# INTRODUCTION TO BIOSTATISTICS by pengxuezhuyes

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```									INTRODUCTION TO
BIOSTATISTICS

Dr. Zafar Mahmood

zafarjan90@yahoo.com
0346-9079308
This session covers:
§ Background and need to know
Biostatistics
§ Origin and development of Biostatistics
§ Definition of Statistics and Biostatistics
§ Types of data
§ Graphical representation of a data
§ Frequency distribution of a data
§ “Statistics is the science which deals
with collection, classification and
tabulation of numerical facts as the
basis for explanation, description
and comparison of phenomenon”.

------ Lovitt
“BIOSTATISICS”
§ (1) Statistics arising out of biological
sciences, particularly from the fields of
Medicine and public health.
§ (2) The methods used in dealing with
statistics in the fields of medicine, biology
and public health for planning,
conducting and analyzing data which
arise in investigations of these branches.
Main Branches of
Biostatistics
§ Descriptive Biostatistics:
§ Methods of producing quantitative
summaries of information in biological
sciences
§ Tabulation and graphical presentations
§ Measures of central tendency
§ Measures of dispersion
Branches of Biostatistics
……
§ Inferential Biostatistics:
§ Methods of making generalizations
about a larger group based on
of that group in biological sciences
§ Estimation
§ Testing of hypothesis
Populations and Samples

§ Before we can determine what
statistical tools and technique to use,
we need to know if our information
represents a population or a sample

§ A sample is a subset which should be
representative of a population
Samples

§ A sample should be representative if
selected randomly (i.e., each data
point should have the same chance
for selection as every other point)

§ In some cases, the sample may be
stratified but then randomized within
the strata
Example

We want a sample that will reflect a
population’s gender and age:
1. Stratify the data by gender

2. Within each strata, further stratify by age

3. Select randomly within each gender/age
strata so that the number selected will be
proportional to that of the population
Population
§ The totality of all the observation whether
finite or infinite in any field of interest is
called population
§ Example
§ Total number of patients in HMC
Parameter and Statistic

§ Parameter: Summary value or
characteristic of population or universe

§ Statistic: Summary value or characteristic
of sample used for making inferences
Origin and development of
statistics in Medical Research
§ In 1929 a huge paper on application of
statistics was published in Physiology
Journal by Dunn.
§ In 1937, 15 articles on statistical methods
by Austin Bradford Hill, were published in
book form.
§ In 1948, a RCT of Streptomycin for
pulmonary tb., was published in which
Bradford Hill has a key influence.
§ Then the growth of Statistics in Medicine
from 1952 was a 8-fold increase by 1982.
C.R. Rao
Douglas Altman   Ronald Fisher   Karl Pearson

Gauss -
Basis of
Biostatistics
Sources of Medical
Uncertainties
1. Intrinsic due to biological,
environmental and sampling factors
2. Natural variation among methods,
observers, instruments etc.
3. Errors in measurement or assessment
or errors in knowledge
4. Incomplete knowledge
Intrinsic variation as a
source of medical
uncertainties
§ Biological due to age, gender, heredity, parity, height,
weight, etc. Also due to variation in anatomical,
physiological and biochemical parameters
§ Environmental due to nutrition, smoking, pollution,
facilities of water and sanitation, road traffic, legislation,
stress and strains etc.,
§ Sampling fluctuations because the entire world cannot
be studied and at least future cases can never be
included
§ Chance variation due to unknown or complex to
comprehend factors
Natural variation despite
best care as a source of
uncertainties
§   In assessment of any medical parameter
§   Due to partial compliance by the patients
§   Due to incomplete information in
conditions such as the patient in coma
Medical Errors that cause
Uncertainties
§ Carelessness of the providers such as physicians,
surgeons, nursing staff, radiographers and pharmacists.
§ Errors in methods such as in using incorrect quantity or
quality of chemicals and reagents, misinterpretation of
ECG, using inappropriate diagnostic tools,
misrecording of information etc.
§ Instrument error due to use of non-standardized or
faulty instrument and improper use of a right instrument.
§ Not collecting full information
§ Inconsistent response by the patients or other subjects
under evaluation
Incomplete knowledge as a
source of Uncertainties
§ Diagnostic, therapeutic and prognostic
uncertainties due to lack of knowledge
§ Predictive uncertainties such as in
survival duration of a patient of cancer
§ Other uncertainties such as how to
measure positive health
Biostatistics is the
science that helps in
managing medical
uncertainties
biostatistics:
§ Medicine is becoming increasingly
quantitative.
§ The planning, conduct and interpretation
of much of medical research are
becoming increasingly reliant on the
statistical methodology.
§ Statistics pass through the medical
literature.
CLINICAL MEDICINE

§ Documentation of medical history of
diseases.
§ Planning and conduct of clinical studies.
§ Evaluating the merits of different
procedures.
§ In providing methods for definition of
“normal” and “abnormal”.
Role of Biostatistics in
patient care
§ In increasing awareness regarding diagnostic,
therapeutic and prognostic uncertainties and
providing rules of probability to delineate those
uncertainties
§ In providing methods to integrate chances with value
judgments that could be most beneficial to patient
§ In providing methods such as sensitivity-specificity
and predictivities that help choose valid tests for
patient assessment
§ In providing tools such as scoring system and expert
system that can help reduce epistemic uncertainties
PREVENTIVE MEDICINE

§ To provide the magnitude of any health
problem in the community.
§ To find out the basic factors underlying
the ill-health.
§ To evaluate the health programs which
was introduced in the community
(success/failure).
§ To introduce and promote health
legislation.
Role of Biostatics in Health
Planning and Evaluation
§ In carrying out a valid and reliable health
situation analysis, including in proper
summarization and interpretation of data.

§ In proper evaluation of the achievements
and failures of a health programme
Role of Biostatistics in
Medical Research
§ In developing a research design that can
minimize the impact of uncertainties
§ In assessing reliability and validity of
tools and instruments to collect the
infromation
§ In proper analysis of data
Example: Evaluation of Penicillin (treatment
A) vs Penicillin & Chloramphenicol
(treatment B) for treating bacterial
pneumonia in children< 2 yrs.
§ What is the sample size needed to demonstrate the
significance of one group against other ?
§ Is treatment A is better than treatment B or vice versa ?
§ If so, how much better ?
§ What is the normal variation in clinical measurement ? (mild,
moderate & severe) ?
§ How reliable and valid is the measurement ? (clinical &
§ What is the magnitude and effect of laboratory and technical
error ?
§ How does one interpret abnormal values ?
WHAT DOES BIO-
STAISTICS COVER ?
Planning
Design
Execution (Data collection)
Data Processing
Data analysis
Presentation
Interpretation
Publication
BASIC CONCEPTS
Data : Set of values of one or more variables recorded
on one or more observational units

Sources of data    1. Routinely kept records
2. Surveys (census)
3. Experiments
4. External source
Categories of data
1. Primary data: observation,  questionnaire, record form,
interviews, survey,
2. Secondary data: census, medical record, registry  etc
TYPES OF DATA or VARIABLE

§ QUALITATIVE DATA
§ DISCRETE QUANTITATIVE
§ CONTINOUS QUANTITATIVE
Qualitative Data or Variable

§ a variable or characteristic which cannot
be measured in quantitative form but can
only be identified by name or categories,
for instance place of birth, ethnic group,
type of drug, stages of breast cancer (I,
II, III, or IV), degree of pain (minimal,
§ moderate, severe or unbearable).
Quantitative Data or Variable
§ A quantitative variable is one that can be
measured and expressed numerically and they
can be of two types (discrete or continuous).
§ The values of a discrete variable are usually
whole numbers, such as the number of
episodes of diarrhea in the first five years of life.
§ A continuous variable is a measurement on a
continuous scale. Examples include weight,
height, blood pressure, age, etc.
TYPES OF DATA or VARIABLE …

§ Although the types of variables could be
(qualitative) and quantitative , it has been
a common practice to see four basic
types of data (scales of measurement).
§ Nominal, Ordinal, Interval & Ratio data
Qualitative Nominal data

§ Data that represent categories or names. There is no
implied order to the categories of nominal data. In
these types of data, individuals are simply placed in the
proper category or group, and the number in each
category is counted. Each item must fit into exactly one
§ category.
§ The simplest data consist of unordered, dichotomous,
or "either - or“ types of observations, i.e., either the
patient lives or the patient dies, either he has some
particular attribute or he does not.
Nominal scale data Example

§ survival status of propanolol - treated and
§ control patients with myocardial infarction
Status 28 days       Propanolol      Control
after hospital   -treated patient   Patients

Alive              38             29

Total              45             46

Survival rate         84%            63%
Some other examples of nominal data

Example: Sex ( M, F)
Exam result (P, F)
Blood Group (A,B, O or AB)
Color of Eyes (blue, green,
brown, black)
Anemia's ( Microcytic, Macrocytic
Religion - Christianity, Islam, Hinduism, etc
Qualitative Ordinal data

§ The ordinal scale data have order among
the response classifications (categories).
The spaces or intervals between the
categories are not necessarily equal.
§ It is similar to nominal b/c the
measurement involve categories,
however, the categories are ordered by
rank.
Ordinal Scale data Examples

§ Pain level (Mild, Moderate, Severe)

§   Tumors (Stage 0, ……, IV)
§   Arthritis (Class 1, ……, 4 )
§   Military Rank (Lt., Capt., Maj., Col.,
General)
Some other examples of ordinal data

Response to treatment
(poor, fair, good)
Severity of disease
(mild, moderate, severe)
Income status
(low, middle, high)
QUANTITATIVE (DISCRETE)

Example: The no. of family members
The no. of heart beats
The no. of admissions in a day

QUANTITATIVE (CONTINOUS)

Example: Height, Weight, Age, BP,
Serum Cholesterol and BMI
Discrete data -- Gaps between possible values

Number of Children

Continuous data -- Theoretically,
no gaps between possible values

Hb
CONTINUOUS DATA

QUALITATIVE DATA

wt. (in Kg.) : under wt, normal & over wt.
Ht. (in cm.): short, medium & tall
Table 1 Distribution of blunt injured patients
according to hospital length of stay
Scale of measurement
Qualitative variable:
A categorical variable

Nominal (classificatory) scale
- gender, marital status, race

Ordinal (ranking) scale
- severity scale, good/better/best
Quantitative Variable:
Quantitative variable:
A numerical variable: discrete; continuous
Numerical discrete data occur when the observations are
integers that correspond with a count of some sort. Some
common examples are: the number of bacteria colonies on
a plate, the number of cells within a prescribed area upon
microscopic examination, the number of heart beats within
a specified time interval, a mother’s history of number of
births ( parity) and pregnancies (gravidity), the number of
episodes of illness a patient experiences during some time
period, etc.
Quantitative Variable…..
Numerical continuous

The scale with the greatest degree of quantification is a
numerical continuous scale. Each observation theoretically
falls somewhere along a continuum (range). One is not
restricted, in principle, to particular values such as the
integers of the discrete scale. The restricting factor is the
degree of accuracy of the measuring instrument most
clinical measurements, such as blood pressure, serum
cholesterol level, height, weight, age etc. are on a numerical
continuous scale.
Quantitative Interval Scale of
measurement

Quantitative variable:
A numerical variable: discrete; continuous

Interval scale :
Data is placed in meaningful intervals and order. The
unit of measurement are arbitrary. There  is no true zero

-     Temperature (37º C -- 36º C;  38º C-- 37º C are equal)
and   No implication of ratio (30º C is not twice  as hot
as 15º C)
Quantitative Ratio Scale of
measurement

Data is presented in frequency distribution
in logical order. A meaningful ratio exists.
There is a true zero

- Age, weight, height, pulse rate
- pulse rate of 120 is twice as fast as 60
- person with weight of 80kg is twice as heavy
as the one with weight of 40 kg.
Scales of Measure

§   Nominal – qualitative classification of
equal value: gender, race, color, city
§   Ordinal - qualitative classification
which can be rank ordered:
socioeconomic status of families
§   Interval - Numerical or quantitative
data: can be rank ordered and sizes
compared : temperature
§   Ratio - Quantitative interval data along
with ratio: time, age.
CLINIMETRICS
A science called clinimetrics in which
qualities are converted to meaningful
quantities by using the scoring system.

Examples: (1) Dummy score based on
appearance, pulse, grimace, activity and
respiration is used for neonatal prognosis.
(2) Smoking Index: no. of cigarettes, duration,
filter or not, whether pipe, cigar etc.,
(3) APACHE( Acute Physiology and Chronic
Health Evaluation) score: to quantify the
severity of condition of a patient
INVESTIGATION

Data Colllection

Inferential Statistiscs
Descriptive Statistics
Data Presentation
Estimation       Hypothesis   Univariate analysis
Measures of Location
Tabulation                                                        Testing
Measures of Dispersion
Diagrams                                                  Ponit estimate       Multivariate analysis
Measures of Skewness &
Graphs                                                  Inteval estimate
Kurtosis
Methods Of Data Collection, Organization
And Presentation
Learning Objectives

•   Identify the different methods of data organization
and presentation

2. Understand the criterion for the selection of a method to organize
and present data

3. Identify the different methods of data collection and criterion that
we use to select a method of data collection

4. Define a questionnaire, identify the different parts of a
questionnaire and indicate the procedures to prepare a
questionnaire
Data Collection Methods
Various data collection techniques can be used such
as:

•   Observation
•   Postal or mail method and telephone interviews
•   Using available information
•   Focus group discussions (FGD)

• Other data collection techniques – Rapid appraisal
techniques, 3L technique, Nominal group techniques, Delphi
techniques, life histories, case studies, etc.
Observation
Observation is a technique that involves systematically selecting,
watching and recoding behaviors of people or other phenomena
and aspects of the setting in which they occur, for the purpose
of getting (gaining) specified information. It includes all methods
from simple visual observations to the use of high level
machines and measurements, sophisticated equipment or
facilities, such as radiographic, biochemical, X-ray machines,
microscope, clinical examinations, and microbiological
examinations
questionnaire
probably the most commonly used research data
collection techniques. Therefore, designing good
“questioning tools” forms an important and time
consuming phase in the development of most research
proposals.
Once the decision has been made to use these
techniques, the following questions should be
considered before designing our tools:
questionnaire…..
1.   What exactly do we want to know, according to the
objectives and variables we identified earlier? Is
questioning the right technique to obtain all answers, or
do we need additional techniques, such as observations
or analysis of records?

2.   Of whom will we ask questions and what techniques will
we use? Do we understand the topic sufficiently to
design a questionnaire, or do we need some loosely
structured interviews with key informants or a focus
group discussion first to orient ourselves?
questionnaire…..
3. Are our informants mainly literate or illiterate? If
illiterate, the use of self-administered questionnaires is
not an option.

4. How large is the sample that will be interviewed?
Studies with many respondents often use shorter,
highly structured questionnaires, whereas smaller
studies allow more flexibility and may use
questionnaires with a number of open-ended
questions.
Face-to-face and telephone
interviews
Face-to-face and telephone interviews have many
A good interviewer can stimulate and maintain the
respondent’s interest, and can create a rapport
(understanding, concord) and atmosphere conducive to the
If anxiety aroused, the interviewer can allay it. If a question
is not understood an interviewer can repeat it and if necessary
(and in accordance with guidelines decided in advance)
provide an explanation or alternative wording.

In face-to-face interviews, observations can be made as well.
Mailed Questionnaire Method

Under this method, the investigator prepares a questionnaire
containing a number of questions pertaining the field of inquiry.
The questionnaires are sent by post to the informants together
with a polite covering letter explaining the detail, the aims and
objectives of collecting the information, and requesting the
respondents to cooperate by furnishing the correct replies and
returning the questionnaire duly filled in. In order to ensure
quick response, the return postage expenses are usually borne
by the investigator.
Use of documentary sources

Clinical and other personal records, death certificates,
published mortality statistics, census publications, etc. are
documentary sources. Examples include:

1. Official publications of Central Statistical Authority
2. Publication of Ministry of Health and Other Ministries
3. News Papers and Journals.
4. International Publications like Publications by WHO, World
Bank, UNICEF
5. Records of hospitals or any Health Institutions.
Problems in gathering data
Common problems might include:

• Language barriers
• Expense
• Inadequately trained and experienced staff
• Invasion of privacy
• Suspicion
•Bias (spatial, project, person, season, diplomatic,
professional)
•Cultural norms (e.g. which may preclude men interviewing
women)
Choosing a Method of Data Collection
Decision-makers (consultants ) need information that is
relevant, timely, accurate and usable. The cost of
obtaining, processing and analyzing these data is high.

The challenge is to find ways, which lead to information
that is cost-effective, relevant, timely and important for
immediate use.

Some methods pay attention to timeliness and reduction
in cost. Others pay attention to accuracy and the
strength of the method in using scientific approaches.
Categories of Data
Primary Data: are those data, which are collected by the
investigator himself for the purpose of a specific inquiry or
study. Such data are original in character and are mostly
generated by surveys conducted by individuals or research
institutions.
The first hand information obtained by the investigator is more
reliable and accurate since the investigator can extract the correct
information by removing doubts, if any, in the minds of the
respondents regarding certain questions.
Categories of Data….
Secondary Data: When an investigator uses data,
which have already been collected by others, such data are
called "Secondary Data". Such data are primary data for the
agency that collected them, and become secondary for
someone else who uses these data for his own purposes.

The secondary data can be obtained from journals, reports,
government publications, publications of professionals and
research organizations.
Types of Questions
Before examining the steps in designing a
questionnaire, we need to review the types of
questions used in questionnaires. Depending on
how questions are asked and recorded we can
distinguish two major possibilities –
1. Open –ended questions,
2. Closed questions.
Open-ended questions
Open-ended questions permit free responses that should
be recorded in the respondent’s own words. The
respondent is not given any possible answers to choose
from.
For example
“Can you describe exactly what the traditional birth
attendant did when your labor started?”

“What do you think are the reasons for a high drop-out
rate of village health committee members?”

“What would you do if you noticed that your daughter
(school girl) had a problem in education?”
Closed Questions
Closed questions offer a list of possible options or answers
from which the respondents must choose. When designing
closed questions one should try to:

• Offer a list of options that are exhaustive and mutually
Exclusive
• Keep the number of options as few as possible.

For example
1. Single
2. Married/living together
3. Separated/divorced/widowed
Closed Questions….
Closed questions may also be used if one is only interested in
certain aspects of an issue and does not want to waste the
time of the respondent and interviewer by obtaining more
information than one needs.
For example, a researcher who is only interested in
the protein content of a family diet may ask:

“Did you eat any of the following foods yesterday? (Circle
yes or no for each set of items)

•   Peas, bean, lentils        Yes    No
•   Fish or meat               Yes    No
•   Eggs                       Yes    No
•   Milk or Cheese             Yes    No
Designing the Questionnaire
Steps involved in designing the questionnaire
1)      Content:
·   Take your Objectives and Variable
·   Decide measure of quantitative variables or levels of qualitative variables to
2)      Formulating Questions
·   Questions need to be clearly worded so as not to confuse the respondent or
arouse extraneous attitudes.
·   Questions should provide a clear understanding of the information sought
·   Be precise; avoid ambiguity and wording that might be perceived to elicit a
specific purpose.
·   Questions may be open-ended, multiple choice, completion or variations of
these.
·       Studiously avoid overly complex questions
3)           Sequencing Questions
·            Sequence of questions should be informant friendly beginning with a natural
conversation questions (e.g., age, marital status, education etc)
·            Restrict yourself to an essential minimum questions while asking personal
information ·
Start then with interesting but non-controversial questions
·            At the end pose more sensitive questions
4)           Formatting the Questionnaire
·            Provide a separate page explaining the purpose of the study, requesting the
informant consent to be interviewed and assuring confidentiality of the data
recorded.
·            Each questionnaire has must have heading and space locating SNO., data and
location of the interviewer.
·            Sufficient space is provided for answer to open-ended questions.
·            Proper and attractive layout
5)       Translation
·   The interview will be conducted in one or more local languages and should be
translated to the original language for standardizing the questions.
Key Principle for Constructing a
Questionnaire

1)   It should be easy for the respondent to read,
2)   Motivate the respondents to answer
3)   Be designed for efficient data processing
4)   Have a well designed professional appearance
5)   Design to minimize missing data
Frequency Distributions

§ data distribution – pattern of
variability.
§ the center of a distribution
§ the ranges
§ the shapes
§ simple frequency distributions
§ grouped frequency distributions
§ midpoint
Tabulate the hemoglobin values of 30 adult
male patients listed below

Patien Hb       Patien Hb       Patien Hb
t No   (g/dl)   t No   (g/dl)   t No   (g/dl)
1      12.0     11     11.2     21     14.9
2      11.9     12     13.6     22     12.2
3      11.5     13     10.8     23     12.2
4      14.2     14     12.3     24     11.4
5      12.3     15     12.3     25     10.7
6      13.0     16     15.7     26     12.5
7      10.5     17     12.6     27     11.8
8      12.8     18     9.1      28     15.1
9      13.2     19     12.9     29     13.4
10     11.2     20     14.6     30     13.1
Steps for making a
table
Step1   Find Minimum (9.1) & Maximum (15.7)

Step2   Calculate difference 15.7 – 9.1 = 6.6

Step3    Decide the number and width of
the classes (7 c.l) 9.0 -9.9, 10.0-10.9,----

Step4   Prepare dummy table –
Hb (g/dl), Tally mark, No. patients
DUMMY TABLE                          Tall Marks TABLE

Hb (g/dl)      Tall marks   No.        Hb (g/dl)     Tall marks    No.
patients                               patients

9.0 – 9.9                              9.0 – 9.9    l             1
10.0 – 10.9                            10.0 – 10.9   lll           3
11.0 – 11.9                            11.0 – 11.9   lll           6
12.0 – 12.9                            12.0 – 12.9
13.0 – 13.9
llll llll     10
13.0 – 13.9
14.0 – 14.9                            14.0 – 14.9   llll          5
15.0 – 15.9                            15.0 – 15.9                 3
lll           2
ll
Total
Total         -             30
Table Frequency distribution of 30 adult male
patients by Hb
Hb (g/dl)       No. of
patients
9.0 – 9.9          1
10.0 – 10.9         3
11.0 – 11.9         6
12.0 – 12.9        10
13.0 – 13.9         5
14.0 – 14.9         3
15.0 – 15.9         2
Total           30
Table Frequency distribution of adult patients by
Hb and gender:
Hb                Gender        Total
(g/dl)
Male        Female

<9.0         0             2      2
9.0 – 9.9      1             3      4
10.0 – 10.9     3             5      8
11.0 – 11.9     6             8     14
12.0 – 12.9    10             6     16
13.0 – 13.9     5             4      9
14.0 – 14.9     3             2      5
15.0 – 15.9     2             0      2

Total        30             30    60
Elements of a Table
Ideal table should have      Number
Title
Foot-notes
Number –      Table number for identification in a report

Title,place      -        Describe the body of the table, variables,
Time period             (What, how classified, where and when)

Column  -      Variable name, No. , Percentages (%), etc.,

Foot-note(s)   - to describe some column/row headings,
special cells, source, etc.,
Table II. Distribution of 120 Corporation divisions according to
annual death rate based on registered deaths in 1975 and 1976

Figures in parentheses indicate percentages
DIAGRAMS/GRAPHS

Discrete data
--- Bar charts (one or two groups)

Continuous data
--- Histogram
--- Frequency polygon (curve)
--- Stem-and –leaf plot
--- Box-and-whisker plot
Example data

68   63   42   27   30   36   28   32
79   27   22   28   24   25   44   65
43   25   74   51   36   42   28   31
28   25   45   12   57   51   12   32
49   38   42   27   31   50   38   21
16   24   64   47   23   22   43   27
49   28   23   19   11   52   46   31
30   43   49   12
Histogram

Figure 1 Histogram of ages of 60 subjects
Polygon
Example data

68   63   42   27   30   36   28   32
79   27   22   28   24   25   44   65
43   25   74   51   36   42   28   31
28   25   45   12   57   51   12   32
49   38   42   27   31   50   38   21
16   24   64   47   23   22   43   27
49   28   23   19   11   52   46   31
30   43   49   12
Stem and leaf plot
Stem-and-leaf of Age     N = 60
Leaf Unit = 1.0

6    1 122269
19     2 1223344555777788888
(11) 3 00111226688
13    4 2223334567999
5    5 01127
4    6 3458
2    7 49
Box plot
Descriptive statistics report:
Boxplot
- minimum score
- maximum score
- lower quartile
- upper quartile
- median
- mean

- the skew of the distribution:
positive skew: mean > median & high-score whisker is longer
negative skew: mean < median & low-score whisker is longer
Pie   Chart
•Circular diagram – total -100%

•Divided into segments each
representing a category

•The amount for each category is
proportional to slice of the pie

The prevalence of different degree of
Hypertension
in the population
Bar Graphs
Heights of the bar indicates
frequency

Frequency in the Y axis
and categories of variable
in the X axis

The bars should be of equal
width and no touching the
other bars
The distribution  of risk factor among cases with
Cardio vascular Diseases
HIV cases enrolment in
USA by gender
Bar chart
HIV cases Enrollment
in USA by gender
Stocked bar chart
Graphic Presentation of
Data
the frequency polygon
(quantitative data)

the histogram
(quantitative data)

the bar graph
(qualitative data)
General rules for designing
graphs
§ A graph should have a self-explanatory
legend
§ A graph should help reader to understand
data
§ Axis labeled, units of measurement
indicated
// break)
§ Avoid graphs with three-dimensional
visualize less easily
Exercise
§ Identify the type of data (nominal, ordinal, interval and
ratio) represented by each of the following. Confirm

§   1. Blood group
§   2. Temperature (Celsius)
§   3. Ethnic group
§   4. Job satisfaction index (1-5)
§   5. Number of heart attacks
Exercise ....
§ 6. Calendar year
§ 7. Serum uric acid (mg/100ml)
§ 8. Number of accidents in 3 - year period
§ 9. Number of cases of each reportable disease
reported by a health worker
§ 10. The average weight gain of 6 1-year old dogs (with
a special diet supplement) was 950grams last month.
Any Questions
thanks

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