tutorial for Beginners
So you are going to be working on SPSS. Welcome to a whole new

world of figures, data and statistics. We understand that it is natural

to be a little apprehensive before you start using this program to

analyze your data or for your class. You must have realized that

it is not child’s play to use the multiple features that SPSS has to

offer. Don’t worry. Our SPSS tutorial will help you navigate through

the whole process and take you through a journey that covers the

basic features of SPSS that everyone uses. You might not turn into

a pro overnight, but you will definitely be much more comfortable

using SPSS. Our examples and exercise problems will help you

understand the features even better. This tutorial will be especially

helpful for students of biology.
                                              SPSS Tutorial for Beginners




Contents
                                                        SECTION I
                                                       Back to Basic

A Review of the StAtiSticS thAt you leARnt (oR did not leARn?) in college ... 6

i. ReSeARch deSign ............................................................................................................. 7
a. aNIMaL RESEaRCH ............................................................................ 7
      a) Selection of species..............................................................................7
         b) Selection of controls.............................................................................7
         c) Feeding of controls ...............................................................................7
         d) Treatment of controls ...........................................................................8
         e) Ethical guidelines .................................................................................8

b. HUMaN RESEaRCH .............................................................................. 8
     a) Case histories .....................................................................................9
         b) Descriptive studies ..............................................................................9
         c) Prospective studies (cohort studies) ......................................................9
         d) Retrospective studies (case-control studies): ....................................... 10
         e) Retrospective-prospective study: a combination ...................................12
         f) Open trials: ........................................................................................12
         g) Cross-over trials: ................................................................................12
         h) Blind trials: ........................................................................................12
         i) Double-blind cross-over interventional trial: ..........................................13
         j) Metabolic studies: ...............................................................................13
         k) In vitro studies: ..................................................................................13

ii) evAluAtion of MeASuRing inStRuMentS ................................................................ 14
a) MEaSURINg SENSItIvIty aNd SpECIfICIty of a tESt.................................. 14
b) SaMpLINg aNd SaMpLE SIzE ................................................................ 15
         a) Sampling procedures ..........................................................................15
         b) Sample Size .......................................................................................15

(iii) SoMe uSeful teRMS to know................................................................................... 16

(iv) typeS of dAtA And AppRopRiAte StAtiSticAl teStS ............................................. 17
       a) The t-test ........................................................................................... 17
         b) Analysis of Variance (AoV) ................................................................. 19
         c) Correlation .........................................................................................20
         d) Regression ......................................................................................... 21
                                                SPSS Tutorial for Beginners




          e) Chi-Square test ..................................................................................22
          f) McNemar test .....................................................................................23
          g) Sign test ............................................................................................24
          h) Mann-Whitney U test ..........................................................................25
          h) Statistical Abuses ..............................................................................26
          j) Quiz to test yourself ............................................................................27
                                              SECTION II
                                              SPSS at Last

SpSS At lASt ......................................................................................................................... 32
CREatINg aNd EdItINg a data fILE ..........................................................33

i) typicAl SpSS SeSSion ..................................................................................................... 35

(ii) cReAting A new dAtA file with the dAtA editoR................................................. 38

(iii) loAding An exiSting dAtA file into the dAtA editoR........................................ 42

(iv) cReAting And executing SpSS coMMAndS ...................................................... 44
      k) The EXPLORE command ....................................................................44
          l)The FREQUENCIES command ..............................................................46
          m) The DESCRIPTIVES command ..........................................................49
          n) The IF and COMPUTE commands ....................................................... 51
          o) The MEANS command .......................................................................53
          p) The T-TEST command ........................................................................54
          q) The ONE-WAY ANALYSIS OF VARIANCE command ...........................59
          r) Scattergrams and Regression ..............................................................65
          s) Multiple Regression ............................................................................69
          t) CHI-SQUARE test using CROSSTABS ................................................ 74
          u) Selection of a Subset of Cases for Analysis .........................................78
          v) The Nonparametric Tests ....................................................................79
          w) Mann-Whitney U test ..........................................................................80
          x) Bivariate Correlations .........................................................................82
          y) Survival..............................................................................................83

SpSS SyntAx windowS ..................................................................................................... 89
  SECTION I
Back to Basic
                                SPSS Tutorial for Beginners




A Review of the Statistics that you learnt
(or did not learn?) in college
   Before we start to work on the actual software, we think it is necessary to go through
some basics of the statistics involved. We included this section because it is not enough
to know to use SPSS. You need to know what test to use in what situation and how to
plan your research. If you think, you already know this stuff, that’s fine. Just skip it or
consider it a review before you plunge into actually using the software. Here are a few
things that will be included in “The basics of Statistics” section.

      	   Research Design
      	   Evaluation of Measuring Instruments
      	   Sampling and Sample Size
      	   Mean, variance, Standard deviation, Degrees of freedom
      	   T-test
      	   Analysis of variance
      	   Correlation and Regression
      	   Chi-square test, Sign test, Man-Whitney U test etc
      	   Statistical abuses




  
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i. Research design
   In order to get good data, you need good research design skills. Even if you are
reading someone else’s research, to understand it better, it helps to know something
about correct and incorrect research design. There are lots of ways to design a research
project and not all of it is documented. Here, we will describe some of the more common
methods plus will give you a few tips for your research design too.


a. aNIMaL RESEaRCH
    Most biomedical research is first conducted using animal models. Much of this
initial animal research cannot be performed in humans due to ethical, cost and/or time
considerations.

a) Selection of species

   The particular species to be used as a model is chosen for one/more of the following
reasons:
   1.       Similarity of the organ system, disease, metabolic pathways, etc. to the
            equivalent in human beings.

   2.       Small size for ease and economy in housing, feeding, manipulation, etc.

   3.       Relatively short life span to allow for life-time studies, studies over more than
            one generation, etc.

   4.       Comparisons to work of other investigators in the same or similar model.

b) Selection of controls

   This is one of the most important considerations in the design of an animal experiment.
Let us say the investigator is performing a study to determine the deficiency of a
particular nutrient on some measurable parameter. Animals in the experimental group
would be fed a diet containing required amounts of all known nutrients except the
nutrient under study (or the diet would be low in the nutrient). The control group would
receive a normal (same in all respects but with the nutrient present) diet.
   The controls need to be similar to the experimental animals in all respects like
weight, age, genetic strain, etc. In fact, a group of animals need to be randomly divided
into experimental animals and controls. To avoid bias, someone other than the principal
investigator can perform the actual separation.

c) Feeding of controls

    Some animals will consume less of an incomplete diet than they will of a nutritionally
complete diet. If the experiment is run as designed above, the investigator may get false
results that show that deficiency of the nutrient influences the variable being measured.
In reality, the variable may have changed because of the low quantity of food consumed
by the experimental animals. To avoid this, it may be best to have a second control

                                                                                          
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                                      Research Design




group that is “pair-fed” to the experimental group. The amount of food that is consumed
by the experimental group is measured and then that amount of the control diet is fed
to the pair-fed controls. In another approach, the mean intake of food eaten by the
experimental animals is calculated each day and all of the control animals are fed this
amount the following day.

d) Treatment of controls

   Do unto your controls as you would do unto your experimental animals. Basically,
try and eliminate other factors which might be different between experimental and
control animals. If some procedure like an injection or a surgery is performed on the
experimental animals, the controls too should receive a sham procedure. Other variables
to consider in animal experiments are: water consumption, non-dietary sources of
nutrients (e.g. zinc from nibbling on cage bars), time of day procedures are done,
amount of space allocated to the animals, amount of exercise, location within the cage,
number of animals per cage, nature of animals in neighboring cages, etc. Also, there
should be concern for diseases that the animals might transmit to each other or to the
investigator and for diseases that the investigator might transmit to the animals.

e) Ethical guidelines

   Ethical guidelines should be followed meticulously to ensure that research is done
in a humane fashion. Animals and their cages should be kept clean, temperature
should be correct, undue and unnecessary distress should be avoided, etc. Usually,
there are committees on campuses that oversee the treatment of animals. Also, your
university is bound to have courses that you need to take before you take on an animal
experiment.


b. HUMaN RESEaRCH
   In human research, there are a lot of other guidelines and considerations. One can
divide the types of research design into
   1. OBSERVATIONAL STUDIES where the investigator does not alter the natural
occurrence of events but records them and formulates hypotheses and/or conclusions
about what he/she observes. Observational studies are of several types including:
   	 Case histories
   	 Descriptive studies
   	 Prospective studies (Cohort studies)
   	 Retrospective studies (Case-control studies)

   2. INTERVENTIONAL STUDIES As opposed to the passive role of the investigator
in observational studies, the researcher takes an active part in these studies. In
interventional studies, the subjects are exposed to (or denied exposure to) a factor or
method of treatment and followed over time to determine the outcome. Individuals may
serve as their own controls or separate groups of control individuals may be used. These
kind of studies have several research design methods:
   	 Open trials
   	 Cross-over trials
   	 Blind trials
   	 Double-blind cross-over trials
   	 Metabolic studies
   	 In vitro studies



 
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                                           Research Design




    Let us have a closer look at these different kinds of research designs and what
information each can provide us with. This is important for statistical analysis because,
in order to interpret your data, you need to know the usefulness and limitations of each
kind of study and how to classify any particular study. Let’s say you have results of a
Retrospective study and you ask the statistical program to compute Absolute Risk, this
would be meaningless because Retrospective studies can only measure Relative Risk.

a) Case histories

   These studies are often referred to as anecdotal evidence. They are widely used as
testimonials in advertising. In science, they may not be of much value as data, but they
do provide an insight into areas of possible further research. But case histories cannot
give definitive evidence that a certain factor is causal for a certain disease or tat a certain
treatment is effective. Many journals separate these articles into a different section of
each issue. These studies serve as a method of rapid communication of clinical findings
and hypotheses to the scientific community and help generate new leads for future
research.
   Example:
   In a recent report, a physician described a case-history in which a patient with
Common cold, experienced complete remission of symptoms following one week of
supplementation with Vitamin C. Let us examine this closely.
   	       Does this report demonstrate that Common cold is caused by Vitamin
            C deficiency? No. This evidence is not sufficient for a conclusion of this
            magnitude. Doing that would be equivalent to saying an infection is caused
            by an antibiotic deficiency.

   	       Does this report demonstrate that most common cold patients can be treated
            successfully with Vitamin C? No. The study has been performed on a single
            patient and the results cannot be extrapolated to a population.

   	       Does this report show that this particular patient was cured by Vitamin C?
            No/Maybe. The patient may have been cured due to other factors/drugs/
            his own immunity/other remedies etc. There was no control for this case.
            There is no way of knowing if the patient would have been cured without
            intervention.

b) Descriptive studies

    These are often large population studies in which data on lots of different variables
is collected. It is somewhat like a census. Statistical analyses on the data collected may
show various relationships that lead to hypotheses for further study. They may also
provide estimates of the magnitude of a particular problem and the frequency of certain
behaviors among the population. Sometimes they may also generate meaningless
correlations (example: most alcoholics in a particular area send their children to
private schools) that need to be neglected. Descriptive studies are also referred to as
epidemiological studies or surveys.

c) Prospective studies (cohort studies)

   A prospective study consists of two samples, one of which has been exposed to the
suspected risk factor (a + b) and one not exposed (c + d). The two samples are followed
through time to determine which group has the higher incidence (or cause-specific
mortality). In other words, a prospective study compares the absolute risk (of illness or

                                                                                            
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death) of those exposed with the absolute risk of those not exposed. An example of a
table of data from this type of study is shown below.


                              Disease            No Disease              Total

          Exposed                  a                       b             a+b

        Not Exposed                c                       d             c+d


    Information provided by this prospective study:
    1. Absolute Risk (Incidence) of the exposed
                a/a+b
           as compared to those not exposed.
               c/c+d
    2. Relative Risk- the ratio of the absolute risk in the exposed to the absolute risk in
those not exposed.
              (a / a + b) / (c / c + d)
    Relative Risk is the best measure of the strength of association between the risk factor
and the disease in question. How much does the causal factor cause the disease?
    A value of 1 means there is no association between the factors being studied. A value
of less than 1 means the factor is protective. A value of more than 1 means the causal
factor under consideration causes the disease. Usually, a 2-fold difference is considered
to be significant (only when a large population is studied).
    These studies usually give some of the strongest evidence of disease causation
available from observational studies. Human prospective studies tend to be very
expensive to undertake and maintain. Also, some may take decades and are only
taken up by federal research agencies. Even those few are often subject to criticisms
on the basis of the controls used, the ability to stick to a particular scientific protocol
over long periods of time, the ethics leaving individuals at risk, exposed to a certain
factor that may be a risk factor, etc. The Framingham heart study is an example of a
cohort study.
    Example of a prospective (cohort study):

                      Lung Cancer deaths          No Lung Cancer deaths               Total
      Smoker*                227                               99,773               100,000
  Nonsmoker                   7                                99,993               100,000


      * = Someone who smokes 25 or more cigarettes a day is defined as a Smoker
      Absolute Risk for Smokers = 227/ 100,000
      Absolute Risk for Nonsmokers = 7/ 100,000

  Relative Risk = (227/100,000)/ (7/100,000) = 227/7 = 32.4 (This means that a
smoker is 32 times more likely to die of lung cancer than a nonsmoker)
  Attributable Risk = 227/100,000 – 7/100,000 = 220/100, 000 (This means that so
many deaths out of 100,000 could have been prevented by eliminating smoking)

d) Retrospective studies (case-control studies):

   A retrospective study consists of two groups, one with the disease (a + c) and the
other without the disease (c + d) under study. The group with the disease consists of


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“cases” and the group without the disease is the group of “controls”. The typical way of
expressing data from such a study would be as below

                                         Disease (cases)              No Disease (controls)
            Exposed                              a                             b
          Not Exposed                            c                             d
                 Total                        a+c                             c+d

   Information provided by such a study design:

   1.        Cases and controls are compared with respect to the proportions that have
             been exposed to the risk factor. The proportion of cases exposed (a / a +
             c) is compared to the proportion of controls exposed (b / b + d) i.e. rate of
             exposure in diseased/rate of exposure in the non-diseased.

   2.        If, in the population at large, the number of persons who have the disease
             is quite small compared to the non-diseased population, Relative Risk may
             be estimated by using the “odds ratio” or cross-product ratio” or “relative
             odds”



         ad
         _____
         bc

   ****** Neither absolute risk (incidence) nor attributable risk can be inferred from a
retrospective study without reference to outside information.
   Then, you may wonder, why are these tests done at all?
   The reasons may be:
   1.        They consume less time

   2.        Consequently they take up less money too

   3.        Epidemiologists can first try out such calculations before undertaking a
             cohort study.

   4.        Subjects need not be controlled because we already have the outcomes.

   5.        These studies are less unethical because we are not denying/ causing
             exposure to any suspected curative/ causative agent.

   6.        Epidemiologists seldom bother about accuracy unlike statisticians (Just
             kidding!)


   Example of a retrospective (case-control study):


                         Lung cancer deaths          Deaths with no lung cancer       Totals

     Smoker                     464                             167                    631
   Nonsmoker                    36                              333                    369
        Totals                  500                             500                   1000


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   Relative odds = (464 x 333) / (167 x 36) = 25.7
   We cannot determine incidence from this data.
   Information from case-control studies does not “prove” causation but gives stronger
evidence than that from case-histories. If similar relationships are found by different
members of the scientific community in different experiments, then the findings are
gradually accepted as strongly suggestive of causation.

e) Retrospective-prospective study: a combination

   Some countries such as Finland have their entire population registered in the national
health program since a very long time. This provides investigators with solid records and
accurate information about any section of the population going back to any period of
time. The investigators can then start with the point at which exposure took place and
then track individuals until the present. This type of study combines the advantages of
both prospective and retrospective studies.

f) Open trials:

   This is the simplest kind of interventional study. In this design, the researcher and
the subjects, both are aware of the nature of treatment and the intended/ expected
results.

   Example: A group of diabetic women were used to study the effect of a particular
herb extract on their fasting blood sugar levels. The fasting blood sugar levels would
be determined at the beginning of the experiment and again after a 10-week period
of receiving the extract. In this instance, each subject served as her own control.
Alternatively, there could have been two groups, one receiving the extract (experimental
group) and one receiving a placebo (controls). In both the above cases, the herb extract
use, the placebo use and the hypothesis being studied would be known to all parties.
   These trials have the benefit of being very easy to conduct and also avoid the
ethical issue of withholding a particular treatment from the control group. The biggest
disadvantage to this method of research design is that knowledge of the treatment
method/ placebo may influence the outcome due to actions and psychology of the
subjects and/or the researchers.

g) Cross-over trials:

   In cross-over trials, two groups of subjects are studied. One group receives the
active treatment for an initial period of time while the second receives a placebo. At
the end of the designated period, the first group is switched to placebo and the second
to the active treatment. This design is used to help eliminate effects caused just due
to participation in an experiment and those due to seasonal variations in the variables
being measured.

h) Blind trials:

    Here, some of all of the participants and/ or researchers are prevented from knowing
the identity of the group receiving the treatment until the conclusion of the experiment.
In a “single-blind” trial, the subjects are denied knowledge of whether they are receiving
the active treatment or placebo but the researchers are aware of the identities of the
experimental groups and controls. In a “double-blind” trial, neither the subjects nor the
researchers know which individuals receive the active treatment or placebo until the
experiment is over and the data has been collected. The latter experimental design helps


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to control for the “placebo effect” as well as to control for experimental bias.
   You may ask- Why should the investigator be “blinded”? The answer remains the same-
To avoid bias. Let’s say the investigator gets a good result from the diabetes experiment
(the herb reduces fasting blood sugar); he will not repeat the experiment because the
“good result” is in the experimental group, which strengthens his hypothesis. If the
same result is obtained in the control group (the placebo reduces fasting blood sugar),
he will definitely repeat the experiment thinking that it is an error. So the treatment
of experimental groups and controls may not be exactly the same. To avoid this, the
investigator’s unbiased colleague does the labeling, feeding and keeping of records.

    Example: Let us say the investigator wants to perform the same experiment- test if
the herb extract influences fasting blood sugar in diabetic women. A group of diabetic
women are randomly divided into two groups of equal size. All relevant characteristics
are similar in both groups (weight, height, age, blood sugar levels, diet etc.) A capsule
is developed for the experiment- one with the extract and one with the placebo. The two
capsules are indistinguishable in appearance. One group receives the extract capsule
for 10 weeks and the other receives the placebo capsule for 10 weeks. The distribution
is done by an individual not directly related to the project. After the final blood samples
have been analyzed and decisions made as to who improved and who did not, the code
is revealed to the investigator as to which group received the extract.

i) Double-blind cross-over interventional trial:

   This is a blending of the double-blind and the cross-over design. It is one of the most
respected forms of trial design for human studies.

j) Metabolic studies:

    These are usually carried our in a relatively small number of subjects who are placed
in a metabolic ward for intensive study. Individuals generally serve as their own controls.
Mineral balance studies would be an example of this kind of experimental study. Here,
the subjects are fed chemically defined diets containing varying and known amounts of
the mineral being studied. Then the losses from hair, skin, swear, urine, feces etc. are
carefully determined. These studies need a lot of time and effort, and any minute error
while performing the study may result in totally erroneous results.

k) In vitro studies:

   In vitro means the study is conducted outside the living body. It may be performed
on cells, tissues, organs etc. in laboratories under specific conditions. This type of
work is very common and generates a lot of data for statistical analysis e.g. cell counts,
isotope counts, optical density, area under the curve, etc. Sometimes the nature of the
laboratory work requires that the data be converted into percent of control for statistical
analysis.




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ii) evaluation of Measuring instruments
   Measuring instruments, whatever their nature, have two properties that must be
evaluated before they can be Used to perform meaningful measurements.

   Precision (or Repeatability) is the ability of a measuring instrument to give
consistent results on repeated trials. For studying precision, we do not need extraneous
information.

   Validity (or accuracy) is the ability of a measuring instrument to give a true measure.
Validity can be evaluated only if there exists an accepted independent method for
confirming the accurate test measurement.

      Validity has two measures: Sensitivity and Specificity.


a) MEaSURINg SENSItIvIty aNd SpECIfICIty of a tESt
   Sensitivity of a test measurement is defined as the percentage of true positives
identified by the test. A high sensitivity would mean that there would be more false
positives.
   Specificity of a test measurement is defined as the percentage of true negatives
identified by the test. A high sensitivity would mean that there would be more false
negatives.
   An effective measurement tool would have an acceptable value for all these
factors.

    Example: Suppose a new test was developed to determine HIV positivity. We call our
test “Test A”. We run our test on a large group of people and then run the PCR reaction
followed by Western immunoblotting for HIV on the same group of people and record
the true outcome.


                                                  True outcome

                                              +ve                  -ve                total

                           +ve              530 (a)              165 (b)              695
 Test A results            -ve                5 (c)              300 (d)              305

                           total          535 (a + c)         465 (b + d)            1000


      Test A results
      a = true positives  Sensitivity = (a / a + c) x 100 = 530/535 x 100 = 99.07 %
      b = false positives
      c = false negatives
      d = true negatives Specificity = ( d / b + d) x 100 = 300/465 x 100 = 64.52 %


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b) SaMpLINg aNd SaMpLE SIzE
a) Sampling procedures

   Most statistical procedures require that our sample be drawn randomly and that
our experimental units (subjects, animals, etc.) be allocated independently (randomly)
to experimental and control groups. If we fail to do this, the validity of our research in
drawing conclusions about the general population is limited. For example if we were
interested in determining the average expenditure of people living in New York and
drew our sample from a list of people living in Brooklyn, we would get an incorrect
idea of the expenditures. Similarly, if we were trying to solve a public health problem
and only used the group of people listed in the telephone directory, we would still be
making a limited conclusion because everyone need not have private phone numbers.
Thus Sampling techniques become very important. The rule we must meet if we are to
have a “fair” sample is that every individual within the population must have an equal
chance of being selected. There are many sampling designs possible, but the three that
are most commonly used are:
   1.       Simple Random Sample: This is something like pulling out names from a
            hat. It may involve the use of a computer and a random number generator.
            A complete randomized list is necessary.

   2.       Systematic Sample: This is a system where every “nth” individual is chosen
            e.g. every 15th diabetic is chosen from a randomized list of diabetics.

   3.       Stratified sample: This is a system in which the population is divided
            into distinct subpopulations (strata) and samples are selected from each
            subpopulation. Each stratum must be weighted in the final calculation of
            results unless that was done by proportionate sampling from each stratum.

b) Sample Size

    The sample size in an experiment is an important feature in its design and the
interpretation of its results. If the sample size if too small, it may be tough or impossible
to find statistically significant results. But that does not automatically imply that the
larger the sample size, the better our experiment. If the sample size is too large, trivial
differences will have very statistically significant values and we will be easily impressed
with the findings. E.g. If we want to determine the differences in mathematical skills in
boys and girls, and we use 100, 000 boys and 100, 000 girls for this study, we might end
up with a statistically significant result even if the actual difference may be unimportant.
Hence, the number of subjects used for a study needs to be chosen very carefully.
    There are several methods and formulae for selection of appropriate sample size and
these must be used before we begin an experiment.




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(iii) Some useful terms to know
Level of significance: the probability of committing a Type I error.


Mean: the arithmetic average.


Null hypothesis: the hypothesis being tested in statistics (that there is no difference
between the groups under study).

p or p value: level of significance e.g. p< 0.05 means that there is a less than 5 % chance
of having committed a Type I error.

Regression: a type of analysis used to establish formulae describing the relationships
between variables.

Standard Deviation: a measure of variability. It is equal to the square root of the
variance.

Standard Error: a special measure of variability inappropriately used by many researchers
to make their results look better.

Type I Error: rejection of a true null hypothesis.


Variance: a measure of the average variability of a data set from the mean.




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(iv) types of data and
Appropriate Statistical tests
    In research, there are two types of data collected. One type is called continuous
(measurement) data. This is data that have an infinite number of possible data points
between each whole number (e.g. infinite number of points between 1.0 and 2.0 like 1.1,
1.2, 1.23, 1.2455, and so on). Examples of such data would be weight, height, blood
sugar, hemoglobin, etc. As long as it is possible to measure at smaller and smaller
increments, we have a continuous variable. The other type of data is called Discrete
(frequency/categorical) data. These data can only be integers (1, 2, 3 and so on).
Examples would be numbers such as number of deaths due to cancer (We cannot have
1.5 deaths). Since the underlying distributions which are possible with these two types
of data are different, we must use different types of statistical tests depending on which
kind of data we are collecting.

   Statistical procedures for continuous data:
   -     t-test
   -     Analysis of variance
   -     Correlation
   -     Regression
   Statistical procedures for discrete data:
   -     Chi-Square test
   -     McNemar test
   -     Sign test
   -     Mann-Whitney U test

a) The t-test

   Many experiments seek to compare data collected from 2 groups of subjects or
animals (an experimental group and a control group). If the data collected are for
a continuous variable, the best test to use would be the “t-test” or the “Student’s t-
test” (Student was a pseudonym used by W. S. Gosset in his statistical writings). The
“t” distribution was developed to overcome a major problem with using the normal
distribution for hypothesis testing. The normal distribution and tests of hypothesis
related to it, require that we have data from every member of the population to calculate
the mean (µ) and the variance (s2). We rarely have this information. Usually we must
rely on data from samples of individuals drawn from a population. The “t” distribution is
used in describing samples and testing hypotheses related to them. (Actually there are
an infinite number of “t” distributions, each one determined by the degrees of freedom
of s2. When the degrees of freedom (n – 1) reaches infinity, the t distribution is same
as normal distribution.)

   Use of a “t-test” requires that the following assumptions are true:
   1. The sample is randomly selected.
   2. The sample is drawn from an underlying normal population.




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   We   must have the following data:
   1.   A mean for each sample (t-test allows comparison of only 2 means)
   2.   The variance for each sample
   3.   The number of individuals in each group

   The hypothesis being tested by a t-test is that two samples are equal
   Ho:  x1 –  x2 = 0
   The alternate hypothesis is that the means are not equal.

    Different research situations call for slightly different versions of the formula for
calculation of the t-test. If the variance of the two samples is equal, a “pooled-variance”
t-test is conducted. E.g. If we are studying blood sugar of males and females, we expect
the variance to be similar for the two groups.

   The formula for pooled-variance t-test is:

                 x1 –  x2
   t = --------------------------
           sp
   ______________________
                (n1 – 1)s12 + (n2 – 1)s22
   where sp = -------------------------------------------
                             n1 + n2 -2
              √
   the degrees of freedom (d.f.) = n1 + n2 – 2

   If the variance of the two samples is not equal, we use the “separate variance” t-test.
This is also called independent t-test. It is calculated with the following formula:

                   x1 –  x2
   t=    ----------------------------------
                _____________
                 s12 + s22
                 ----        ----
                 n1            n2
              √
                                                      [(s12/n1) + (s22/n2)]2
   degrees of freedom (d.f.) =              --------------------------------------------
                                              [(s12/n1)2/ (n1 + 1)] + [(s22/n2)2/ (n2 + 1)]

    After selecting the appropriate formula, we calculate the t-value using the data from
our experiment and then look up the critical of “t” in a table. If our t-value exceeds the
critical value of “t” at our degrees of freedom, then we must reject the null hypothesis
and infer that the alternate hypothesis is true (The means are significantly different).

   Example:
    Suppose we conducted an experiment to determine the effect of a protein supplement
on the body weight of low birth weight babies. The results of the experiments are as
follows:

                                       Experimental group                       Control group
      Mean weight gain                 100 gms                                  88 gms

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     Standard deviation             3                                        3
     Sample size                    25                                       25

    Our variances are equal (3 squared = 9) therefore we will use the pooled-variance
t-test formula.
               100 – 88                 12
    t = ----------------------- = ----------------- = 14.142
           ___________                   _____
         3 √ 1/25 + 1/25               3 √ 0.08

   From a table of t-values we find that with 48 degrees of freedom, our t-value exceeds
the critical value of “t” at the 0.001 level. Therefore we report that the protein supplement
had a significant effect on weight gain.

   Paired t-test: This is a special t-test to use for research designs in which the data are
from paired samples e.g. if we collect data from the same individual before and after a
particular treatment. Here, everyone is his own control. We can calculate a mean change
or mean difference from our experiment and similarly a variance of the differences. Then
we can use the paired t-test formula:



                      x d
   t=              --------------------              [the degrees of freedom is (nd – 1)]
                        _____
                sd √ nd

   Note about statistical tables: The tables for looking up p-values are readily available
online and also in online calculators (the simplest method according to us). Just look for
p-value calculators. And one more thing- Once you start using SPSS for your analysis,
SPSS will look up the p-values for you. So do not worry about the tables. This is true
for all the tests that follow including Analysis of variance, Sign test etc. etc.


b) Analysis of Variance (AoV)

    It would be erroneous to use the t-test when we have more than 2 groups. In this case,
we need to use another test. The most common test for analyzing more than 2 groups
is called “Analysis of variance”. Analysis of variance uses the F-distribution which, like
the t-distribution is a modification of normal distribution. If we are only interested in the
differences between group means, then we would use a one-way analysis of variance.
    If we are also interested in testing for differences within groups, we would need to use
a two-way analysis of variance (not very commonly used in biotechnological research).
If we are to calculate a one-way AoV, we need the following information.

    GT = the sum of all observations (to get this, just add all data points)
    Ti = the sum of the observations in the i-th sample (In a given group, what is the
total sum)
    ni = the number of observations in the i-th sample
    N = total number of observations
        (Ti) 2
    ∑  ------ = the sum of the square of each sample’s total divided by its sample size
(for

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    ni          every group)

   ∑i ∑j (x ij )2 = the sum of the squares of all observations

   k = the number of groups

   The formula for analysis of variance is:

                               (∑ (Ti2 / ni ) ) – (GT2 / N)
                              _______________________
                                       (k – 1)
             F = _______________________________________________
                              (∑i ∑j (x ij )2 ) – ((Ti) 2/ ni )
                             __________________________
                                       (n – k)

    Once we have calculated the F- value, we can compare it to the critical value of ‘F’
in the table. We can then determine whether to accept or reject the null hypothesis that
no difference exists between group means. This will only tell us that at least 2 means
are different- they would be the highest and lowest values. If we want to know which
means are different from each other, we need to perform further tests. Examples include
the Scheffe test (most stringent), the Newman- Keul’s test, Duncan’s multiple range test
and others. Our research situation and our needs will determine which of the above is
appropriate. One interesting thing is that in AoV calculations, if k = 2, we will get the
same results as a t-test. AoV automatically adjusts to ‘t’ which in turn adjusts to a value
of 2.

c) Correlation

    Many a time, it is necessary to examine a relationship between two (or more)
quantitative variables, e.g. height and weight. A simple way to examine the data would
be to create a scatter plot. This is a graph in which the horizontal axis (X-axis) represents
one of the variables and the vertical axis (Y-axis) represents the other. If the points are
totally scattered, we would say that there is no relationship between the 2 variables.
If there exists some sort of linear or curvilinear relationship then the variables are
related.
    If our two variables (x and y) are perfectly related to each other they will form a
straight line. Then we would say they are perfectly correlated and they have a Peason’s
correlation coefficient (r) equal to 1.0. If the variables increase or decrease in unison,
then the r is positive (+ 1.0). If one increases and the other decreases, the r is negative
(-1.0). Of course, in real life it is tough to see such perfectly correlated relationships. If
there is no relationship, then r = 0.0 or vice versa.

   The correlation coefficient can be calculated as follows:
   n = the number of data points
   x = values for the x-axis           x = mean of x
   y = values for the y-axis           y = mean of y

                            ∑xy – (∑x) (∑y)/n
       r=        ______________________________________
                        _____________________________
                       √ (∑x2 – (∑x)2 / n) (∑y2 - (∑y)2/ n)

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   Let us look at an example:

              Person                           height (in)                       weight (lb)
                  1                                  64                             130
                  2                                  65                             148
                  3                                  71                             180
                  4                                  67                             175
                  5                                  63                             120
                  6                                  62                             127
                  7                                  67                             141
                  8                                  64                             118
                  9                                  65                             120
                 10                                  64                             119


   Using the above data we would get

                      90294 – (652) (1378/10)
       r = ____________________________________________ = + 0.8353                             (d.f =
n-2= 8)
                    _____________________________________
             √ ((42570 - 6522 / 10) (194724 – 13782 / 10))

    The correlation coefficient can be tested for statistical significance using a table of r
values or by using a special t-test. Either way, it is necessary to calculate the d.f. (degrees
of freedom) which for this calculation (correlation coefficient) is equal to n-2. The special
t-test is calculated using the following formula. Here we ignore the sign of r.
                          ______________
     t =        r √ (n-2) / (1 – r2)

   Using the above data we would get:
                          ______________
   t =       0.8353      √ (8) / (0.3023)
   =       4.297 with 8 degrees of freedom.
   From a t-table, we would find that p< 0.01.
   This means that there is a significant correlation between the variables.
   The correlation coefficient is a measure of the strength of the association between
2 variables on a scale of 0 to 1.0. A better way to interpret the association is to square
the coefficient. Then r2 will measure the proportion of the variation in the two variables
that is common to both variables, i.e. what percentage of the variation in one variable
can be predicted by the other.
   In this case:
   r2 = 0.8353 2
   = 0.6977
   or in other words: 69.77 % of the variation in weight can be explained by height.

d) Regression

    Another related way of looking at the relationship between two quantitative variables
is regression analysis or regression. In regression analysis, one of the variables is logically
dependent on (or influenced by) the other variable. For example, heart rate might be
influenced by age. In the jargon of regression analysis, heart rate would be a dependent

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variable and age would be the independent variable, since it is not logically influenced
by heart rate.
    By convention, in regression analysis, the y-axis of a plot is used for the dependent
variable and the x-axis for the independent variable. As in correlation analysis, we can
use a scatter plot, but in addition, regression analysis will provide the best fitting straight
line through our plot. To describe the line, we must have two pieces of information: the
slope of the line, b and the y-intercept of the line, a. The slope measures how much the
y- variable changes for each unit of change in the x-variable (+ means the line rises and
– means the line falls). The y-intercept tells us where the line starts (i.e. the value of y
when x = 0). Once we have this information we can use the formula for a straight line:

   y = a + bx
   The slope of the line can be calculated by the following formula:
                     ∑xy – (∑x) (∑y) / n
   b=        ______________________________
                       ∑x2 – (∑x)2 / n
   The table with data (that we used for the correlation coefficient) can be used here,
but is not a real example for regression analysis. Using the table gives us:
   B = 448.4/59.6 = 7.52 (means that for every unit of x increase y will increase 7.52
units).
   The y-intercept can be calculated since logic dictates that the best fitting line must
pass through the pint at the mean of x, mean of y. And since:

   y = a + bx                then:  y = a + b x
   Or equivalently

   a =  y - b x

   All that is required is that we calculate  x and  y to be able to obtain a. Using the
data table, the means of y and x are 137.8 and 65.2 respectively. So:
   a = 137.8 – (7.52 x 65.2)     = -352.73

  This type of calculation can be very useful in the laboratory. For example, if we
know the concentration of a standard protein and we measure absorbance of unknown
samples, using regression, we can calculate the unknown concentrations of the protein
samples. This is a very commonly used calculation.

e) Chi-Square test

    For research situations in which frequency and/or categorical data are collected, a
different set of statistical procedures must be used. One of the most common of these
procedures is called the Chi-square test. This test can handle any number of groups
and any number of possible outcomes. For simplicity, we will look at a test with a 2 x
2 situation (two groups and two possible outcomes). The formula for calculating Chi-
square is as follows:
                                    __                __
                                                      
                                    ( O – E)     2
                                                       
              χ2 =                 ---------------- 
                                          E            
                                                      
                                                   

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   Where:
   O = the observed frequency
   E = the expected frequency = (Tr x Tc ) / N
   Tr = row total
   Tc = column total
   N = total number of observations
   d.f. = (r-1) (c-1)
   r = number or rows and c = number of columns

   Example :
   Suppose we conducted an experiment to determine the possible detrimental effect of
a new drug on birth weight of rats- Pregnant rats were given either the drug or a placebo
and the results were observed in their offspring. Data collected:
                                  Control group      Experimental group         Total

  # of low birth weight rats                   10                                40          50

  # of low birth weight rats                   90                                80          170

              Total                           100                                120        220


Calculations:
       O                 E                  O-E                     (O-E) 2            (O-E) 2/ E
       10              22.73              -12.73                   162.0529              7.1295
       90              77.27               12.73                   162.0529             2.0972
       40              27.27               12.73                   162.0529             5.9425
       80              92.73              -12.73                   162.0529              1.7476
                                                                                       ________
                                                             Chi-Square value           16.9168



   We then compare this value (16.2) to the critical value of Chi-square in the Chi-
square table and make our decision about our hypothesis. Here p < 0.005. So the new
drug causes low birth weight in rats compared to the placebo.
   One problem with Chi-square test: Here if E < 5.0 then there is distortion in data.
When we do (O-E), the gap between the points decreases as the numbers get smaller.
This can be prevented by using Yates’ correction i.e. (| O – E | - 0.5 ) 2 is used as
numerator in the formula in such cases. (Do not worry about this at all. SPSS does this
automatically. We put in this information just to show off a little bit.)

f) McNemar test

  In case of the Chi-square test, one prerequisite is that the groups are independent
and not related, matched or paired. For experiments in which paired samples or “before
and after” experiments, the more appropriate test would be the McNemar test. It is a
modified type of Chi-square test. The data are arranged as follows:


                                                         AFTER
                                                            -                          +
                                +                           A                          B
     BEFORE
                                -                           C                          D


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   In this test, we are only concerned with the observations that changed during the
experiment i.e. cells A and D of the table. Since A + D represents the total number of
observations that changed ½ (A + D) would be expected to change in one direction
and ½ (A + D) in the other direction if our experiment had no effect on outcome (If null
hypothesis is true, A and D would be the same).

                                           (A – D) 2
        χ
        2
                                   =       ---------
                                            (A + D)
    Example: Suppose we want to test whether or not the presence of a particular object
in the room influenced the biting behavior of dogs caged in the room. To conduct our
experiment, we would need a room full of caged dogs, the suspected object and an
artificial hand for the dogs to bite. The hand could be placed in the cage of each dog in
the absence and presence of the suspected object. If the hand is bitten, we would record
a +ve response and if not bitten, a – ve response. Our data can be shown as follows:

                                                                              AFTER
                                                               -                       +
                                +                             10                       20
       BEFORE                   -                             50                      120


  χ2                          = (110) 2 / 130
                              = 93.08
   The interpretation is similar to the Chi-square test. So the null hypothesis can be
rejected.

g) Sign test

    Occasionally, in some research designs, quantitative data are impossible or
impractical, but it may be possible to rank with respect to each other, the two members
of a pair. The sign test is applicable to a research design of 2 related samples when the
experimenter wishes to establish that two conditions are different. E.g. a skin rash can
only be classified as mild, moderate and severe. Or the degrees of pain can be classified
by the patient as same, improved or worsened and so on. The only underlying assumption
of this test is that the variable under consideration has a continuous distribution.
    In this test, we assign a plus (+) or a minus (-) sign to each pair for the variable of
interest. If the experimental conditions have made no difference, then we would expect
an equal number of pluses and minuses. (If the members of a pair are not different they
can be dropped from the analysis.) We need to only determine N (number of pairs) and
the x (number of fewer signs). And compare to the table for sign test.
   Example:
    Suppose we were attempting to determine the effect of low iron intake on taste acuity
for sourness. After eight weeks on a low iron diet, a group of 17 volunteers were asked
to taste two sour solutions ( one 1 % citric acid and the other 0.5 % citric acid) and
compare if the first was sourer (+), same (0) or less sour (-) than the second.




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        Subject #                      Result                           Subject #   Result
           1                             -                                 10         -
           2                             -                                 11         -
           3                             -                                 12         -
           4                             -                                 13         +
           5                             0                                 14         -
           6                             +                                 15         0
           7                             -                                 16         -
           8                             0                                 17         -
           9                             +

    From the results N = 14 and x = 3.
    The table for sign test shows that the one-tailed probability for such an occurrence
is p = 0.029. Since this is less than our level of significance (0.05) we can infer that low
iron intake decreases ability to distinguish sourness.

h) Mann-Whitney U test

   After the ordinal level of measurement has been achieved, Mann-Whitney U test can
be used to test if two independent groups have been drawn from the same population.
This is one of the most powerful of the nonparametric tests. The null hypothesis is that
both groups have the same distribution. The alternate hypothesis is that one group
ranks higher (better) than the other. If the experiment has no effect then we expect the
groups to be equal.
   To conduct the test, we must first assign a score to each subject: combine the data
from the two groups; and rank the scores in order of increasing size. We let n1 = the
number of cases in the smaller of the groups and n2 = number of cases in the larger. To
determine U, we focus on the smaller groups (if groups are of equal size, just pick any
one). The value of U is equal to the number of times that a score in the larger group
precedes a score in the smaller group. We then compare our U to the table for Mann-
Whitney U test.

   Example:
    The effect of zinc deficiency on learning was studied on rats. Ten control rats are fed
a nutritionally complete diet while experimental rats are fed a low zinc diet for 10 weeks.
Initially, all rats had been trained to imitate a leader rat in a T maze. The experimenter
records the number of trials each rat requires to reach a criterion of 10 (in a row) correct
imitations in 10 trials. The more the trials required, the more the memory affected. The
data are presented below:


        Control rats                                        Experimental rats
             78
             64                                                        110
             75                                                        70
             45                                                        53
             82                                                         51
             77                                                        93
             62                                                        68
             76                                                        57
             48                                                        54
             90


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      Group C C E E E E C C E E C C C C C C E E

      Score 45 48 51 53 54 57 62 64 68 70 75 76 77 78 82 90 93 110


   We determine U by counting the number of C scores preceding each E score.
   U = 2 + 2 + 2 + 2 + 4 + 4 + 10 + 10 = 36
   From the table for Mann-Whitney U test, we see that to achieve the 0.05 level of
significance, U value must be equal or less than 17. Our U value is 36. So we infer that
zinc deficiency did not affect learning in this experiment.

h) Statistical Abuses

   Scientific research abounds with misapplication of statistical methods. Many a
time, reviewers detect these errors and investigators have to repeat their statistical
analysis, causing a lot of expenditure of time and effort. But sometimes, some errors of
application go unnoticed and end up being published. This is rarely due to an intention
to mislead; rather it is often the result of insufficient deliberation and study of the
particular experimental problem. It’s probably right to say that the majority of problems
and difficulties in handling one’s experimental data are caused by haste and consequent
superficiality if not errors on the part of the investigator. The researcher who rushes
into an experiment, hurries the data collection and rushes the publication of his results
runs the risk of wasting his entire effort just to save a little time in the beginning. It
has been said that if you really want to mess things up, use a computer. Indeed, the
widespread use of computerized statistical software packages lead to misapplications
and misinterpretations of results.
   The major areas of errors include:
   1. Sample Size selection
   2. Inappropriate Statistical tests
   3. Inappropriate display of results

   Sample size selection
     Very small samples are unlikely to give good estimates of true population values.
One unusual animal or subject can have a big effect on the outcome. The findings of
such studies are viewed by skepticism by most scientists. Would you use a new drug
if it were launched after testing it in 2 rats? Very small samples make it tough to find
statistical significance even if there may be biological significance.
     Very large samples also have their own problems. If the sample is sufficiently large,
any numerical difference between groups can be shown to be statistically significant,
whether there is any actual biological significance or not.

   Inappropriate statistical tests
   These are difficult to spot without a certain amount of statistical expertise. Most
common of these would be the use of t-tests when there are more than two groups under
study, using tests meant for continuous data on discrete data and false assumptions
about the independence of samples and homogeneity of variances.

   Examples:
   Example 1:
   t-tests are designed for no more than 2 samples. If we have an experiment in which
there are five groups of subjects (Groups A-E) we might wish to make the following
comparisons:
   A vs B, A vs C, A vs D, A vs E, B vs C, B vs D, B vs E, C vs E and D vs E


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    In all, ten different comparisons. If we consider 0.05 to be an acceptable level of
significance, we might conduct 10 t-tests and never realize that we actually have a 31 %
probability (instead of a 5 % probability) of having a statistically significant finding.
   Example 2:
    Sometimes, literature may have findings in which t-tests were used in the analysis of
categorical or frequency data. These findings are meaningless if based on the outcome
of the wrong statistical procedure. If we use 1’s to code for males and 2’s to code for
females, what does it mean if we get a mean of 1.37? Absolutely nothing.
   Example 3:
   One of the most common errors will be when the researcher uses a statistical procedure
that makes a waste of his data. Conversion of measurement data to ranks or categories
or percentages may allow us to use a statistical procedure that is arithmetically easier
to compute but makes a much weaker statement about our findings.

   Inappropriate display of results obtained
   Scientific literature and scientific meetings (more so) are filled with examples of the
misuse of data representation techniques. These are also extremely common on television
and in presentations before government committees. Many of them are conscious
attempts to mislead. There are specific ways to present data and misrepresentation
may make data seem more significant than it really is.




    In the above graph, A is the mean heart rate of 30 females and B is the mean heart
rate of 30 males. A and B look significantly different from each other, in the graph. This
is because the graph is plotted from 60 to 76. If the graph had been plotted from 0 to
100, the difference between A and B would not seem so high. In reality, the difference
between A and B is not significant. But if we were unethical and wanted to present this
data to an audience to convince them that the heart rate of males was much higher than
females, we could easily represent the data in this manner and achieve our end. This is
extremely misleading and an incorrect way of representing statistical results.

j) Quiz to test yourself

   Have a look at the questions/problems below. You will be able to solve them yourself.
Our tutorial has not provided solutions. If you find it impossible to get the solution for
any particular problem, feel free to contact us anytime.

   I) Name the type of association between the risk factor and disease in each of the
examples below:

   A.       It has been observed that people who have low cholesterol are more likely to
            be interested in travel than individuals who do not. What is the most likely
            type of association to explain this finding?

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   B.     Vitamin C deficient diets especially on ships are responsible for a lot of
          people suffering from bleeding disorders, the disease being called scurvy.
          What is the association between Vitamin C and scurvy?

   C.     Studies have discovered a high incidence of rickets in the Scandinavian
          countries. Rickets is a Vitamin D deficiency disease and Vitamin D is made in
          our skin from exposure to sunlight. What is the association between sunlight
          exposure and rickets in these people?


   II) Give the appropriate statistical test for each of the following research designs

   A.     Eight groups of mice (n = 40) were fed either a complete normal diet (Group
          I or controls) or diets restricted in protein as follows: Group II = 10 % less
          protein, Group III = 25 % less protein, Group IV = 20 % less protein, and
          Group V = 30 % less protein. Mean weight gains were compared after feeding
          these diets for 12 weeks. Investigators compared each mean to the control
          group.

   B.     In the same research project described in “A”, numbers of rats who gained
          less than 90 % of the weight gained by the control rats were compared.

   C.     Mean fasting plasma cholesterol concentrations were determined in a group
          of individuals before an after 10 weeks of taking Lipitor.

   D.     Hypertensive men were placed on a diet which included a daily dose of 10
          gms of corn oil or fish oil for 36 weeks. The number of men whose diastolic
          blood pressure dropped by 5 mm Hg or more was compared for the two
          groups.

   E.     A group of rats was split into a control group and experimental group. The
          experimental group received three weeks of zinc deficient diet while the
          control group received an adequate diet. At the end of the experiment, the
          rats were scored as to their ability to solve a maze problem. The investigators
          wished to determine if the experimental groups have lower ranking scores
          than the controls.

   F.     An experiment was conducted to determine the effect an iron supplement
          diet had on memory in a group of low income children. The children were
          assessed on their ability to remember a nine digit number two minutes after
          having been shown the number. The children were tested before and after six
          months of supplementation. Individuals were scored as correct or incorrect
          before and after the supplementation period.
   III) An investigation was performed to determine the relationship between breast
cancer and coffee consumption. Breast cancer cases and healthy controls were
interviewed to determine their history of coffee consumption. The results are presented
below:


                                Breast cancer cases                Healthy controls     Total
  Less than 2 cups a day                   350                               375        725
  More than 2 cups a day                   150                               125        275
           Total                           500                               500        1000


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                                     SPSS Tutorial for Beginners
                                 Types of data and appropriate statistical tests




   What is the absolute risk of having breast cancer among women drinking more than
2 cups of coffee per day?

   IV) Your project for your grant proposal will examine the effect of various diets on
the prevention of protein cross linkage in rats treated with the pro-oxidant doxorubicin.
You intend to compare three different antioxidants as dietary supplements. You feed four
groups of rats a semi-purified diet which contains either no antioxidant (control group)
or one of the antioxidants under study. You need to now tell your professor how many
animals to buy. How do you determine the sample size for each group of rats?

   V) For each of the following, state the type of study design:

   A.       A national survey indicated that high fiber diets were associated with low
            incidence of stroke.

   B.       An obstetrician reported that four of pregnant patients with severe morning
            sickness were in good health and free of symptoms after one week of
            supplementation with pyridoxine.

   C.       A study was conducted to determine if fish consumption might be related to
            future coronary heart disease (CHD) incidence. A group of patients with CHD
            was matched to a group of controls shown to be free of CHD. Medical records
            were searched and interviews were conducted to determine the level of past
            fish intake. It was determined that low fish intake was positively associated
            with CHD.

   D.       The association between high fiber diets and colon cancer was studied in a
            group of 5000 vegetarians and a group of 4000 individuals who ate mostly
            beef and did not have high fiber diets. The two groups were followed for a
            period of 10 years. At the end of the period incidences of colon cancer were
            compared.


   VI) An investigator developed a new assay for determination of sickle cell anemia.
The table below displays the results of an experiment. (A positive test indicates a
sickle cell patient)


     Traditional Methodology
                                                     Sickle cell                   Normal   Total
                         Sickle cell                 91                            12       103
     New test            Normal                      9                             38       47
                         Total                       100                           50       150

   Choose the correct answers:
   The sensitivity of this test is:
   a. 100/150 = 66.7 %
   b. 91/100 = 91 %
   c. 12/50 = 24 %
   d. 38/50 = 76 %

   The specificity of this test is:
   b. 91/103 = 88.3 %


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                           Types of data and appropriate statistical tests




   c.   103/150 = 68.7 %
   d.   38/50 = 76 %
   e.   47/150 = 31.3 %

    As we have said before, if you get stuck on any of the above problems, do ask us
for the solution.




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 SECTION II
SPSS at Last
                               SPSS Tutorial for Beginners




SpSS at last
    Now that we have given you a brief (was it?) introduction to the basics of statistics,
we think that you will be able to understand SPSS much better and faster and will not
struggle with every tiny step of the tutorial that SPSS offers with its package. In this
SPSS tutorial, we shall be covering the basics of how to use SPSS. Students usually
use SPSS for their classes and more importantly for their research analysis. Let other
people talk about how tough it is to work on SPSS. We will show you how simple it is.
The versions of SPSS may keep changing. Do not panic and go to the store to buy the
latest version every time it is launched. The basic features have stayed the same since
a very long time just like any other software program (Think about it- Do you see any
change in MS Word in the past five years?)

   Now straight to the tutorial. When you open SPSS (obviously by double-clicking on
the icon) you will see this window.




   If you want to run the tutorial, you know what to do. You can access the tutorial
anytime via the Help pull down menu on the data editor.


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                                             SPSS at last




   We suggest you take the tutorial at some point of time, especially if you need
information about every teeny-weeny aspect of every icon. As for now, you can take this
tutorial and start actually using SPSS. After all that is what you bought this for, right?

   In order to use SPSS for statistical analysis, you must first have a file containing data
to be analyzed.


CREatINg aNd EdItINg a data fILE
   There are several ways of doing this.
   	       You can create your data file using the Data Editor of SPSS. This may be the
            easiest way to work with SPSS. (We will tell you how to go about this).

   	       You can use a spreadsheet software package such as MS Excel. You might
            want to do this because let’s say you already have a lot of data on Excel and
            want to transfer it to SPSS you would not want to type everything all over
            again. You would then need to follow the instructions associated with that
            software package. WARNING: This is not a simple Copy and Paste procedure.
            Be sure to save your data file as a tab-delimited text file. Otherwise, this
            process itself will become your greatest headache. (You can specify your
            variable names on the first line of your Excel spreadsheet and load them
            directly into SPSS when you Open the file. You can get more instructions
            regarding this in the SPSS Help section).

   	       You can enter your data in a word-processing software package such as MS
            Word. Again you need to separate your variables with Tabs and not spaces.
            And you must save the file as Text only.

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     	     You can enter your data into a command file between the “BEGIN DATA”
            and “END DATA” commands.
     NOTE: This should be done only for very small data sets.


    Regardless of how you create your data file, the first step is to determine what the data
are and how you plan to organize the whole thing. It is recommended that you use fixed-
field format for your data until you become an SPSS-pro. You don’t have to worry about
this. SPSS itself uses a fixed-format system for your data by default. Free-field format
may seem tempting, but before you step into that arena, remember that- it is difficult to
edit if your files are large and a lot of steps and additional typing will be required if you
have missing data. (Any real experiment is bound to have some missing data).
    Once you have created a data file you can start performing statistical analysis on
your data using SPSS.




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                                   SPSS Tutorial for Beginners




i) typical SpSS Session
    Now that we have given you a brief (was it?) introduction to the basics of statistics,
we think that you will be able to understand SPSS much better and faster and will not
struggle with every tiny step of the tutorial that SPSS offers with its package. In this
SPSS tutorial, we shall be covering the basics of how to use SPSS. Students usually
use SPSS for their classes and more importantly for their research analysis. Let other
people talk about how tough it is to work on SPSS. We will show you how simple it is.
The versions of SPSS may keep changing. Do not panic and go to the store to buy the
latest version every time it is launched. The basic features have stayed the same since
a very long time just like any other software program (Think about it- Do you see any
change in MS Word in the past five years?)
    Now straight to the tutorial. When you open SPSS (obviously by double-clicking on
the icon) you will see this window.




                                                                                     35
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                                SPSS Tutorial for Beginners
                                        Typical SPSS session




   If you want to run the tutorial, you know what to do. You can access the tutorial
anytime via the Help pull down menu on the data editor.




   We suggest you take the tutorial at some point of time, especially if you need
information about every teeny-weeny aspect of every icon. As for now, you can take this
tutorial and start actually using SPSS. After all that is what you bought this for, right?
   In order to use SPSS for statistical analysis, you must first have a file containing data
to be analyzed.

     Creating and Editing a Data File
     There are several ways of doing this.
     	     You can create your data file using the Data Editor of SPSS. This may be the
            easiest way to work with SPSS. (We will tell you how to go about this).

     	     You can use a spreadsheet software package such as MS Excel. You might
            want to do this because let’s say you already have a lot of data on Excel and
            want to transfer it to SPSS you would not want to type everything all over
            again. You would then need to follow the instructions associated with that
            software package. WARNING: This is not a simple Copy and Paste procedure.
            Be sure to save your data file as a tab-delimited text file. Otherwise, this
            process itself will become your greatest headache. (You can specify your
            variable names on the first line of your Excel spreadsheet and load them
            directly into SPSS when you Open the file. You can get more instructions
            regarding this in the SPSS Help section).

     	     You can enter your data in a word-processing software package such as MS
            Word. Again you need to separate your variables with Tabs and not spaces.
            And you must save the file as Text only.

     	     You can enter your data into a command file between the “BEGIN DATA”
            and “END DATA” commands.

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                                   SPSS Tutorial for Beginners
                                          Typical SPSS session




   NOTE: This should be done only for very small data sets.


    Regardless of how you create your data file, the first step is to determine what the data
are and how you plan to organize the whole thing. It is recommended that you use fixed-
field format for your data until you become an SPSS-pro. You don’t have to worry about
this. SPSS itself uses a fixed-format system for your data by default. Free-field format
may seem tempting, but before you step into that arena, remember that- it is difficult to
edit if your files are large and a lot of steps and additional typing will be required if you
have missing data. (Any real experiment is bound to have some missing data).
    Once you have created a data file you can start performing statistical analysis on
your data using SPSS.
   Step 1 : Open SPSS. The program will load and the Data entry Window will open.




   Step 2: Get your data. How you do this depends on the method used to create your
           data file.

   Step 3: Generate SPSS commands. Select your commands from the pull down
          menus of the toolbar at the top of the screen or load them into SPSS as an
          SPSS syntax file.
   Getting Started
    We suggest that you begin each SPSS session in the following way (especially if you
plan to print out your results for your professor or for whatever reason). This will minimize
the amount of paper output you generate (Not all universities offer free printing. At 10
cents a page, you can get a burger by saving 25 pages. Just don’t blame us when you
get fat). Select Options from the Edit pull down menu on the toolbar at the top of the
screen. From the Options dialog box, select the Viewer tab at the top of the dialog box.
Click on Infinite in the Text Output Page Size section of the dialog box. Also, click
Display commands in the log to cause your commands to appear on your output. Then
click on OK. This will cause SPSS to use the minimum amount of paper possible when
you print your output at the end of your session. SPSS, left by itself, issues a lot of “end
of page” commands that are pretty much gibberish for you and your professor and
consume too many papers while printing.




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                             SPSS Tutorial for Beginners




(ii) creating a new data file with
the data editor
   Click on the “Variable View” tab at the bottom of the Data Editor. Note that the
spreadsheet labels have changed. Instead of “var” at the top of each column, “Name”,
“Type”, “Width”, etc. appear at the top of each column. Each row corresponds to a
variable (i.e. each row corresponds to one column in the data and provides all the
information about one particular column)




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                                   SPSS Tutorial for Beginners
                               Creating a New Data File with the Data Editor




   Let us say you type “Age” under variable name, the other values appear as they are
set by default. You can change all the values as per your requirements.




   First you need to decide on names for each of your variables.

   Rules involved in creating variable names

   	       Variable names must begin with a letter or the @ symbol


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                            Creating a New Data File with the Data Editor




   	       They cannot contain the following symbols (&, !, ?, ‘, /) or blanks

   	       They cannot exceed 8 characters in length

   	       The following have other specific meanings for SPSS and cannot be used
            as variable names by themselves- ALL, AND, BY, EQ, GE, GT, LE, LT, NE,
            NOT, OR, TO, WITH (Though it is possible to use ALL1/ALL2 and so on)
   Our tip : Avoid using symbols in variable names. That way, you won’t need to
remember which ones are okay and which ones are not.

   Enter a name for your variable in the 1st box. By default, the variable type is numeric
with a w.d. (width. decimal) format of 8.2. If this is incorrect, click on the … button in
the Type box to specify the correct type in the Variable Type dialog box. If the column
width and number of decimal points are incorrect, fix them in their boxes.

    Variable LABELS and VALUE labels can be used to make your output easier to
understand. A variable LABEL is used to descriptively label the variables. Its use makes
the output easier to read and can be very useful if the output is used over a long time
period. Each label cannot exceed 60 characters (most procedures will only print 40 at
a time and some will print even fewer)

   Example of a variable LABEL:
   “Liver weight in Grams”
   “Plasma Cholesterol mg/dL”

   A VALUE label is used to descriptively label the values of a variable. Its use makes
the output simpler to read and can be very useful if the output is used very a long time
period. Similar to variable labels, each label must not exceed 60 characters (Most
procedures will only print 20 of them).

  Example of a VALUE label:
  For a variable named COMMUNITY,
  A value of 1 could have the label Asian, a value of 2 could have the label African
American, and a value of 3 could have the label Hispanic and so on…


   For   a variable named AGE,
   1      0-10 years
   2      11-20 years
   3      20-45 years
   4      45-65 years
   5      65 years+

   Missing Data
   The presence of missing data is very common in any kind of research. You will
always come across dead mice, sick children, non-compliant adults, unfilled forms,
lost samples and so on. You can’t really do anything about it, other than planning for it
while creating your data file. You can enter a special code to indicate missing data or
you can leave the item blank. The good thing about SPSS is that any blank or period




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                                     SPSS Tutorial for Beginners
                                 Creating a New Data File with the Data Editor




(“.”) is considered missing data unlike some other software programs which consider a
blank as zero (can’t even imagine the amount of distortion that would cause).

   Saving your information
    Now proceed to name the remaining variables (columns) of your spreadsheet. Then
click on the Data View tab at the bottom of the Data Editor to enter your data (This is
very easy for us to list as a step, but will take a long long time. Beware of errors while
entering your data. Slow and steady is the best way to go). Finally, save your data to
your disc by using the File pull down menu from the toolbar and selecting Save As.
Name your file, select the format of the file with the Save as type option. And you have
saved your file.
   Exercise
   The following data are total cholesterol levels in mg/dL for 8 groups of subjects.
Create a data file and use SPSS to list it back onto paper.


  Group       Group       Group          Group          Group         Group      Group
                                                                                         Group 8
    1           2           3              4              5             6          7
    181        249         260             296           334            250      223      320

    177        325          261            245           340            232      305      345

   200         425         263             306           356            220       210     340

    171          -          276            309           350            235      309      325

   159         272         235               -           374              -      254      341

    173         217          -               -             -            243      236      333




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(iii) loading an existing data file
into the data editor
   So you are ready with some data to analyze? No? Oops, then what are we going to
do? Learning SPSS needs data and the more the better. OK, let’s learn it without data.
But again, that would be like fishing without going to the water at all. OK. OK. Relax.
Doesn’t matter if you do not have any data at this stage. We will provide you with all the
data required to learn SPSS from our tutorial. After that, of course, you will need your
own set of data (Isn’t it the other way round? You need SPSS to analyze data and not
data to…..). Tired of our meaningless chatter? Sorry. Let’s go ahead.
   So now you have a few data files on your hard disk or diskette. They can be loaded onto the
SPSS Data Editor by using the File pull down menu and selecting Open and then clicking on
Data. If the file is not in SPSS format (e.g. a text file or a file from a spreadsheet program like MS
Excel), use the Files by type part of the Open dialog box to display the appropriate file type,
then highlight your file and click on Open. Your file will be loaded into the SPSS Data Editor. If
you have not defined your variables, set their names, types, etc. you need to do that right now, and
then save your data file to your disc using Save As from the File pull down menu, as described
above. Unless you specify otherwise, it will be saved as an SPSS data file and will include your
variable names, type specifications, etc. A file in this format is only readable by SPSS.




   Fixed Format: Data files are most often fixed format. This is simper to read, edit
and understand. Fixed format means that the data for a given variable occupies the
same line columns and line position for each case (Note: If there is more than one line
of data per case, you must use the RECORDS subcommand to specify the number if
lines per case).


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                              Loading an existing Data File into the Data Editor




   Example:
   ID #           Columns 1-3
   Weight         Columns 5-9
   Height         Columns 11-13
   001 065.3 091…….
   002 141.3 171…….
   003 12.4  154…….

    Free-field format: This is another form of data organization. The variables are in the
same order for each case but do not necessarily occupy the same line columns for each
case. The data for each variable must be separated by one or more spaces or a comma
in the data file. According to us, it is better to stick to the fixed format while preparing
data files for SPSS especially since in the free-field format, there will always arise the
problem of missing data (part and parcel of any experiment).

   Example:
   ID WEIGHT HEIGHT
   001 65.3 91
   002 141.3 171
   003 122.4 154




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(iv) creating and executing
SpSS commands
   Now that you have a working data set, you can begin to create and execute some
SPSS commands from the pull down menus (or if you want to get technical- by tying
them directly into an SPSS Syntax Window).

k) The EXPLORE command

    The first thing to do when you get data from any research project is to examine
the data in detail. It does not matter whether the procedure used to do this is simple
or complicated. The basic point is- If the data is incorrect, conclusions will be faulty
and the whole experiment will come to naught. To avoid this it is better to eyeball your
data using SPSS first to look for any errors. Errors can enter data at multiple steps.
Measurement can be in error due to poor technique, faulty instruments, or careless
observers. Recording of data into a notebook can be done incorrectly or illegibly.
Transcription to an electronic format can be in error. Data can be corrupted by defective
disks, faulty hardware or software, computer viruses, user errors, etc. Some errors are
relatively easier to spot e.g. an LDL cholesterol of 0.0 or 5000.00 mg/dL. Others may
be difficult, if not impossible e.g. an LDL cholesterol value of 312 mg/dL recorded as
123 mg/dL. Unless you begin your data analysis with a careful check of your collected
data, errors can distort your findings.
    Careful editing of data files by comparing them to the original raw data is a good
first step. Careful examination of the data displayed on the screen or a print out can
help with this task too. The command EXPLORE can help us a lot in this process.
EXPLORE can help us look at our data in different ways to determine if the data seem
reasonable. EXPLORE can also help us to decide, in some cases, on the appropriate
statistical tests to use.
    This command will allow the examination of summary statistics such as range,
median, mean, mode, measures of variability, measures of skewedness, etc. as well as
displaying the data in a variety of graphic output formats. If you need extra information
about this command, refer to the base manual.
    Use the Analyze pull down menu from the toolbar and select Descriptive Statistics
and then Explore. The Explore dialog box will appear.




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                                  Creating and Executing SPSS Commands




    (To open this box, you need to have some data on your data editor of SPSS. This is
just an example file).
    You can then select the variables of interest (one or more “dependent” variables)
and choose one or more grouping variables (factors). By default, you will get box plots,
stem-and-leaf plots and basic descriptive statistics for each dependent variable (either
for the whole group or separated by a grouping variable). You can suppress the display of
plots or descriptive statistics. You can choose additional statistics and plots as described
below.
    In the Explore dialog box, you can click on the Statistics button and choose
one or more of the following to be displayed
    Descriptives
    This is the default SPSS uses. It includes the mean and its confidence intervals,
median, 5 % trimmed mean, standard error, variance, standard deviation, minimum,
maximum, range, interquartile range (IQR), skewedness and its standard error, kurtosis
and its standard error. IQRs are computed by the H AVERAGE method. This is a weighted
average method and is described in detail in the base manual.
    By default, 95 % confidence interval is displayed. The dialog box offers the choice
to set this to any value between 1 % and 99.99 %.
   M-estimators
     This produces M-estimators that are robust maximum-likelihood estimators of
location. This kind of statistical analysis is not used in Biological research. Do refer to
the manual for more information.
     n	 HUBER(c)          produces Huber’s M-estimator with a default of c=1.339.
     n	 ANDREW(c) produces Andrew’s wave estimator with a default of c=1.34π.
     n	 TUKEY(c) produces Tukey’s biweight estimator with a default of c+4.685
     Outliers
     This displays the cases with the five highest and five lowest values for each variable.
It is labeled “Extreme values” on the output sheet.
     Percentiles
     This command displays the 5th, 10th, 25th, 50th, 75th, 90th and 95th percentiles using
the H AVERAGE or weighted average at X(W+1)p method to calculate the percentiles. It
also displays Tukey’s hinges (25th, 50th and 75th percentiles). Refer to the manual for
more details.
     Grouped Frequency tables
     This displays tables for the total samples and broken down by any factor variables.

  In the Explore dialog box, you can click on the Plots button and choose
one or more of the following to be displayed.
Box plots You can choose one of the following alternatives.
Factor levels together This is the default. It displays side by side box plots for a given
dependent variable for each group defined as a factor variable. If no factors have been
defined, a box plot for the total sample is displayed.
Dependents together This displays side by side box plots for a given group for each
dependent variable.
None This suppresses the display of box plots.
Descriptive       You can choose one or both of the following alternatives.
Stem-and-leaf This is the default. A stem-and-leaf plot is produced in which each
observed value is divided into two components-leading digits (stem) and trailing digits
(leaf). See the manual for more details.
Histogram A histogram is printed. The range of observed values for the variable is

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                               Creating and Executing SPSS Commands




divided into intervals and the number of cases in each interval is displayed.
Spread vs. level with Levene’s Test A spread-versus-level plot is produced with
the slope of the regression line and Levene’s test for homogeneity of variances. If no
factor variable has been defined, this plot is not produced. You can choose one of the
following.
   None : No plots or tests are produced

   Power estimation : For each group, the natural log of the median is plotted against
         the log of the interquartile range. Estimated power is also displayed. Use this
         to determine an appropriate transformation of your data.

   Transformed : The data are transformed according to user-specified power. One of
          the alternatives below needs to be selected.

   	      Natural log: This is the default. A natural log transformation.

   	      1/square root: The reciprocal of the square root is calculated for each data
           value.

   	      Reciprocal: A reciprocal transformation

   	      Square root: A square root transformation

   	      Square: Data values are squared

   	      Cube: Data values are cubed

   Untransformed : No data transformation is performed i.e. The power value is 1

   Normality plots with tests : Normal probability and dendrended probability plots
         are produced with a number of test statistics.


  In the Explore dialog box, you can click on the Options button and choose
one of the following as a method to handle missing values
   Exclude cases listwise This is the default. Cases with missing data for any dependent
         or factor variable are excluded from all analyses.

   Exclude cases pairwise Only cases with no missing values for variables in a cell
         are included in the analysis of that cell. A case may have missing data for
         variables not used in that cell.

   Report values Missing values for factor variables are treated as an additional
         category and reported as such in all output.
   The EXPLORE command is a very useful and powerful tool for understanding any
data generated by our research. It needs to be explored in much more detail for those
of you who wish to use it more (For the rest of you, on with the tutorial). Do use the
Base manual for this.

l)The FREQUENCIES command

    This command produces tables of frequency counts and percentages for the values
of individual variables. By default, a table is created that displays counts for each value
of a variable, the counts percentaged over all cases and over all cases with nonmissing
values and the cumulative percentage over all cases with nonmissing values. The values

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                                   SPSS Tutorial for Beginners
                                  Creating and Executing SPSS Commands




are ordered from lowest to highest. All variable labels and value labels are printed if
they have been defined. These defaults can be altered with a number of subcommands.
Also, bar charts, histograms and statistics can be chosen.
   Select the FREQUENCIES command by clicking on the Analyze pull down menu
on the toolbar and then select Descriptive Statistics and then Frequencies. The
Frequencies dialog box will open and allow you to select variables for generating
output. If all you want is the default, just click the OK button. You can also select optional
output from the dialog box.

   Display frequency tables This is the default. To suppress frequency tables, click
on the little box to remove the check mark.




   Statistics
   This command controls the display of statistics. By default, no statistics are displayed.
One or more of the following choices may be used.
   Under the Percentiles Values box, you can select one or more of the following:
   n	 Quartiles: Displays the 25th, 50th and 75th percentiles.
   n	 Cut points for n equal groups: Displays percentile values that divide the
sample into equal-sized groups. 10 is the default. You can enter any positive integer
between 2 and 100. The number of percentiles displayed is one fewer than the number
of groups specified.
   n	 Percentile(s): Displays user-specified percentiles. You can enter any percentile
value between 0 and 100, and then click on Add. You can continue to add additional
percentile values to build a list which will be displayed. You can remove or change your
entered percentiles before execution of the command by highlighting them and clicking
the appropriate button

   Under the Dispersion box, you can select one or more of the following:
   n	 Standard deviation
   n	 Variance
   n	 Range
   n	 Minimum

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  n	 Maximum
  n	 S.E mean (Standard error of the mean)

  Under the Central Tendency box you can select one or more of the following:
  n	 Mean
  n	 Median
  Under the Distribution box, you can select one or more of the following:
  n	      Skewness: This is a measure of how much a distribution is shifted (right
          or left) from a normal distribution. Positive values indicate a right shift and
          negative values, a left shift.

  n	      Kurtosis: This is a measure of spread of a distribution for a given standard
          deviation. Positive values indicate that the distribution is more peaked than
          a normal distribution and negative values indicate a flatter distribution.




   Charts
   This allows selection of bar charts and histograms and some control over how bar
charts are labeled. You can choose only one of the following:
  n	      None: This is the default. No charts are displayed.

  n	      Bar chart(s): Scale is determined by the frequency of the largest category
          plotted.

  n	      Pie chart(s): It is possible to plot the graph as a pie chart showing
          percentages.

  n	      Histogram(s): Available for numerical variables only. The maximum number
          of intervals plotted is 21.




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   n	 Mode
   n	 Sum




  With normal curve superimposes a normal curve over the histogram.
  The Chart Values display box allows control of the vertical axis label for bar charts
and pie charts using one of the following:
  n	 Frequencies: This is the default. The label is frequencies.
   n	       Percentages: The label is percentages.
   Format
   This controls the output of frequency tables.
   Under the Order by box, you can select one of the following
   n	       Ascending values: This is the default. Sorts categories by ascending order
            or values

   n	       Descending values: Sorts categories by descending order or values

   n	       Ascending counts: Sorts categories by ascending order of frequency
            counts

   n	       Descending counts: Sorts categories by descending order of frequency
            counts
   If you have selected percentiles or a histogram, you get the output for Ascending
values, regardless of your selection here.




   You can also control the printing of large tables and the printing of multiple
variables.

m) The DESCRIPTIVES command

   This command generates a listing containing the variable name, variable label,


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mean, standard deviation, minimum and the maximum. Additionally, the standard error
of the mean, variance, kurtosis, skewness, range and sum may be requested under the
Options subcommand. To use the DESCRIPTIVES command, select Analyze from the
toolbar and then Descriptive Statistics and then Descriptives. A dialog box will appear
which will allow you to select variables, select additional descriptive statistics and set the
order that the variables are displayed in. This is a very useful tool for a quick summary
of your data.




   Exercise
   Using our data file diet.sav and the commands Frequencies and Descriptives, answer
the following:

   How many and what percent of individuals fall into the following categories?
                                  #                                 %
   Males                   ___________                         __________
   Females                 ___________                         __________
   Asians                  ___________                         __________
   Orientals               ___________                         __________


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   African Americans                ___________                          __________


   For each of the following, give the mean, standard deviation, minimum and maximum
values without using the Frequencies command:

                                         Mean                 SD            Min-Max
   Age                                 ________             _______         _______
   Kilocalories                        ________             _______         _______
   Fat                                 ________             _______         _______
   Protein                             ________             _______         _______
   Carbohydrate                        ________             _______         _______
   Total cholesterol                   ________             _______         _______
   Polyunsaturated fatty acids         ________             _______         _______
   Saturated fatty acids               ________             _______         _______
   Calcium                             ________             _______         _______


n) The IF and COMPUTE commands

   These commands are extremely useful when preparing data and creating new
variables from the raw data file.
   The COMPUTE command allows us to create a new variable or modify an existing
variable. Choose the command from the toolbar using the Transform and Compute pull
down menus. The Compute Variable dialog box will appear. You will be able to modify
an existing variable or create a new one. Type in the name of the new variable (or an
existing one) in the Target Variable box. Click on the Numeric Expression box and select
variables and operators from the calculator pad or type them in from the keyboard.

   Arithmetic   operators are:
   +             Addition
   -             Subtraction
   *             Multiplication
   **            Exponentiation
   /             Division


   Numeric functions are:
   ABS        Absolute Value
   TRUNC      Truncate
   SQRT       Square Root
   LG 10      Base 10 Logarithm
   RND        Round
   MOD10      Modulus
   EXP        Exponential
   LN         Natural Logarithm
   SIN        Sine
   COS        Cosine
   ATAN       ArcTangent

  There are a number of other functions available.
  Since it is possible to define some fairly complex expressions, it is important to
understand the order in which operations are performed. Numeric functions are

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performed first, exponentiation next, then multiplication and division and finally, addition
and subtraction. Expecting this hierarchy, expressions are evaluated left-to-right. The
order of operations can be controlled by using parentheses.

   Examples:

   X = A + B * 2
   X = (A + B) * 2

  If A = 4 and B = 5, then the first expression would equal 14 while the second would
equal 18.

   Examples:

   RATIO = (A + B) * (C + D)/ (E – F) **2
   STANDARD = 142.675
   X = ABS (Y)
   TEST2 = TEST1 + 3




   The IF command causes a variable to be created or modified when certain conditions
are met. In other words, the Compute command is only executed for those cases for
who the IF command is true.
   A logical expression is an expression that can be evaluated as true, false or missing,
based on conditions found in the data. Logical expressions can be simple logical relations
among variables, or they can be complex logical tests involving variables, constants,
functions, relational operators and logical operators.

   Relational operators are:
   =            Equal to
   <            Less than
   >            Greater than
   ~=           Not equal to
   <=           Less than or equal to


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   >=             Greater than or equal to

   Logical operators are:
   &           And
   |           Or
   ~           Not

   Example:
   IF (x < 12)             COMPUTE A = B + 2
   IF (SEX = ‘F’)          COMPUTE IRONRDA = 18 + Y
   IF (AGE < 22)           COMPUTE AGEGROUP = 1




o) The MEANS command

   This command produces tables of means, standard deviations and group counts for a
dependent variable within groups defined by one or more independent variables. Several
other SPSS procedures are capable of displaying similar output. Use the Analyze pull
down menu and choose Compare Means and then select the Means command.
   The Means dialog box will allow you to select those dependent variables for which
you want means calculated and allow you the option of selecting grouping (independent)
variables. You can also “layer” your independent variables to further subdivide your
sample. By default you will get the mean, standard deviation and count.




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   You can choose the Options dialog box to alter this list or to add a number of other
descriptive statistics. You can also control the use of variable and value labels and
choose an analysis of variance or/and a test for linearity.




p) The T-TEST command

    This command is for performing t-tests. To use this command, select the Analyze
pull down menu and choose Compare Means followed by selection of the appropriate
t-test i.e. independent or paired depending on your data.
    For non-paired data, select Independent-Samples T test and the Independent
Samples t-test dialog box will be opened. Select the variable(s) for which you want a
t-test performed and identify the grouping variable. The grouping variable must include
a definition of the group codes within the grouping variable. Use the Define Groups
dialog box to do this.
Example:
   To conduct a t-test on the variable, KCAL, between two groups coded as 1 and 2 in
a variable called SEX you would select KCAL as a test variable, SEX as the grouping
variable and then define group 1 as 1 and group 2 as 2 in the dialog boxes (meaning

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group 1 = 1 = male and group 2 = 2 = female).
    You can also select the Options dialog box to change how missing data are handled,
alter label displays and change the confidence interval.




   The output will be similar to the following:
T-Test

                                         Group Statistics


                                                                                                Std. Error
   CHOL        SEX
               1                  N 16              Mean
                                                     350.00          Std. Deviation
                                                                            29.781                Mean
                                                                                                    7.445
               2                    16               225.00                    67.382              16.845




                                                      Independent Samples Test


                           Levene's Test for
                          Equality of Variances                                    t-test for Equality of Means
                                                                                                                            95% Confidence
                                                                                                                             Interval of the
                                                                                               Mean        Std. Error          Difference
 CHOL   Equal variances      F          Sig.          t         df         Sig. (2-tailed)   Difference    Difference      Lower        Upper
                             7.258        .011        6.787           30             .000       125.000        18.417       87.387      162.613
        assumed
        Equal variances
                                                      6.787    20.645                .000      125.000            18.417    86.659     163.341
        not assumed

   Levene’s test is performed to find if we should use unequal variances t value or equal
variances t value. If p> 0.05 we use equal variance t value. Here p for Levene’s test is
0.011, which means we must use the unequal variance t test p value that is 0.000 (<
0.05) which means that our test is significant. There is a significant difference in the

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Kcal consumption between males and females.
   For paired data, we select Paired-Samples T test and the respective dialog box is
opened. Then we select the two variables containing the paired data (click on the first
one, hold down the Shift key and click on the second one). The Options dialog box is
identical for both the T tests. Here we do not have paired data.




   Exercise
   A few problems to test your t-test quotient

    I) The data below were collected during an animal feeding experiment. One group of
rats was provided a complete diet (controls) and the other group was fed a diet low in
protein (deficient diet). Determine if the deficient diet produced a different weight gain
(in gms) as compared to the control diet.


               Deficient Diet                                          Control Diet
      Rat        Initial Wt        Final Wt              Rat            Initial Wt.   Final Wt.
       1            222              352                  1                223           417
       2            224              370                  2                 219          416
       3            225              360                  3                224           415
       4            224              381                  4                225           417
       5            227              352                  5                226           419


Answer the following:
                                    Control Group                      Deficient Group
   Mean Initial Wt.               _________                      _________
   Standard Deviation             _________                      _________
   Statistical test used          _________                      _________
   Level of significance          _________                      _________
   Mean Final Wt.                 _________                      _________
   Standard Deviation             _________                      _________
   Statistical test used          _________                      _________
   Level of significance          _________                      _________

   Decision on the effect of the deficient diet ________________________________.

   II) An experiment was conducted to determine the effect of a high salt mean on
the systolic blood pressure of subjects. Blood pressure was determined in 12 subjects

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before and after ingestion of a test meal containing 10.0 gms of salt. The data obtained
were:


              Subject                     SBP before meal                SBP after meal
                 1                             120                            148
                 2                             130                            144
                 3                             133                            148
                 4                             120                            115
                 5                             123                            122
                 6                             140                            157
                 7                             131                            144
                 8                             120                            134
                 9                             125                            140
                10                             130                            169
                11                             131                            133
                12                             140                            153

   What is the mean SBP for each time period?
    __________                __________

   What is the standard deviation for each time period?
    __________                      __________
   Are the means statistically different? ___________
   Which statistical test did you use? _______________________
   What was the level of significance? ______________

   III) Compare mean hematocrit levels (%) from the two groups below:


       Mice from Group X                    Mice from Group Y
               40.5                                  43.9
               39.3                                   47.4
               41.5                                   46.7
               40.5                                   47.9
               40.4                                   43.7
               41.8                                  54.3
               39.3                                   48.7
                                                     46.4
                                                      47.8
                                                     49.2
                                                     56.5


   Note: hematocrit means % Red blood cells in peripheral blood. Each data point
above represents the arithmetic mean of 3+ determinations. (Hint: Do you know the
normal mouse hematocrit? It is about 39-49 %)
   Mean hematocrit for group X mice     ____________
   Standard deviation                   ____________
   Mean hematocrit for group Y mice     ____________

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  Standard deviation                      ____________
  Which statistical test did you use?     ____________
  What is the level of significance?      __________
  Was there a biological significance? (Note: this is different from statistical significance.
Look at the normal values and decide the biological significance).

   IV) Compare means for Coenzyme Q levels in whole blood from cardiomyopathy
patients. Group 1 is placebo treated and Group 2 received 100 mg/day of CoQ. The data
are listed below. (A clinical improvement is seen in patients with CoQ concentrations
at or above 2.5 microg/ml)


            CoQ concentrations (microg/ml)
          Group 1                           Group 2
              0.7                               2.2
              0.9                               3.0
              1.1                               2.3
              0.5                               1.4
              0.4                               2.5

   Group 1 mean CoQ level _______
   Standard deviation     _______
   Group 2 mean CoQ level _______
   Standard deviation     _______

   Which statistical test did you use? _________
   Level of significance was __________
   Was there a biological difference between groups in this experiment? (Note: Look at
the value needed to see a biological improvement.)

   V) The data below are from a six week animal study in which rats in the experimental
group received 35 % of their energy as ethanol. Control rats received the same diet with
dextrin substituted for the ethanol calories. All animals were fed ad libitum and both
diets were nutritionally complete.


                       Experimental                                                Control
         Initial wt.                    Final wt.                    Initial wt.             Final wt.
            89                            283                             89                   335
            93                            287                             87                   342
            87                            292                             87                   344
            90                            285                             90                   336
             91                           267                             91                   321
            88                            295                             88                   348
            86                            280                             86                   332
            95                            282                             95                   331
            87                            284                             93                   336
            89                            296                             89                   349


                                             Experimental                Control
   Mean initial weight                       ___________                 __________
   Standard Deviation                        ___________                 __________
   Statistical test used was?                ___________                 __________

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   Level of significance was?              ___________                   __________
   Mean weight gain                        ___________                   __________
   Standard Deviation                      ___________                   __________
   Statistical test used was?              ___________                   __________
   Level of significance was?              ___________                   __________

   Was there a biological difference between the groups in this experiment?

q) The ONE-WAY ANALYSIS OF VARIANCE command

    Oneway Analysis of Variance is a technique used to compare group means when
there are more than two groups of subjects. The Oneway Analysis of Variance dialog
box can be opened by selecting the Analyze pull down menu followed by Compare
Means and then One-way ANOVA. The dialog box will allow you to select those
variables (dependent) for which you would like to conduct oneway analysis of variance.
You must also select and define the grouping variable (Factor).
    You can open the Contrasts dialog box to test for trends or to define a priori contrasts.
If you wish to test for trends, select polynomial and define the Degree. You can choose
to test for linear, quadratic, cubic, 4th degree or 5th degree polynomials.
    You can open the Post Hoc dialog box to conduct post hoc multiple comparison
of means tests at the 0.05 p-level. You can choose one or more of the following: Least
significant difference, Bonferroni, Duncan’s multiple range test, Student-Newman-Keuls,
Tukey’s honestly significant difference, Tukey’s b and/or Scheffe. You can also select
the way the means are calculated.
    You can open the Options dialog box to control the way missing data are handled,
to print out descriptive statistics for each group, to print out the Levene’s statistic and
to control the display of labels.
EXAMPLE:
    Suppose an experiment were conducted to determine dietary status of the three
racial groups in our data.
    A oneway AoV test can be performed on the variables KCAL (kcal consumption),
PROT (protein consumption), VITA (Vitamin A) and FE (iron). The variable which defines
the groups to be compared is RACE. The minimum code used to define groups is 1 and
maximum is 3. A Scheffe multiple range test can be performed to compare the group
means to one another if the AoV is significant. The Scheffe procedure will be performed
at the 0.05 level of significance. A table containing group sample sizes, means, standard
deviations, standard errors, minimums, maximums and 95 % confidence intervals for
each variable tested can be displayed.




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  The output obtained will be similar to this.


ONEWAY
  KCAL PRO VITA FE BY RACE
  /STATISTICS DESCRIPTIVES
  /MISSING ANALYSIS
  /POSTHOC = SCHEFFE ALPHA(.05).




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   ONEWAY
                                                      Descriptives


                                                                            95% Confidence Interval for
                                                                                      Mean
  KCAL   Asian              N 11   Mean
                                   2711.36   Std. Deviation
                                                   355.507    Std. Error
                                                               107.189     Lower Bound Upper Bound
                                                                               2472.53         2950.20     Minimum
                                                                                                               2195    Maximum
                                                                                                                           3241
         African American     12   2865.17        421.962      121.810         2597.06          3133.27        2195        3241
         Oriental              9   2641.00        375.573      125.191         2352.31          2929.69        2195        3241
         Total                32   2749.25        386.605        68.343        2609.86          2888.64        2195        3241
  PRO    Asian                11     96.64         11.084         3.342          89.19           104.08          80         120
         African American     12     99.83         13.750         3.969          91.10           108.57          80         120
         Oriental              9     96.33         12.114         4.038          87.02           105.65          80         120
         Total                32     97.75         12.136         2.145          93.37           102.13          80         120
  VITA   Asian                11   4983.45        947.277      285.615         4347.07          5619.84        2973        6570
         African American     12   5228.00       1573.407      454.203         4228.31          6227.69         973        6570
         Oriental              9   4298.44       1700.459      566.820         2991.36          5605.53         977        5966
         Total                32   4882.50       1436.305      253.905         4364.66          5400.34         973        6570
  FE     Asian                11    10.336         3.7583        1.1332          7.812           12.861          4.8        16.5
         African American     12    11.017         4.3626        1.2594          8.245           13.789          4.8        16.5
         Oriental              9     9.567         4.1914        1.3971          6.345           12.788          4.8        16.5
         Total                32    10.375         4.0240         .7114          8.924           11.826          4.8        16.5




                                              ANOVA


                                 Sum of
  KCAL      Between Groups      Squares
                                282491.8         df    2      Mean Square
                                                               141245.894             F.941          Sig.
                                                                                                       .402
            Within Groups       4350866               29       150029.869
            Total               4633358               31
  PRO       Between Groups        83.788               2              41.894             .271             .764
            Within Groups       4482.212              29             154.559
            Total               4566.000              31
  VITA      Between Groups      4614641                2      2307320.525              1.128              .338
            Within Groups      59337495               29      2046120.515
            Total              63952136               31
  FE        Between Groups        10.838               2               5.419             .320             .729
            Within Groups        491.142              29              16.936
            Total                501.980              31


   Since the p values are not significant, Scheffe’s test has no meaning in this case.




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POST HOC TESTS
                                                    Multiple Comparisons


 Scheffe


                                                                Mean
                                                              Difference                              95% Confidence Interval
 Dependent Variable
 KCAL                 (I) RACE
                      Asian              (J) RACE
                                         African American         (I-J)
                                                                -153.803      Std. Error
                                                                               161.684     Sig.
                                                                                             .640   Lower-570.91 Upper 263.31
                                                                                                          Bound          Bound
                                         Oriental                  70.364      174.095       .922        -378.76        519.49
                      African American   Asian                   153.803       161.684       .640        -263.31        570.91
                                         Oriental                224.167       170.800       .433        -216.46        664.79
                      Oriental           Asian                    -70.364      174.095       .922        -519.49        378.76
                                         African American       -224.167       170.800       .433        -664.79        216.46
 PRO                  Asian              African American           -3.197        5.189      .828         -16.58          10.19
                                         Oriental                      .303       5.588      .999         -14.11          14.72
                      African American   Asian                       3.197        5.189      .828         -10.19          16.58
                                         Oriental                    3.500        5.482      .817         -10.64          17.64
                      Oriental           Asian                        -.303       5.588      .999         -14.72          14.11
                                         African American           -3.500        5.482      .817         -17.64          10.64
 VITA                 Asian              African American       -244.545       597.094       .920      -1784.92        1295.83
                                         Oriental                685.010       642.929       .573        -973.61       2343.63
                      African American   Asian                   244.545       597.094       .920      -1295.83        1784.92
                                         Oriental                929.556       630.759       .351        -697.67       2556.78
                      Oriental           Asian                  -685.010       642.929       .573      -2343.63         973.61
                                         African American       -929.556       630.759       .351      -2556.78         697.67
 FE                   Asian              African American           -.6803       1.7178      .925         -5.112          3.751
                                         Oriental                    .7697       1.8497      .917         -4.002          5.542
                      African American   Asian                       .6803       1.7178      .925         -3.751          5.112
                                         Oriental                  1.4500        1.8147      .729         -3.232          6.132
                      Oriental           Asian                      -.7697       1.8497      .917         -5.542          4.002
                                         African American         -1.4500        1.8147      .729         -6.132          3.232




HOMOGENEOUS SUBSETS

                           KCAL

             a,b
  Scheffe
                                                 Subset
                                                for alpha
                                                  = .05
  RACE
  Oriental                        N       9         1
                                                  2641.00
  Asian                                  11       2711.36
  African American                       12       2865.17
  Sig.                                               .425

  Means for groups in homogeneous subsets are displayed.
    a.
    b. Uses Harmonic Mean Sample Size = 10.513.
           The group sizes are unequal. The harmonic mean
           of the group sizes is used. Type I error levels are
           not guaranteed.




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                       PRO

           a,b
   Scheffe
                                         Subset
                                        for alpha
                                          = .05
   RACE
   Oriental                  N    9         1
                                            96.33
   Asian                         11         96.64
   African American              12         99.83
   Sig.                                      .813

   Means for groups in homogeneous subsets are displayed.
     a.
     b. Uses Harmonic Mean Sample Size = 10.513.
        The group sizes are unequal. The harmonic mean
        of the group sizes is used. Type I error levels are
        not guaranteed.

                      VITA

           a,b
   Scheffe
                                         Subset
                                        for alpha
                                          = .05
   RACE
   Oriental                  N    9         1
                                          4298.44
   Asian                         11       4983.45
   African American              12       5228.00
   Sig.                                      .343

   Means for groups in homogeneous subsets are displayed.
     a.
     b. Uses Harmonic Mean Sample Size = 10.513.
        The group sizes are unequal. The harmonic mean
        of the group sizes is used. Type I error levels are
        not guaranteed.

                        FE

           a,b
   Scheffe
                                         Subset
                                        for alpha
                                          = .05
   RACE
   Oriental                  N    9         1
                                            9.567
   Asian                         11        10.336
   African American              12        11.017
   Sig.                                      .724

   Means for groups in homogeneous subsets are displayed.
     a.
     b. Uses Harmonic Mean Sample Size = 10.513.
        The group sizes are unequal. The harmonic mean
        of the group sizes is used. Type I error levels are
        not guaranteed.




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   The subset for alpha = 0.05 box is not divided for any variable analyzed. If the
variables had been different, this box would have been divided into 1, 2 and so on. The
groups that are in separate boxes are different from each other.
Exercise
   I) The data below were collected from an animal feeding experiment. Analyze the
data using SPSS and answer our questions.


      Group         Rat number           Initial wt.            Final wt.       Brain wt.
        A                1                   80                   335              6.7
        A                2                   79                   342              6.6
        A                3                   89                   353              7.1
        A                4                   85                   337             6.5
        A                5                   83                   334             6.8
        B                1                   82                   335             4.3
        B                2                   85                   345              4.7
        B                3                   87                   357             4.3
        B                4                   82                   335             4.5
        B                5                   83                   343              4.6
        C                1                   80                   398              8.1
        C                2                   86                   405             8.2
        C                3                   87                   398              7.3
        C                4                   84                   398              7.6
        C                5                   86                   395              8.2


                                        Group A      Group B                 Group C
   Initial weight (means +/- SD)        _______      _______                 _______
   Statistical significance ________
   Statistical test used _________
   Your interpretation of the results_______________

                                         Group A     Group B                 Group C
   Weight gain (means +/- SD)            _______     _______                 _______
   Statistical significance ________
   Statistical test used _________
   Which groups were different from each other? _______________
   Your interpretation of the results ____________________

                                         Group A              Group B        Group C
   Brain wt as a % of
   body weight (means +/- SD)            _______     _______                 _______
   Statistical significance ________
   Statistical test used _________
   Which groups were different from each other? _______________
   Your interpretation of the results ____________________

    II) An experiment was conducted to determine the effect of various diets containing
different levels of protein on weight gain in rats. The data are presented below:


       Diet A                Diet B                      Diet C                Diet D
        89                    112                         125                   159
        97                    110                         128                   159


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           90                      120                         134           166
           90                      113                         126           167
           93                      106                         127           161
           86                      106                         122           165
           99                      108                         128           159
           82                      116                         140           159
           92                      105                         130           158
           92                      105                         130           158
           90                      106                         123           157


                                  Weight Gains (g)
                                   (Means +/- s.d.)
   Group   A               ______________________
   Group   B               ______________________
   Group   C               ______________________
   Group   D               ______________________

   Which groups are significantly different from each other? _____________
   Which test did you use? ______________
   Level of Significance? ________________
   Was there a linear trend to the results? _____________
   Which test did you use? _______________
   Level of significance? _____________

   III) Use SPSS to test for polynomial trends in the following data:


           Group A                            Group B                    Group C
                13                               169                      2197
                15                               225                      3375
                16                               256                      4096
                17                               289                      4913
                20                               400                      8000


                                           (Mean +/- SD)
   Group A                          ________________________
   Group B                          ________________________
   Group C                          ________________________

   Which groups are significantly different from each other? _______
   What test did you use? _______________
   Level of significance? ________________
   What test did you use? ________________
   Level of significance? _________________
   What type trend existed? _______________

r) Scattergrams and Regression

   SPSS can be used to generate a scatterplot of data as well as a variety of statistics
describing and testing the plot. This command can be useful for eyeballing your data. It
can also be used for a variety of purposes including the generation of data for a standard

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curve for lab assays. This is actually a number of different but related procedures that
can be found under the Analyze pull down menu with the selection of Regression
followed by the selection of the desired procedure. We will only try a few of them.
    A scattergram can be a simple way to view your data. It is an excellent way to detect
outliers (that even may be errors). To get a quick scattergram, select the Graphs pull
down menu and choose Scatter. The Scattergram dialog box will appear. You would
normally choose Simple Scattergram and click the Define button to choose the
variables to be used in your graph.




    You can then identify the Y-axis variable and the X-axis variable and control labeling
of the graph.
    This is an example of a simple scatterplot generated with SPSS.

        3250




        3000




        2750
 KCAL




        2500




        2250




        2000


               80   90        100           110          120
                              PRO



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    You can also use SPSS to generate the information needed to define a standard curve
and calculate unknowns from laboratory work. Open the absorbance.sav data file. Use
the Analyze pull down menu, select Regression and then Curve Estimation. The
following dialog box will open:




    Select the dependent (Y-axis) variable and the independent (X-axis) variable. You will
use the default (linear) model. You can also control labeling. SPSS will display a plot of
the data. This is not the important output. Close the Chart Carousel window and look
at the results in the output window.
    EXAMPLE:
    Suppose a set of standards were measured spectroscopically to determine the
absorbances associated with the concentration of Vitamin X listed below.


          Vitamin X                       Absorbance
             10.6                             0.110
             15.4                             0.165
             20.2                             0.220
             25.5                             0.271
             30.2                             0.318
             35.8                             0.370


   The Output window has a chart and the data we need to plot a straight line.
   Y = intercept + slope * (X)
   Or
   Y = B0 + B1 * (X)

  Curve Fit
MODEL: MOD _ 1.
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Independent:              Absorbance

  Dependent Mth                Rsq          d.f.              F            Sigf            b0      b1

  VitaminX LIN               .998            4           2052.68          .000         -.5490   96.9697

Where b0 is the Y-intercept and b1 is the slope.



                                       VitaminX


 40.00                                                                      Observed
                                                                            Linear


 35.00



 30.00



 25.00



 20.00



 15.00



 10.00


          0.100   0.150    0.200    0.250   0.300     0.350       0.400
                              Absorbance

    Therefore our straight line (standard curve) would be:
    Y = -0.5490 + 96.9697 * (X)

   We could now use this information to create a Compute command to convert a set of
absorbances into concentrations of Vitamin X and use List Cases to print them out.

    Exercise
    I) Use SPSS to create a scatterplot of Kcal and Total cholesterol from the diet.
sav data file. Is there any pattern or is it just random?
   II) Use SPSS to determine a standard curve for an assay called Bradford assay to
measure protein concentrations. In this, we first determine the absorbances of some
known concentration protein samples, that we call standards. Then we plot a curve and
determine our correlation coefficient, Y intercept and slope. With that information we
can calculate protein concentrations of unknown samples if we get their absorbance
values. Draw the curve on a sheet of graph paper and compare it to the curve drawn by
the computer. Use SPSS’ formula function for a straight line (Y = A + BX) to determine
protein concentrations in the unknowns (Note: Let X = absorbance and Y = protein
concentration). Plot absorbance on the X axis and protein concentrations on the Y
axis.


    Standard curve data
                                              Absorbance at 595
         Protein (microg)
                                            nm
         20                                   0.160
         30                                         0.192
         40                                         0.255



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     50                            0.296
     60                            0.352
     70                            0.357

     80                            0.390

     90                            0.451

     100                           0.500


   Correlation coefficient _____________
   Y-intercept _____________
   Slope ____________
   Therefore straight line formula = Y = A + BX = ________________
   So X (unknown) = _______________


   Data from unknown samples


     Protein (microg)           Absorbance at 595 nm
                                              0.37
                                              0.43
                                              0.31
                                              0.37
                                              0.24
                                              0.58

   Calculate the protein concentrations using the formula function/Compute of SPSS.

s) Multiple Regression

   This command is used to produce multiple regression equations and associated
statistics and plots. You can use SPSS to generate a multiple regression analysis. Use
the Analyze pull down menu and select Regression and then Linear. The following dialog
box will appear:




                                                                                  
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   Select your variable of interest and place it in the dependent variable box. Then
select each of the predictors that you want used in your equation and place them in the
independent(s) box. Select the appropriate method. Stepwise is the suggested method.
This will identify the best predictor and generate output, then the best predictor which
goes with the first and so on.

   REGRESSION

                Descriptive Statistics


   KCAL       Mean
              2749.25    Std. Deviation
                               386.605              N 32
   CHO         334.75            51.285               32
   FAT         113.25            23.267               32
   PRO          97.75            12.136               32
   FIB          11.75             1.951               32
   CA          818.50           173.161               32
   CHOL        287.50            81.599               32




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                                           a
                   Variables Entered/Removed


                     Variables                Variables
     Model
     1               Entered                  Removed                     Method
                                                                         Stepwise
                                                                         (Criteria:
                                                                         Probabilit
                                                                         y-of-
                                                                         F-to-enter
                    CA                                          .        <= .050,
                                                                         Probabilit
                                                                         y-of-
                                                                         F-to-remo
                                                                         ve >= .
                                                                         100).
     2                                                                   Stepwise
                                                                         (Criteria:
                                                                         Probabilit
                                                                         y-of-
                                                                         F-to-enter
                    FAT                                         .        <= .050,
                                                                         Probabilit
                                                                         y-of-
                                                                         F-to-remo
                                                                         ve >= .
                                                                         100).
     3                                                                   Stepwise
                                                                         (Criteria:
                                                                         Probabilit
                                                                         y-of-
                                                                         F-to-enter
                    CHO                                         .        <= .050,
                                                                         Probabilit
                                                                         y-of-
                                                                         F-to-remo
                                                                         ve >= .
                                                                         100).
     4                                                                   Stepwise
                                                                         (Criteria:
                                                                         Probabilit
                                                                         y-of-
                                                                         F-to-enter
                    PRO                                         .        <= .050,
                                                                         Probabilit
                                                                         y-of-
                                                                         F-to-remo
                                                                         ve >= .
                                                                         100).
     5                                                                   Stepwise
                                                                         (Criteria:
                                                                         Probabilit
                                                                         y-of-
                                                                         F-to-enter
                    FIB                                         .        <= .050,
                                                                         Probabilit
                                                                         y-of-
                                                                         F-to-remo
                                                                         ve >= .
                                                                         100).
     6                                                                   Stepwise
                                                                         (Criteria:
                                                                         Probabilit
                                                                         y-of-
                                                                         F-to-enter
                    CHOL                                        .        <= .050,
                                                                         Probabilit
                                                                         y-of-
                                                                         F-to-remo
                                                                         ve >= .
                                                                         100).
         a.
              Dependent Variable: KCAL




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                         Model Summary


                                       Adjusted        Std. Error of
  Model
  1             R.895a R Square
                           .801        R Square
                                            .795       the Estimate
                                                            175.198
  2              .983b     .966             .964             73.443
  3                   c
                 .999      .997             .997             21.887
  4             1.000d    1.000            1.000               .000
  5             1.000e    1.000            1.000               .000
  6                   f
                1.000     1.000            1.000               .000
      a.
      b. Predictors: (Constant), CA
      c. Predictors: (Constant), CA, FAT
      d. Predictors: (Constant), CA, FAT, CHO
      e. Predictors: (Constant), CA, FAT, CHO, PRO
      f. Predictors: (Constant), CA, FAT, CHO, PRO, FIB
        Predictors: (Constant), CA, FAT, CHO, PRO, FIB, CHOL




For instance, in the Model Summary table, a value of 0.795 for calcium means that
53 percent of change in Kcal can be predicted if we have the Calcium intake. Then
a value of 0.964 below that means that if we have both Calcium and Fat intake, we
can predict 96 percent of the change in Kcal and so on.




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                                            Coefficientsa


                              Unstandardized              Standardized
                                Coefficients               Coefficients
   Model
   1           (Constant)      B
                            1113.479 Std. Error
                                         151.926              Beta          t
                                                                            7.329    Sig.
                                                                                       .000
               CA              1.998           .182                 .895   10.998      .000
   2           (Constant)    683.316         73.224                         9.332      .000
               CA              1.412           .091                 .632   15.563      .000
               FAT             8.038           .675                 .484   11.905      .000
   3           (Constant)    218.675         34.632                         6.314      .000
               CA               .334           .068                 .150    4.916      .000
               FAT             9.189           .212                 .553   43.352      .000
               CHO             3.634           .210                 .482   17.278      .000
   4           (Constant)       .000           .000                              .         .
               CA               .000           .000                 .000         .         .
               FAT             9.000           .000                 .542         .         .
               CHO             4.000           .000                 .531         .         .
               PRO             4.000           .000                 .126         .         .
   5           (Constant)       .000           .000                              .         .
               CA               .000           .000                 .000         .         .
               FAT             9.000           .000                 .542         .         .
               CHO             4.000           .000                 .531         .         .
               PRO             4.000           .000                 .126         .         .
               FIB              .000           .000                 .000         .         .
   6           (Constant)       .000           .000                              .         .
               CA               .000           .000                 .000         .         .
               FAT             9.000           .000                 .542         .         .
               CHO             4.000           .000                 .531         .         .
               PRO             4.000           .000                 .126         .         .
               FIB              .000           .000                 .000         .         .
               CHOL             .000           .000                 .000         .         .
       a.
            Dependent Variable: KCAL




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                                                     f
                                   Excluded Variables


                                                                              Collinearity
                                                                Partial        Statistics
  Model
  1         CHO            In
                      Beta.102a        t .474      Sig.
                                                     .639     Correlation
                                                                      .088    Tolerance.147
            FAT           .484a      11.905          .000             .911            .705
            PRO           .220a       1.280          .211             .231            .219
            FIB          -.146a      -1.214          .235            -.220            .450
            CHOL          .013a        .104          .918             .019            .423
  2         CHO           .482b      17.278          .000             .956            .133
            PRO          -.009b       -.111          .913            -.021            .204
            FIB          -.124b      -2.697          .012            -.454            .450
            CHOL          .143b       3.028          .005             .497            .406
  3         PRO           .126c            .             .          1.000             .184
            FIB          -.063c      -5.991          .000            -.755            .422
            CHOL          .021c       1.205          .239             .226            .321
  4         FIB           .000d            .             .                .           .181
            CHOL          .000d            .             .                .           .305
  5         CHOL          .000e            .             .                .           .223
      a.
      b. Predictors in the Model: (Constant), CA
      c. Predictors in the Model: (Constant), CA, FAT
      d. Predictors in the Model: (Constant), CA, FAT, CHO
      e. Predictors in the Model: (Constant), CA, FAT, CHO, PRO
      f. Predictors in the Model: (Constant), CA, FAT, CHO, PRO, FIB
        Dependent Variable: KCAL

   Additional subcommands exist if the input is a matrix or if the user wishes to write
the matrix to an external file; if the user wishes to examine residuals; or if plots of
various types are desired. These can be used under the “syntax window system” of
creating commands. The Regression procedure can be very complex. The order of
subcommands is very important in determining the output. It is therefore imperative
that the manual be studied carefully when using this procedure.

t) CHI-SQUARE test using CROSSTABS

   When discrete data have been collected, it is often desirable to use the Chi-square
test. One way to have SPSS calculate the Chi-square for us is the use the Crosstabs
procedure. The Crosstabs command has a variety of parts, many of which are optional.
The discussion below is intended to clarify some of the information provided in the
manual.
   Use the Analyze pull down menu and select Descriptive Statistics and then
Crosstabs. The following dialog box will appear:




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  Select your row and column variables. Select the Statistics button and choose
Chi-square.




   You can also control what is printed into the cells of the table by selecting the Cells
option.




   By default, you will get only Counts.
   You can also control the Format of the output by selecting the Format option.

   The output would look similar to the following:

   CROSSTABS

                                  Case Processing Summary


                                                   Cases
                          Valid                    Missing                     Total
  RACE * SEX         N 32         Percent
                                   100.0%        N 0     Percent
                                                             .0%           N 32      Percent
                                                                                      100.0%




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                   RACE * SEX Crosstabulation


  Count
                                SEX
  RACE         1           1    5      2    6      Total11
               2                7           5          12
               3                4           5           9
  Total                        16          16          32




                                      Chi-Square Tests


                                                                         Asymp. Sig.
   Pearson Chi-Square                      Value a
                                              .535           df    2      (2-sided)
                                                                                 .765
   Likelihood Ratio                           .537                 2             .764
   Linear-by-Linear
                                                .000               1            1.000
   Association
   N of Valid Cases                               32
          a.
               2 cells (33.3%) have expected count less than 5. The
               minimum expected count is 4.50.
   Looking at the p values, we can infer that there is no significant difference in the
distribution.


    Exercise
    I) The following data were collected from an experiment to determine the outcome of
a zinc supplement program on the performance of children on a standardized intelligent
test. Determine statistical significance by Chi-square.


                                            Improved                   Did not improve              Total
               Control                             6                          17                     23
      Supplemented                                19                           8                     27
                Total                             25                          25                     50


   Chi-square value = __________
   p < _____________

   II) The following data were collected from an experiment on the effects of a daily 30
minute jogging schedule on weight loss. The control group spent 30 minutes watching
a TV commercial of a tooth whitening product.




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    Group          Initial wt.     Final wt.             Group           Initial wt.    Final wt.
                      251            252                                    244           236
                      229            226                                    231           208
                      240            241                                    241           241
                      229            225                                    257           258
                      243            245                                    253           234
                      308            309                                    299           302
                      196            202                                    196           184
                      222            221                                    232           225
                      207            200                                    243           196
                      274            268                                    264           268
    Control           239            220            Experimental            220           225
                      251            251                                    221           211
                      209            196                                    209           197
                      220            217                                    229           216
                      294              300                                  298              285


   A successful weight loss is defined by the experimenters as being at least five pounds.
Determine if the percentages of successful weight loss were different in the two groups.
(Hint: In your calculations, divide the groups into successful weight loss and no successful
weight loss, controls and experimentals)
                                           Controls                Experimentals
   Percentage of successful wt.loss        _______                 _______
   Chi-square value       _______
   p<                     _______

   III) We wish to evaluate the presence of breast cancer as a risk factor for subsequent
cancer in the other breast. From a group of 55-65 yr old women, you select a group of
breast cancer cases and a group of controls (not currently suffering from breast cancer).
You use a questionnaire and a thorough search of cancer registry records to determine
past histories of breast cancer. Your data are presented below.


                                   Cancer                   No Cancer
                                                                                       Total
                                   (cases)                  (controls)
    Previous cancer                  12                            6                    18
  No previous cancer                 38                           44                    82
          Total                      50                           50                   100


   Chi-square value = _____________
   p < ___________

    As you can see, this is a retrospective study, which means you can calculate relative
risk.
    Relative risk (cross product ratio) = ______________

   That means that a person with cancer in one breast is _________ times more likely
to have breast cancer in the other breast than a person who does not suffer from breast


                                                                                                   
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cancer at all.
   Do you think this value is significant biologically?

u) Selection of a Subset of Cases for Analysis

   Many a time, you might like to run a statistical test on selected subsets of your data.
For example you may have a huge data file and decide that you want to look only at
the males in your data. SPSS allows you to create a permanent data file to analyze only
males or do so temporarily. Use the Data pull down menu and select Select cases.
The following dialog box will appear.




   Click the If condition is satisfied button and click on If. The following box will
then appear:




   Set your conditions for case selection and your data file will now look like this:

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   You can now choose whatever statistical procedure(s) you want to perform on this
subset of cases.

   NOTE: The Filtered button (the default) allows you to use Select cases again
to undo or alter your selection. The Deleted button makes this a permanent case
selection. You can then save the new data as another file and work on it.

v) The Nonparametric Tests

   SPSS allows the user to perform a number of nonparametric statistical tests. The
tests available can be grouped into broad categories depending on the type of the
experimental data you have e.g. one-sample tests, related-sample tests and independent-
samples tests. These tests are found in the Analyze pull down menu on selecting
Nonparametric Tests and then choosing the appropriate category. You may make
one of the following choices:


    Chi-square…                           Gives a one-sample Chi-square test.

    Binomial…                             Gives a        binomial        test for a dichotomous
                                          variable.

    Runs…                                 Gives a “runs” test to determine if the order of
                                          occurrence of two values of a variable is random.

    1-sample K-S…                         Gives     a    one-sample        Kolmogorov-Smirnov
                                          test.

    2 Independent Samples…                Allows a choice of tests comparing 2 independent
                                          groups of cases By default, the Mann-Whitney U
                                          test is performed. Other tests that can be chosen
                                          include: K-S Z, Moses extreme reactions or

                                                                                            
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                                      Wald-Wolfowitz runs.

      K Independent Samples…          By default you get a Kruskal-Wallis H statistic
                                      computed. You can opt for a Median test.

      2 Related Samples…              By default you get a Wilcoxon test (for ranked
                                      data). You can choose a Sign test or a McNemar
                                      test.

      K Related Samples…              By default you get a Friedman test. You can
                                      choose a Kendall’s W or a Cochran’s Q.

For each of these, you have choices as to which statistics are displayed an how labels
and missing data are handled. We will examine two of these as examples.

w) Mann-Whitney U test

   A Mann-Whitney U test can be obtained by selecting the 2 Independent Samples
option under the Nonparametric Tests menu. The following dialog box will appear.




   Since Mann-Whitney U test is the default, we will select our variables to test and our
grouping variable. We must of course define our groups similar to previous tests. The
output looks similar to the following:


   NPAR TESTS


   Mann-Whitney Test


                           Ranks


  AGE      SEX
           1          N 16          Rank
                               Mean 17.34              Ranks
                                                Sum of 277.50
           2            16           15.66               250.50
           Total        32



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             Test Statisticsb


   Mann-Whitney U                AGE
                                114.500
   Wilcoxon W                   250.500
   Z                              -.510
   Asymp. Sig. (2-tailed)          .610
   Exact Sig. [2*(1-tailed                 a
                                    .616
   Sig.)]
      a.
      b. Not corrected for ties.
         Grouping Variable: SEX
  Here a 0.616 significance means there is no significant difference between ages of
males and females in the data. (Since we do not have ranking data here, we used ages.
But ideally this test would be used to compare ranks).

  Median test
  A Median test can be obtained by selecting K Independent Samples under the
Nonparametric Tests menu. The following dialog box will appear:




   Since we need to perform a median test we must deselect Kruskal-Wallis H (the
default) and choose Median test. We can then select the variable(s) to be tested and
the grouping variable. We must define the range of values of our grouping variable. The
output will be similar to the following:

   NPAR TESTS


   Median Test

                   Frequencies


                                      SEX
   AGE      > Median            1    8         2    8
            <= Median                8              8



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   In this data, we have equal distribution; therefore our significance level is 1.0 which
means that there is no significant difference in the medians of ages in males and
females.

x) Bivariate Correlations

   There are multiple ways to use SPSS to get correlation coefficients. W can select
Correlate from the Analyze pull down menu and then select Bivariate. The following
dialog box will appear.




    We can define variables to be used to create a correlation coefficient matrix. By
default, we get Pearson’s correlation coefficients. Our output will be similar to the
following:

   Correlations




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   We do not get r2 by using this procedure. If we want the r2 value, we can calculate it
with a calculator or choose Regression and then Linear under the Analyze pull down
menu. Here we would choose Enter under the Method box. This would give us the r
and r2.




                          Model Summary

                                       Adjusted R      Std. Error of
 Model          R        R Square
                                        Square         the Estimate
 1             .583(a)          .340           .318            19.211
a Predictors: (Constant), PRO

The r2 value means that 34 percent of the fat intake can be predicted by
protein intake. (Since this is not the kind of data you would use for regression
analysis, do not try to make sense out of this statement.)

y) Survival

    The SURVIVAL command produces life tables, plots and related statistics for
examining the length of time between two events (let’s say exposure and development
of disease). Cases can be classified into groups, and separate analyses and comparisons
obtained for the groups. The time interval between two dates can be calculated with the
SPSS date and time conversion functions (e.g. YRMODA).

     Example:

   If the data file contains dates of important events such as diagnosis or outcome, you
can use the Compute command and the YRMODA function to calculate elapsed time.


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Use the survival.sav data file provided to you to work on this function. The outcomes
are either 1 (died) or 2 (survived). The treatments are either 1 (Vitamin A), 2 (Beta
Blocker), 3 (ACE inhibitor) or 4 (Aspirin).

   Use the Compute command to calculate a variable xyz (time elapsed between
exposure and the event i.e. death)




   xyz will now be created as a new variable on your data file and will provide you
the number of years elapsed between the two dates. You can then use the survival
analysis command to compute median “survival time” for various groups within your
experiment.
   The Survival command can be found under the Analyze pull down menu. Then
select Life Tables. The following dialog box will appear:




   Place your variable defining the time elapsed in the Time box. The Display Time
Intervals boxes are for defining the number of time units that will be displayed on your
output. The Status box is for defining your outcome and the Factor box is for defining
your grouping variable. Look at the examples below.




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  You can also select the Options button to generate statistical testing your groups
and to control the Output.




   The output will be similar to the following:

Available workspace allows for exact comparisons of                174762 observations


This subfile contains:          40 observations

 Life Table
   Survival Variable      xyz          survival
                 for      treatmen
                                                               =           1   Vitamin A

          Number   Number    Number    Number                            Cumul
Intrvl    Entrng   Wdrawn    Exposd      of       Propn      Propn       Propn    Proba-
Start      this    During      to      Termnl     Termi-     Sur-        Surv     bility   Hazard
Time      Intrvl   Intrvl     Risk     Events     nating     viving      at End   Densty    Rate
------    ------   ------    ------    ------     ------     ------      ------   ------   ------
     .0     19.0       .0      19.0         .0     .0000     1.0000      1.0000    .0000    .0000
   1.0      19.0       .0      19.0         .0     .0000     1.0000      1.0000    .0000    .0000
   2.0      19.0       .0      19.0         .0     .0000     1.0000      1.0000    .0000    .0000
   3.0      19.0       .0      19.0         .0     .0000     1.0000      1.0000    .0000    .0000
   4.0      19.0       .0      19.0         .0     .0000     1.0000      1.0000    .0000    .0000
   5.0      19.0       .0      19.0         .0     .0000     1.0000      1.0000    .0000    .0000
   6.0      19.0       .0      19.0         .0     .0000     1.0000      1.0000    .0000    .0000


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  7.0       19.0        .0      19.0        .0     .0000     1.0000      1.0000    .0000    .0000
  8.0       19.0        .0      19.0        .0     .0000     1.0000      1.0000    .0000    .0000
  9.0       19.0        .0      19.0        .0     .0000     1.0000      1.0000    .0000    .0000
 10.0+      19.0       4.0      17.0      15.0     .8824      .1176       .1176      **       **

**       These calculations for the last interval are meaningless.

The median survival time for these data is               10.00+


           SE of     SE of
 Intrvl    Cumul     Proba-    SE of
 Start     Sur-      bility    Hazard
 Time      viving    Densty     Rate
-------    ------    ------    ------
      .0    .0000     .0000     .0000
    1.0     .0000     .0000     .0000
    2.0     .0000     .0000     .0000
    3.0     .0000     .0000     .0000
    4.0     .0000     .0000     .0000
    5.0     .0000     .0000     .0000
    6.0     .0000     .0000     .0000
    7.0     .0000     .0000     .0000
    8.0     .0000     .0000     .0000
    9.0     .0000     .0000     .0000
   10.0+    .0781       **        **




Life Table
  Survival Variable       xyz           survival
                for       treatmen
                                                               =           2   Beta Blocker

        Number      Number    Number    Number                           Cumul
Intrvl Entrng       Wdrawn    Exposd      of      Propn      Propn       Propn    Proba-
Start    this       During      to      Termnl    Termi-     Sur-        Surv     bility   Hazard
Time    Intrvl      Intrvl     Risk     Events    nating     viving      at End   Densty    Rate
------ ------       ------    ------    ------    ------     ------      ------   ------   ------
     .0   10.0          .0      10.0         .0    .0000     1.0000      1.0000    .0000    .0000
   1.0    10.0          .0      10.0         .0    .0000     1.0000      1.0000    .0000    .0000
   2.0    10.0          .0      10.0         .0    .0000     1.0000      1.0000    .0000    .0000
   3.0    10.0          .0      10.0         .0    .0000     1.0000      1.0000    .0000    .0000
   4.0    10.0          .0      10.0         .0    .0000     1.0000      1.0000    .0000    .0000
   5.0    10.0          .0      10.0         .0    .0000     1.0000      1.0000    .0000    .0000
   6.0    10.0          .0      10.0         .0    .0000     1.0000      1.0000    .0000    .0000
   7.0    10.0          .0      10.0         .0    .0000     1.0000      1.0000    .0000    .0000
   8.0    10.0          .0      10.0         .0    .0000     1.0000      1.0000    .0000    .0000
   9.0    10.0          .0      10.0         .0    .0000     1.0000      1.0000    .0000    .0000
  10.0+   10.0          .0      10.0      10.0    1.0000      .0000       .0000      **       **

**       These calculations for the last interval are meaningless.

The median survival time for these data is               10.00+



           SE of     SE of
 Intrvl    Cumul     Proba-    SE of
 Start     Sur-      bility    Hazard
 Time      viving    Densty     Rate
-------    ------    ------    ------
      .0    .0000     .0000     .0000
    1.0     .0000     .0000     .0000
    2.0     .0000     .0000     .0000
    3.0     .0000     .0000     .0000
    4.0     .0000     .0000     .0000
    5.0     .0000     .0000     .0000
    6.0     .0000     .0000     .0000
    7.0     .0000     .0000     .0000
    8.0     .0000     .0000     .0000
    9.0     .0000     .0000     .0000
   10.0+    .0000       **        **



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 Life Table
   Survival Variable      xyz           survival
                 for      treatmen
                                                               =           3   ACE inhibitor

        Number      Number    Number    Number                           Cumul
Intrvl Entrng       Wdrawn    Exposd      of      Propn      Propn       Propn    Proba-
Start    this       During      to      Termnl    Termi-     Sur-        Surv     bility   Hazard
Time    Intrvl      Intrvl     Risk     Events    nating     viving      at End   Densty    Rate
------ ------       ------    ------    ------    ------     ------      ------   ------   ------
     .0    7.0          .0       7.0         .0    .0000     1.0000      1.0000    .0000    .0000
   1.0     7.0          .0       7.0         .0    .0000     1.0000      1.0000    .0000    .0000
   2.0     7.0          .0       7.0         .0    .0000     1.0000      1.0000    .0000    .0000
   3.0     7.0          .0       7.0         .0    .0000     1.0000      1.0000    .0000    .0000
   4.0     7.0          .0       7.0         .0    .0000     1.0000      1.0000    .0000    .0000
   5.0     7.0          .0       7.0         .0    .0000     1.0000      1.0000    .0000    .0000
   6.0     7.0          .0       7.0         .0    .0000     1.0000      1.0000    .0000    .0000
   7.0     7.0          .0       7.0         .0    .0000     1.0000      1.0000    .0000    .0000
   8.0     7.0          .0       7.0         .0    .0000     1.0000      1.0000    .0000    .0000
   9.0     7.0          .0       7.0         .0    .0000     1.0000      1.0000    .0000    .0000
  10.0+    7.0         3.0       5.5       4.0     .7273      .2727       .2727      **       **

 **      These calculations for the last interval are meaningless.

 The median survival time for these data is              10.00+



           SE of     SE of
 Intrvl    Cumul     Proba-    SE of
 Start     Sur-      bility    Hazard
 Time      viving    Densty     Rate
-------    ------    ------    ------
      .0    .0000     .0000     .0000
    1.0     .0000     .0000     .0000
    2.0     .0000     .0000     .0000
    3.0     .0000     .0000     .0000
    4.0     .0000     .0000     .0000
    5.0     .0000     .0000     .0000
    6.0     .0000     .0000     .0000
    7.0     .0000     .0000     .0000
    8.0     .0000     .0000     .0000
    9.0     .0000     .0000     .0000
   10.0+    .1899       **        **



 Life Table
   Survival Variable      xyz           survival
                 for      treatmen
                                                               =           4   Aspirin

        Number      Number    Number    Number                           Cumul
Intrvl Entrng       Wdrawn    Exposd      of      Propn      Propn       Propn    Proba-
Start    this       During      to      Termnl    Termi-     Sur-        Surv     bility   Hazard
Time    Intrvl      Intrvl     Risk     Events    nating     viving      at End   Densty    Rate
------ ------       ------    ------    ------    ------     ------      ------   ------   ------
     .0    4.0          .0       4.0         .0    .0000     1.0000      1.0000    .0000    .0000
   1.0     4.0          .0       4.0         .0    .0000     1.0000      1.0000    .0000    .0000
   2.0     4.0          .0       4.0         .0    .0000     1.0000      1.0000    .0000    .0000
   3.0     4.0          .0       4.0         .0    .0000     1.0000      1.0000    .0000    .0000
   4.0     4.0          .0       4.0         .0    .0000     1.0000      1.0000    .0000    .0000
   5.0     4.0          .0       4.0         .0    .0000     1.0000      1.0000    .0000    .0000
   6.0     4.0          .0       4.0         .0    .0000     1.0000      1.0000    .0000    .0000
   7.0     4.0          .0       4.0         .0    .0000     1.0000      1.0000    .0000    .0000
   8.0     4.0          .0       4.0         .0    .0000     1.0000      1.0000    .0000    .0000
   9.0     4.0          .0       4.0         .0    .0000     1.0000      1.0000    .0000    .0000
  10.0+    4.0         1.0       3.5       3.0     .8571      .1429       .1429      **       **

 **      These calculations for the last interval are meaningless.



                                                                                                    
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 The median survival time for these data is             10.00+



           SE of    SE of
 Intrvl    Cumul    Proba-    SE of
 Start     Sur-     bility    Hazard
 Time      viving   Densty     Rate
-------    ------   ------    ------
      .0    .0000    .0000     .0000
    1.0     .0000    .0000     .0000
    2.0     .0000    .0000     .0000
    3.0     .0000    .0000     .0000
    4.0     .0000    .0000     .0000
    5.0     .0000    .0000     .0000
    6.0     .0000    .0000     .0000
    7.0     .0000    .0000     .0000
    8.0     .0000    .0000     .0000
    9.0     .0000    .0000     .0000
   10.0+    .1870      **        **




 Comparison of survival experience using the Wilcoxon (Gehan) statistic
   Survival Variable xyz        survival
          grouped by treatmen

  Overall comparison         statistic            11.350    D.F.          3   Prob.    .0100

  Group    label                   Total N        Uncen       Cen       Pct Cen   Mean Score

      1    Vitamin A                      19         15          4        21.05       9.0526
      2    Beta Blocker                   10         10          0          .00     -19.1000
      3    ACE inhibitor                   7          4          3        42.86      -3.5714
      4    Aspirin                         4          3          1        25.00      11.0000

Abbreviated    Extended
Name           Name

treatment       treatment


   The main values to look for are the median survival times and finally the overall
comparison table for the probability value. Here the probability value is 0.01 which
means that there is no significant difference in the survival of the differently treated
groups.




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SpSS Syntax windows
   It is possible to bypass the pull down menus (If you are like me, you would probably
ask- Why would anyone want to do that? But believe me, some people do and this is for
their benefit.) To do this one has to type SPSS commands directly into an SPSS syntax
window or load commands from a file into an SPSS syntax window. You can then modify
the commands or execute them. To use SPSS to type directly into a syntax window, use
the File pull down men and select New and then select SPSS Syntax. A blank syntax
window will appear. You can now type SPSS commands directly into the window and
execute them by clicking the execute button. Remember to end each command with a
period. You can also use the File/Open pull down menu to load a file containing SPSS
commands into the syntax window.
   In addition, SPSS has trizillions (just kidding!) of commands available. Here is a brief
outline of many of them. (arranged in alphabetical order)

   THE ADD VALUE LABELS COMMAND
   The Add Value labels command adds or alters value labels without affecting the
value labels that have already been assigned for that variable. In contrast, Value labels
adds or alters value labels but deletes all existing value labels for that variable.

   THE AGGREGATE COMMAND
   The Aggregate command creates a new data file from your old data file by aggregating
groups of cases into single cases. The values for one or more variables are used to define
the groups. The grouping variables are called break variables. All cases in the old file
with identical values for the break variable become a break group. Each break group is
assigned a single value for each newly created variable. There are nineteen aggregate
functions for creating new variables. The functions include:
   SUM           The sum across cases
   MEAN          The mean across cases
   SD            The standard deviation across cases
   MAX           The maximum value across cases
   MIN           The minimum value across cases.
   PGT           Percentage of cases greater than some value
   PLT           Percentage of cases lesser than some value
   PIN           Percentage of cases between two values inclusive
   POUT          Percentage of cases not between two values
   FGT           Fraction of cases greater than some value
   FLT           Fraction of cases lesser than some value
   FIN           Fraction of cases between two values inclusive
   FOUT          Fraction of cases not between two values
   N             Weighted number of cases in break group
   NU            Unweighted number of cases in break group
   NMISS         Weighted number of missing cases




                                                                                       
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   NUMISS       Unweighted number of missing cases
   FIRST        First nonmissing observed value in break group
   LAST         First nonmissing observed value in break group

   Example:
   Suppose we had a large data file named EXPERIMENT.DAT and wished to construct
a new data file named FEEDING.DAT containing mean Kilocalorie consumption for each
day rather than individual data for each mouse. We can use Aggregate to do this.
   Our command might look something like this:
   AGGREGATE OUTFILE = ‘FEEDING.DAT’
         /BREAK = FEEDING
        /AVGKCAL = MEAN (KCAL).

    THE AUTORECODE COMMAND
    The Autorecode command recodes the values of both string and numeric variables
to consecutive integers and puts the new values into a different variable called the target
variable.
    Example:
    If we have a category called Race and our variable labels were
    1 = White
    2 = Hispanic
    3 = African American
    4 = Asian
    We can recode this as 1 = White and 2 = Non-White


   THE ANoVA COMMAND
   This command does not exist in the toolbar. We need to create it in the Syntax
window. It performs analysis of variance for data from experiments with factorial
designs. A factorial design is used when the researcher wishes to study the effects of
several factors simultaneously. The ANoVA command also allows the user to perform
analysis of covariance procedures. Other SPSS commands which also perform ANoVA
are ONEWAY and MEANS.
   Example:
   Suppose a researcher wants to study the relationships between total kilocalorie
consumption, sex and race, the following command may be used:
   ANOVA VARIABLES = KCAL BY SEX (1,2) RACE (1,4)
          /STATISTICS = 3.

   THE CORRELATION COMMAND
   This command produces Pearson product-moment correlations with one-tailed
probabilities. We can also opt for additional output including univariate statistics,
covariances and cross-product deviations.
   Example:
   CORRELATION VARIABLES = HEIGHT WEIGHT AGE
        /VARIABLES = HEIGHT WEIGHT WITH AGE
       /OPTIONS = 2 3
      /STATISTICS = 1


    The first VARIABLES subcommand causes a square matrix of correlation coefficients
to be created among the variables HEIGHT, WEIGHT AND AGE. The second VARIABLES



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subcommand requests that a rectangular correlation matrix be created in which HEIGHT
and WEIGHT are the rows and AGE is the column. The OPTION 2 requests pairwise
deletion of missing values. OPTION 3 requests two-tailed probabilities. STATISTICS 1
requests means, standard deviations and counts for each variable.


    THE COUNT COMMAND
    This command creates a new variable for each case that contains a count of the
number of occurrences of a particular value or range of values across a list of variables.
In social science, for instance, we can have responses to several questions such as 1 =
strongly agree 2 = agree 3 = neutral 4 = disagree 5 = strongly disagree and then count
how many 1s, 2s… we have.

    Example:
    COUNT X = Y,Z,W (2)
    A new variable X is created for each case. It will contain a count of the number of
times a value of 2 was found across the variables Y, Z and W. Therefore the value of X
will be 0, 1, 2 or 3.


   THE DISPLAY COMMAND
   This command gives detailed information about the variables in the active file. It
gives the variable name and label, value labels, missing value flags, the variable type
and the variable width. Not a very useful command if you ask us.


   THE EXPORT AND IMPORT COMMANDS
   The Export command is used to produce a portable ASCII (“the text” in Windows.
ASCII is the table which codes for each letter or number in let’s say MS Word) data file
and dictionary that can be read with the Import command in SPSS on a computer.
These commands too are hardly used. You might use it to export your output to Word
(But why do that when you can Copy and Paste onto MS Word anything from your
output?)


   THE GET AND SAVE COMMANDS
   The Save command produces an SPSS system file which includes all data and a
data dictionary with variable and values labels, if specified, missing value flags and print
formats for each variable. The Get command retrieves a system file created by a Save
command. We can see these commands in the output window when we open files.


   THE INCLUDE COMMAND
   This command allows you to execute SPSS commands from a file. This allows you to
use your favorite text editor (such as MS Word) to create an SPSS command file rather
than using Review. The @ character can be used in place of Include.
   Example:
   If you had created your commands in a file named XYZ.CMD you could execute it
directly with the following:
   Include ‘XYZ.CMD’.
   This command too is not used much anymore.

   THE MISSING VALUE COMMAND
   This command is used to declare user-missing values for specified variables. System
generated missing values are assigned when the raw data for a given variable is blank

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or when an illegal calculation is requested.

   Example:
   Missing Value list of variables (n).
   Where “n” is the value to be used to identify missing data.

   THE N OF CASES COMMAND
   This command limits the number of cases in the active file to the first “n” cases
   You may try this command to see if every command runs correctly.

   Example:
   N of Cases n.

    THE RECODE COMMAND
    This command changes the coding of an existing variable or list of variables on a
value-by-value basis. When it is possible to use it, Recode command is much more
efficient than a series of If commands used to produce the same transformation. This
command does not require us to know much about our data.
    There are a number of keywords which can be used with this command. They are:

      LO or LOWEST    specifies the lowest value found (including user-missing values,
                      but not system-missing values)
      HI or HIGHEST   specifies the highest value found (including user-missing values,
                      but not system-missing values)
      THRU            specifies a value range, inclusive of end values
      MISSING         specifies user- and system- missing vales for recoding
      SYSMIS          specifies system-missing values only
      ELSE            includes all values not already specified including the system-
                      missing value

   Example:
   RECODE INCOME (LO THRU 500 = 1) (501 THRU 1000 = 2) (1001 THRU HI =
3)/RACE (2 THRU HI = 2).

   THE REPORT COMMAND
   The report command produces case listings and summary statistics in a format
specified by the user. The user has considerable control over the appearance of the
output. There are dozens of subcommands and specifications for this procedure. It is
usually used for Business reports. No p value, significance etc are generated.

   THE SAMPLE COMMAND
   This transformation temporarily draws a random sample of cases for use in the next
procedure. This may help us when we have a really huge data file (10000s of cases).

    Examples:
    Sample .25.
    This would build a random sample of approximately 25 % of cases from the active
file.
    Sample 50 From 2600
    This would build a random sample of 50 cases from the first 2600 cases in the active
file. If there are fewer than 2600 cases in the active file, a sample of 50/2600 % will be


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built.

   THE SAVE COMMAND
   See the “Get” command

    THE SORT CASES COMMAND
    This command records the sequence of cases in the active file based on the values
of one or more variables. This command is again used for printing out business reports.
Its syntax is as follows:

   Sort Cases By variable (A or D) variable (A or D) etc.

   The cases are sorted for each variable listed. The default is ascending order (A). To
sort in descending order specify (D). After the initial sort with the first variable, additional
variables cause successive sorts to be performed within categories as determined by the
preceding sort(s). Up to 10 variables may be used as sort keys. This command uses a
large amount of disk space for scratch files.

    THE SUBTITLE COMMAND
    This command is now rarely used. It inserts a left-justified subtitle on the second
line of each page of output. The default is a blank line. The subtitle can be up to 64
characters long. If the subtitle is enclosed in quotes or apostrophes, it will be printed
exactly. If they are omitted, it will be printed in upper-case. The syntax is:
    Subtitle any string 64 or fewer characters

   THE TITLE COMMAND
   This prints a centered title on the first line of each page. The date and page number
are also printed.

    THE TRANSLATE COMMAND
    This command either creates an active file from or translates the active file e.g. Excel
file to a file from a spreadsheet program.

   The Begin Data and End Data commands
   (Under data definition)

   These commands are used when we do not wish to use a separate data file. Normally
this is used only when we have a small amount of data. This allows us to include our
data in our command file. This used to be useful when punch cards were used to feed
commands.
   Example:
   BEGIN DATA.
   1     3.4    158
   2     2.9    166
   3     3.0    178
   END DATA

   THE SET COMMAND
   (Under information and settings)
   This command changes how SPSS runs. When SPSS is started the defaults of the
Set command are in force. Subcommands include:



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     NULLINE        controls whether a blank line functions as a command terminator.
                    Default is YES.
     DIRECTORY       sets the folder from which and to which files are read or written.
                    Default is the SPSS folder. NOTE: You can also set the default
                    directory (folder) from the File pull down menu.
     UNDEFINED      controls whether a warning is displayed for each occurrence of
                    non-numeric data where numeric data is expected. Default is
                    YES.
     BLANKS         controls interpretation of blanks in the data file. Allows the
                    conversion of blanks to a number. Default is to assign blanks as
                    System Missing.
     FORMAT         controls format of output. Default is F8.2
     LENGTH         sets the numbers of lines per page of output. Default is 60. NONE
                    suppresses page ejects issued by SPSS procedures.
     WIDTH          sets page width for output. Default is 80 characters.
     PRINTBACK       controls display of SPSS commands in output files. Default is
                    YES.
     HEADER         controls display of the generic SPSS header at the top of each
                    ‘page’ of output. Default is YES.
     CASE           allows conversion of variable names and value labels to upper
                    case on output. Default is UPLOW i.e. variable names and value
                    labels are displayed in upper or lower case as entered.
     COMPRESSION controls the use of data compression for work files during the
                    SPSS session. Compression saves disk space but slows operation.
                    For most modern machines the slowing is unnoticeable. Default
                    is YES.
     SEED           sets the ‘seed’ for the random number generator. Default is
                    2000000.
     MXLOOPS        sets the maximum number of iterations of the LOOPS command
                    for each case. Default is 40.
     BOX             sets the characters used in CROSSTABS and other procedures
                    which draw boxes. Defaults are the screen graphics characters
                    that may print incorrectly on some printers.
     BLOCK          specifies the character to be used in icicle plots. Default is a slid
                    block. ]
     HISTOGRAM      specifies the character to be used in icicle plots. Default is a solid
                    block. ]
     TB1            sets the characters used in TABLES commands to draw boxes.
                    Defaults are screen graphics characters which may print
                    incorrectly on some printers.
     CCA, CCB, CCC,
     CCD, CCE       allows specification of up to 5 different custom formats for
                    displaying currency.
     CP1, LP1       these apply to the SPSS Categories product.

 THE SHOW COMMAND
 This command displays a table of the current specifications on the Set command

 THE WEIGHT COMMAND
 This command is used to weight cases according to sampling weights which have



4                                       CHILLIBREEZE PUBLICATIONS | http://www.chillibreeze.com
                                   SPSS Tutorial for Beginners
                                         SPSS syntax windows




been provided for each case. This is usually used in research designs having complex
sampling plans or in situations when one or more groups have been over- or under-
sampled.

   THE WRITE COMMAND
   This command is used to write cases from the active file to an ASCII file on the
disk.


   We believe in learning by doing. SPSS comes with a great Help section.
We compiled this tutorial with a lot of quizzes and exercise problems so that
we could help you learn and understand SPSS better. Test yourself each
time you learn an SPSS command and soon you will master all the essential
commands.
   Here we come to the end of our tutorial. Hope you gained as much from
it as we hoped you would. Our 100 page+ association with you has been
nice and we bid farewell to you with a heavy heart and wish you luck in your
ventures using SPSS.




                                                                                5
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