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Statistic Introduction

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					What is Statistics
 WE RESEARCHERS
 WE RESEARCHERS
USE STATISTICS THE
USE STATISTICS THE
 WAY A DRUNKARD
 WAY A DRUNKARD
USES A LAMP POST,
 USES A LAMP POST,
MORE FOR SUPPORT
MORE FOR SUPPORT
       THAN
       THAN
  ILLUMINATION.
  ILLUMINATION.
          Statistics
The branch of mathematics
that deals with the
        collection,
        collection,
       organization,
       organization,
       analysis,
       analysis, and
      interpretation
     of numerical data.
         Statistics
        is especially
     useful in drawing
   general conclusions
    about a set of data
from a sample of the data.
            DATA
          -----DATUM.
SINGULAR -----DATUM.
       --------DATA.
PLURAL --------DATA.
WE MAY DEFINE DATA AS
NUMBERS AND THERE IS
TWO KINDS OF NUMBERS
THAT WE USE IN
STATISTICS THE RESULTS OF
: COUNTING AND
MEASUREMENTS.
MEASUREMENTS.
       variable
ANY ASPECT OF AN
INDIVIDUAL THAT IS
MEASURED, LIKE
BLOOD PRESURE,
AGE,
SEX etc.
  Variables divide into
     different types

QUALITATIVE
(CATEGORICAL)

QUANTITATIVE
(NUMERICAL)
              Read
       not to contradict
          and confute,
         not to believe
    and take for granted,
not to find talk and discourse,
 but to weigh and consider.

      Sir Francis Bacon
WHAT MAKE STATISTICS UNIQUE?



     ITS ABILITY TO
        QUANTIFY
      UNCERTAINTY,
      UNCERTAINTY,
       TO MAKE IT
        PRECISE.
        PRECISE.
  Good thinking!
I’m 95 % confident
that this afternoon
    I will score
  has probability
      between
  73 % and 77 %
      of being
    best player
A more positive example in statistics is
the SALK POLIO VACCINE in 1954
vaccine trials were performed on some
400,000 children, with strict controls to
eliminate biased results.


 Good statistical analysis of the
  results firmly established the
     vaccine’s effectiveness,
             and to day
    POLIO is almost unknown.
To accomplish their feats of mathematical
     LEGERDEMAIN (STATISTICIANS)
RELY ON THREE RELATED DISCIPLINE:


Data analysis
 The gathering, display, and summary
                of data
Probability
 The law of chance
Statistical Inference
 The science of drawing statistical
 conclusions from specific data, using a
 knowledge of probability.
        Objectives of this course
At the end of the course the students
           will be able to

1.   organize data
2.   summarize data
3.   reach decision about
     a large body of data
     by examining
     only small part of the data.
Objective number 1 and 2
      we will discuss in


DESCRIPTIVE STATISTICS.

Objective number 3
      we will discuss


INFERENCIAL STATISTICS
What is biostatistics
          Biostatistics is
        in effect, two words
       and two fields of study
             combined.

The   bio part involves biology,
      the study of living things.
  The statistics part
       involves
        ollection,
      Collection,
Organization, Analysis,
Organization, nalysis,
          and
    interpretation
  of numerical data
     Biostatistics
     is the application
         of statistics
to a wide range of topics in
  biology. It has particular
  biology.
  applications to medicine
             and
          agriculture.
       to agriculture.
Statistics calculations
   are an important
 part of data analysis,
but   interpreting data
          also
        requires
a great deal of judgment
            Understanding
     the statistical calculations
         is only a small part
                  of
1.   evaluating clinical
2.   pharmaceutical
3.   biological research.
    Why
 is it hard
  to learn
statistics?
     The terminology is deceptive
You have to understand :
1.   Significant
2.   Error
3.   Hypothesis
4.   Null hypothesis
5.   Confidence interval
Level of significant
p value
Population
Sample
Paired and unpaired
samples
    Remember
      The phrase
statistically significant
            is
        seductive
           and
            is
often   misinterpreted.
   Statistics
        is
at the interface
        of
 mathematics
      and
    science
         However
       You can learn
           to use
       statistical test
        and interpret
         the results
            even
if you don’t fully understand
       how they work.
Inductive reasoning
    often described
           as
"going from the specific
   to the general."
          AND
     It is based on
            observing
        specific instances
       of a certain quality
     in individual members
          of a group of
1. people
2. animals or
3. events
         noting
 the individual members
         in which
     a certain quality
          occurs
belong to a certain group
   generalizing
  to the conclusion
         that
   other members
    of that group
have the same quality.
        For example
if you were to go to a cat show,
you would see many breeds
of cats with tails.
After walking up and down,
you might begin to notice
a pattern,
and your reasoning
might go something like this:
–Siamese cats have tails.
–Persian cats have tails.
–Himalayan cats have tails.
–Russian Blues have tails.
–American Tabbies have tails.
After a while, you would probably
    come to the conclusion -


      All cats
     have tails
The problem with this
    conclusion is
  that it isn't true.

 The manx
is one breed of cat
 that has no tail.
    So the conclusion

             of
  an inductive argument
can be shown to be wrong
   if only one instance
        does not fit
   the general pattern.
The Manx is a breed of cats with a naturally
                               spine.
     occurring mutation of the spine.
          For this reason
           the result of
      an inductive argument
       is never considered
       to be TRUE or FALSE
              instead
we refer to the conclusions reached
               through
        inductive reasoning
                 as
      MORE OR LESS RELIABLE.
Before proceeding, think about this
            question:



    What would make the
 conclusion from an inductive
   argument MORE reliable?
    In inductive reasoning,

the more specific instances
       you observe,
     the more reliable
     your conclusion.
           Because
       the conclusion from
     an inductive argument
      cannot be considered

       true or false
the conclusion must be qualified.
         The conclusion
from your observations about cats
  and their tails might be qualified
    in one of the following ways:
–Many cats have tails.
–Some cats have tails.
–Most cats have tails.
            Cats,
    general,
–in general, have tails.
–Cats tend to have tails.
         A conclusion
           that is
        more or less
           reliable
  The more specific instances
            observed
the more reliable the conclusion.
Deductive reasoning
 Inductive Reasoning
 allows you to learn
    something new
  about the world.

 Deductive Reasoning
allows you to apply what
    you have learned.
The classic example of
a deductive argument
All men are mortal.
              man.
Abdullah is a man.
     Therefore
Abdullah is mortal.
            mortal.
   The first premise


("All men are mortal.")

      is the result
            of
  inductive reasoning.
   The second premise
         identifies
    a specific member
of that group (Abdullah).
 While Inductive Reasoning


results in conclusions that are more
or less reliable,
Deductive Reasoning results
in conclusions
                  false:
that are true or false:
   In order for the conclusion
                  of
 a deductive reasoning process
             to be true,
        all of its premises
           must be true.
.
      Most people
      would agree
           that
the first premise given
         is true.
    Most people
 would also agree
       that
the second premise
   given is true
 IF both of the premises are true,
                   then
 the conclusion must also be true
if and only if it follows necessarily
                  from
          the information
       given in the premises.
           Suppose
we return to our observations
         about cats
        and their tails
     and the conclusion
        we arrived at
           by using
    inductive reasoning:
Most cats have     Remember that this
     tails.        conclusion had to be
                         qualified.

 Ra is a cat.    I could show you pictures.



Ra has a tail.           Therefore,
                      this conclusion
                    follow necessarily?
       A trick question:

  When it rains, the streets get wet.
        The streets are wet.
              Therefore,
         it has been raining.
Is the conclusion valid?
Why or why not?
  The conclusion to that trick
    question is NOT valid:

– When it rains, the streets get
  wet.
– The streets are wet.
– Therefore, it has been raining.
The conclusion of a deductive
argument must follow necessarily
from the argument's premises;
however, the first premise in this
argument is a conditional statement.
(It gives a condition under which
something becomes true.) The
statement can be restated like this:
    IF it rains,
      THEN
the streets get wet.
   The problem with the conclusion
        from the above argument
   is that there are other conditions
which may cause the streets to get wet:
snow, sleet or other forms of
precipitation besides rain
fire hydrants being opened
people washing their cars in the streets
flooding
                       IF-
  When a premise using IF-THEN
   (or in our example WHEN)

is given, the second premise must
give the specific condition stated in
the first premise: the IF part of the
statement:
  When it rains, the streets get wet.
        It has been raining.
              Therefore,
        the streets are wet.
Giving the second part of a
   conditional statement
     (the THEN part),
         results in
   an invalid argument.
Another way of looking at this
problem is to think in terms of
      our first argument
      (about Abdullah):
Step in Process     Socrates          Rain Argument
                    Argument


Identify a shared All men are         All rainy days
quality of the set: mortal            cause the streets
                                      to get wet.

Identify a member Abdullah is a man It is raining today.
of the set:


Valid conclusion:   Abdullah is       The streets are
                    mortal.           wet.
All men are mortal.
Abdullah is mortal.
     Therefore,
Abdullah is a man.
•This conclusion does not follow necessarily
             from the premises
                  because
             Abdullah could be
                   a cat,
                  a mule,
                   a dog,
          or any other living thing.

				
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