Biostatistics Data Presentation

©Rohit Bhaskar
BIOSTATISTICS
Presented By
Rohit Bhaskar
Physiotherapy Student
At Uttar Pradesh University
Of Medical Sciences

STATISTICS - is a science of compiling,
classifying, and tabulating numerical data
and expressing the results in a
mathematical and graphical form.
BIOSTATISTICS - is that branch of statistics
concerned with the mathematical facts
and data related to biological events.
©Rohit Bhaskar

• Constant
– Quantities that do not vary e.g. in
biostatistics, mean, standard deviation are
considered constant for a population
• Variable
– Characteristics which takes different
values for different person, place or
thing such as height, weight, blood
pressure
©Rohit Bhaskar

• Parameter
– It is a constant that describes a population e.g. in a college
there are 40% girls. This describes the population, hence it is
a parameter.
• Statistic
– Statistic is a constant that describes the sample e.g. out of 200
students of the same college 45% girls. This 45% will be statistic as
it describes the sample
• Attribute
• A characteristic based on which the population can be
described into categories or class e.g. gender, caste,
religion
©Rohit Bhaskar

WHAT IS STATISTICS ??
• The following essential features of statistics are evident from
various definitions of statistics:
a) principles and methods for the collection of presentation, analysis
and interpretation of numerical data of different kinds.
1. Observational data, qualitative data.
2. Data that has been obtained by a repetitive operation.
3. Data affected to a marked degree of a multiplicity of
causes.
b) The science and art of dealing with variation in such a way as to
obtain reliable results.
©Rohit Bhaskar

c) Controlled objective methods whereby
group trends are abstracted from
observations on many separate
individuals.
d) The science of experimentation which
may be regarded as mathematics applied
to observational data.
©Rohit Bhaskar

WHY STATISTICS ??
• Variabilty in measurement can be handled using statistics. Eg:
investigator makes observations according to his judgement of the
situation.
(Depending upon his skills, knowledge, experience.)
• Epidemiology and Biostatistics are sister sciences or disciplines.
• Epidemiology collects facts relating to group of population in places,
times and situation.
• Biostatistics converts all the facts into figures and at the end
translates them into facts, interpreting the significance of their
results.
©Rohit Bhaskar

USES OF BIOSTATISTICS
1. Totest whether the difference between two populations is real
or by chance occurrence.
2. Tostudy the correlation between attributes in the same
population.
3. Toevaluate the efficacy of vaccines.
4. Tomeasure mortality and morbidity.
5. Toevaluate the achievements of public health programs
6. Tofix priorities in public health programs
7. Tohelp promote health legislation and create
administrative standards for oral health.
©Rohit Bhaskar

©Rohit Bhaskar
DATA COLLECTION
Presented By
Rohit Bhaskar
Of Medical Sciences

COLLECTION OF DATA
• The collective recording of observations
either numerical or otherwise is called data.
• Demographic data comprises details of
population size, disrtibution, geographic
distribution , ethnic group , socio-economic
factors and their trends over time.
• It is obtained from census and other public
service reports.
©Rohit Bhaskar

• Depending upon the nature of the
variable, data is classified into:
1. Qualitative data - attributes or qualities.
a)discrete
b)continuous
2. Quantitative data - through
measurements using calipers.
©Rohit Bhaskar

Sources of statistical data
Data can be collected
EXPERIMENTS
Performed to collect
data for
investigations and
research by one or
more workers.
SURVEYS
Carried out for
Epidemiological studies in
the field by trained teams to
find incidence or prevalence
of health or disease in a
community.
RECORDS
Records are
maintained as a
routine in registers
and books over a long
period of time provide
readymade data.
PRIMARY SECONDARY
Data obtained by the
investigator himself.
Data has already
recorded. Eg: hospital
records©Rohit Bhaskar

Primary data can be obtained using any
one of the following methods:
Direct personal
interviews
Oral health
examination
Questionnaire
method
•Face-to-face contact
with the person.
•Subjective phenomena.
•Accurate and any
ambiguity can be clarified.
•Cannot be used
in extensive
studies.
• When information
is needed on
health status.
• Cannot be used in
extensive studies.
• Includes treatment
• List of Questions
pertaining to the
survey“questionnaire”
is prepared.
• Various informants
are requested to
supply the
information.
©Rohit Bhaskar

©Rohit Bhaskar
SAMPLING & SAMPLING DESIGN
Presented By
Rohit Bhaskar
Of Medical Sciences

Sampling and sample design
• Population:- group of all individuals who are the
focus of the investigation is known as population.
• Cencus enumeration:- if the information is
obtained from each and every individual in the
population.
• Sample: means the group of individuals who
actually available for investigation.
• Sampling units: the individual entities that form
the focus of the study.
• Sampling frame/list:list of sampling units
©Rohit Bhaskar

Sample selection
• Purposive selection
• Representing the population
as a whole.
• Great temptation to
deliberately or purposively
select the individual who
seen to represent the
population under study.
• Random selection
• Sample of units is
selected in such a way
that all the characteristics
of the population is
reflected in the sample.
• Random indicates the
chance of the
population unit being
selected in the sampe.
©Rohit Bhaskar

Sampling Design
BASED UPON TYPE AND NATURE OF THE POPULATION
AND THE OBJECTIVES OF THE INVESTIGATION.
1. Sample random sampling
2. Systematic random sampling
3. Stratified random sampling
4. Clusture sampling
5. Multiphase sampling pathfinder survey
©Rohit Bhaskar

Sample random sampling
• Each and every unit in the population has an
equal chance of being included in the sample.
• Selection of unit is by chance only.
Two methods
Lottery
methods
•Population units
are numbered on
separate slip.
•Shuffled and
blindfold
selection.
Table of random
numbers
•Random arrangement of
digits from 0-9 in rows
and columns.
•Selection is done either in
a horizontal or vertical
direction
©Rohit Bhaskar

Systematic random sampling
• Select one unit at random and then selecting
additional units at evenly spaced interval till the
sample of required size has been drawn.
Stratified random selection
• Population to be sampled is subdivided into
groups (age/sex/genetic) known as Strata. ( i.e
each group is homogenous in characteristics.)
• Then a simple randon selection is done from
each stratum.
• More representative, provide greater accuracy
and concentrate on wider geographical area.
©Rohit Bhaskar

Cluster sampling
• The population forms natural groups or clusters
such as village, wards blocks or children of a
school.
• Sample of the clusters is selected and then all
the units in each of the selected cluster is
surveyed.
• Simpler, less time and cost.
• High standard of errors.
©Rohit Bhaskar

Multiphase sampling
• Part of information is collected from the whole sample and
part from the sub sample.
• First phase: All the children in school are surveyed.
• Second phase: Only the ones with oral health problems.
• Third phase: section that needs treatment are selected.
• Sub-samples further becomes smaller and smaller.
• Adapted when the interest is in any specific disease.
©Rohit Bhaskar

Multistage sampling
• First stage is to select the groups or clusters.
• Then subsamples are taken in as many
subsequent stages as necessary to obtain
the desired sample.
©Rohit Bhaskar

Errors in sampling
Sampling errors
•Faulty sample design
•Small sample sie
Non-Sampling errors
•Coverage errors- due to non-
response or non cooperation of
the informant.
•Observational errors: interview bias,
imperfect experimental technique.
•Processing errors: statistical analysis
©Rohit Bhaskar

©Rohit Bhaskar
Presented By
Rohit Bhaskar
Of Medical Sciences
DATA PRESENTATION

Data presentation
– Tables are simple device used for the presentation of statistical
data.
– PRINCIPLES:
– Tables should be as simple as possible.(2-3 small tables).
– Data should be presented according to size or importance,
chronologically or alphabetically.
– Should be self explanatory.
– Each row and column should be labelled concisely and clearly.
• Tabulation
• Graphic representation - charts and diagrams
Tabulation
©Rohit Bhaskar

– Specific unit of measure for the data should be given.
– Title should be clear, concise and to the point.
– Total should be shown.
– Every table should contain a title as to what is
depiceted in the table.
– In small table, vertical lines seperating the column may
not be necessary.
– If the data are not orignal, their source should be
given in a footnote.
©Rohit Bhaskar

TYPES OF TABLES
MASTER
TABLE
Contains all
the data
obtained from
a survey
SIMPLE
TABLE
One way tables
which supply the
answer to questions
about one
characteristic of data
only.
FREQUENCY
DISTRIBUTION
TABLE
Two column frequent
table.
First column list the
classes into which the
data are grouped.
Second column lists
the frequency for
each classification
©Rohit Bhaskar

• Most convincing and appealing ways of depicting
statistical results.
• Principles
1. Every diagram must be given a title that is self explanatory.
2. Simple and consistent with the data.
3. The values of the variable are presented on the horizontal
or X-axis and frequency on the vertical line Y-axis.
4. Number of lines drawn in any graph should not be many.
5. Scale of presentation for X-axis and Y- axis should
be mentioned.
6. The scale of division of both the axes should be
proportional and the divisions should be marked along
the details of the variable and frequencies presented on
the axes.
Charts and diagrams
©Rohit Bhaskar

• Represents qualitative data.
• Bars can be either vertical or horizontal.
• Suitable scale is chosen
• Bars are usually equally spaced
• They are of three types:
• simple bar chart
• multiple bar chart
• component /proportional bar chart
Bar chart
©Rohit Bhaskar

• when number of observations is very
large and class interval is reduced
the frequency polygon losses its
angulations becoming a smooth
curve known as frequency curve
Frequency curve
©Rohit Bhaskar

Pictogram
• Popular method of presenting data
to the common man through small
pictures or symbols.
Spot map/shaded map/Cartogram
• These maps are prepared to show
geographic distribution of frequencies
of characteristics
©Rohit Bhaskar

©Rohit Bhaskar
Measures of Central Tendency
Presented By
Rohit Bhaskar
Of Medical Sciences

Measures of statistical averages or central tendency
• central value around which all the
other observations are distributed.
• Main objective is to condense the entire mass of
dat and to facilitate the comparison.
• the most common measures of central
tendency that are used in sental sciences:
– mean
– median
– mode
©Rohit Bhaskar

• Refers to arithmetic mean
• It is obtained by adding the individual
observations divided by the total number
of observations.
• Advantages –it is easy to calculate, most
useful of all the averages.
• Disadvantages –influenced by abnormal
values.
Mean
©Rohit Bhaskar

• When all the observation are arranged either in
ascending order or descending order, the
middle observation is known as median.
• In case of even number the average of the
two middle values is taken.
• Median is better indicator of central value as it is
not affected by the extreme values.
Median
©Rohit Bhaskar

• Most frequently occurring observation in a data is called
mode
• Not often used in medical statistics.
• EXAMPLE
• Number of decayed teeth in 10 children
• 2,2,4,1,3,0,10,2,3,8
• Mean = 34 / 10 = 3.4
•
• Median = (0,1,2,2,2,3,3,4,8,10) = 2+3 /2
• = 2.5
• Mode = 2 ( 3 Times)
Mode
©Rohit Bhaskar

©Rohit Bhaskar
MEASURES OF DISPERSION
Presented By
Rohit Bhaskar
Of Medical Sciences

MEASURES OF DISPERSION
• Dispersion is the degree of spread or variation of
the variable about a central value.
• Helps to know how widely the observations
are spread on either side of the average.
• Most common measures of dispersion are:
1. RANGE
2. MEAN DEVIATION
3. STANDARD DEVIATION
©Rohit Bhaskar

RANGE MEAN DEVIATION
STANDARD
DEVIATION
•Defined as the
difference between
the value of the
largest item and the
smallest item.
•Gives no information
about the values that
lie between the
extreme values.
•It is the average of
the deviation from
the arithematic
mean.
•M.D= Ʃ(X-Xi)
n
•Ʃ-sum of
•X- arithematic mean
•Xi- value of each
observation in the
data
•n- number of
observation in the
data
•Most important and
widely used measure
of studying dispersion.
•Greater the S.D , greater
will be the magnitude of
dispersion from the
mean.
•Smaller S.D means a
higher degree of
uniformity of the
observations.
• S.D
=
Ʃ(X-Xi)²
n
©Rohit Bhaskar

Coefficient of variation
• It is used to compare attributes having
two different units of measurement e.g.
height and weight
• Denoted by CV
• CV = SD X 100 / Mean
• and is expressed as percentage
©Rohit Bhaskar

• When the data is collected from a very large
number of people and a frequency distribution is
made with narrow class intervals, the resulting
curve is smooth and symmetrical- NARROW
CURVE.
• These limits on either side of measurement are
called
confidence limits .
Normal distribution/normal curve/
Gaussian distribution
©Rohit Bhaskar

STANDARD NORMAL DEVIATION
• There may be many normal curves but only one standard
normal curve
• Characteristics
• Bell shaped
• Perfectly symmetrical
• Frequency increases from one side reaches its highest and
decreases exactly the way it had increased .
• Total area of the curve is one, its mean is zero and standard
deviation is one.
• The highest point denotes mean, median and mode which
coincide.
©Rohit Bhaskar

Z-TEST
• Used to test the significance of difference in
means for large samples.
• Criteria:
1. Sample must be randomly selected.
2. Data must be quantitative.
3. The variable is assumed to follow a
normal distribution in the population.
4. Samples should be larger than 30.
©Rohit Bhaskar

• When different samples are drawn from the same
population, the estimates might differ - sampling
variability.
• It deals with technique to know how far the difference
between the estimates of different samples is due to
sampling variation.
a) Standard error of mean
b) Standard error of proportion
c) Standard error of difference between two means
d) Standard error of difference between two proportion.
Tests of significance
©Rohit Bhaskar

1. Standard error of mean: Gives the
standard deviation of the means of
several samples from the same
population.
Example : Let us suppose, we obtained a
random sample of 25 males, age 20-24
years whose mean temperature was 98.14
deg. F with a standard deviation of 0.6.
What can we say of the true mean of the
universe from which the sample was
drawn?
©Rohit Bhaskar

Standard Error of Proportion
•Standard error of proportion may be defined as a unit
that measures variation which occurs by chance in the
proportions of a character from sample to sample or
from sample to population or vice versa in a qualitative
data.
©Rohit Bhaskar

Standard Error of Difference Between two Means
•The standard error of difference between the two means is 7 .5.
•The actual difference between the two means is (370 - 318) 52, which is more
than twice the standard error of difference between the two means, and
therefore "significant".
©Rohit Bhaskar

• A null hypothesis or hypothesis of no
difference (H0) asserts that there is no
real difference in sample and the
population in particular matter under
consideration and the difference found is
accidental and arised out of sampling
variations.
• The alternative hypothesis of significant
difference (H1) stated that there is a
difference between the two groups
compared.
©Rohit Bhaskar

• A test of significance such as Z-test is
performed to accept the null hypothesis
H0 or to reject it and accept the alternative
hypothesis H1.
• To make minimum error in rejection or
acceptance of H0, we divide the sampling
distribution or the area under the
normalcurve into two regions or zone.
i. A zone of acceptance
ii.A zone of rejection.
©Rohit Bhaskar

• The distance from the mean at which H0 is
rejected
is called the level of significance.
• It falls in the zone of rejection for H0,
shaded areas under the curves and it is
denoted by letter P which, indicates the
probability or relative frequency of
occurrence of the difference by chance.
• Greater the Z value, lesser will be the P.
©Rohit Bhaskar

• Degree of freedom:
Defined as the number of independent members
in the sample.
EXAMPLE:-
X+Y+Z/3=5
Out of 3 values, we can choose only 2 of them
freely, but the choice of the third depends upon
the fact that the total of the three values should
be 15.
©Rohit Bhaskar

SIGNIFICANCE OF DIFFERENCE BETWEEN MEANS OF
SMALL SAMPLE & STUDENT T TEST
• Small samples or their Z values do not follow normal
distribution as the large ones do.
• So, the Z value based on normal distribution will not give
the correct level of significance or probability of a small
sample value occurring by chance.
• In case of small samples, t-test is applied instead of Z-test.
• It was designed by W.S.Gossett whose pen name was
Student. Hence, this test is also called Student’s t-test.
©Rohit Bhaskar

• There are two types of student t Test
• Unpaired t test Paired t test
• Criteria for applying t-test
• 1. Random samples
• 2. Quantitative data
• 3. Variable normally distributed
• 4. Sample size less than 30.
©Rohit Bhaskar

• This test is applied to unpaired data of
independent observations made on individuals
of two different or separate groups or samples
drawn from two populations, to test if the
difference between the two means is real or it
can be attributed to sampling variability .
• EXAMPLE: between means of the control
and experimental groups.
Unpaired t test
©Rohit Bhaskar

The CHI SQUARE TEST FOR QUALITATIVE DATA(X²
TEST)
• Developed by Karl Pearson.
• Chi-square (x²) Test offers an alternate method of
testing the significance of difference between two
proportions. It has the advantage that it can also
be used when more than two groups are to be
compared.
• It is most commonly used when data are in
frequencies such as in the number of responses
in two or more categories.
©Rohit Bhaskar

• Important applications in medical statistics
as test of:
• 1. Proportion
• 2. Association
• 3. Goodness of fit.
• Test of Proportions
• As an alternate test to find the
significance of difference in two or more
than two proportions.
©Rohit Bhaskar

• Test of Association
• The test of association between two
events in binomial or multinomial samples
is the most important application of the
test in statistical methods. It measures the
probability of association between two
discrete attributes.
• Two events can often be studied for their
association such as smoking and cancer,
treatment and outcome of a disease,
vaccination and immunity, nutrition and
intelligence, etc.
©Rohit Bhaskar

• Test of Goodness of Fit
• Chi-square (χ2) test is also applied as a
test of “goodness of fit”, to determine
if actual numbers are similar to the
expected or theoretical numbers—
goodness of fit to a theory.
©Rohit Bhaskar

Analysis of Variance (ANOVA) Test
• Not confined to comparing two sample means,
but more than two samples drawn from
corresponding normal populations.
• Eg. In experimental situations where several
different treatments (various therapeutic
approaches to a specific problem or various
drug levels of a particular drug) are under
comparison.
• It is the best way to test the equality of three
or more means of more than two groups.
©Rohit Bhaskar

• Requirements
– Data for each group are assumed to be
independent and normally distributed
– Sampling should be at random
• One way ANOVA
– Where only one factor will effect the result
between 2 groups
• Two way ANOVA
– Where we have 2 factors that affect the result or
outcome
• Multi way ANOVA
– Three or more factors affect the result or outcomes
between groups
©Rohit Bhaskar

CORRELATION AND REGRESSION
• Correlation: When dealing with
measurement on 2 sets of variable in a
same person, one variable may be
related to the other in same way. (i.e
change in one variable may result in
change in the value of other variable.)
• Correlation is the relationship between
two sets of variable.
• Correlation coefficient is the magnitude or
degree of relationship between 2
variables. (varies from -1 to +1).
©Rohit Bhaskar

• Obtained by plotting scatter diagram (i.e one
variable on x-axis and other on y-axis).
• Perfect Positive Correlation
• In this, the two variables denoted by letter X and Y
are directly proportional and fully correlated with
each other.
• The correlation coefficent (r) = + 1, i.e. both
variables rise or fall in the same proportion.
• Perfect Negative Correlation
• Values are inversely proportional to each other, i.e.
when one rises, the other falls in the same
proportion,
i.e. the correlation coefficient (r) = –1.
©Rohit Bhaskar

Regression
• Toknow in an individual case the value of one
variable, knowing the value of the other, we calculate
what is known as the regression coefficient of one
measurement to the other.
• It is customary to denote the independent variate by
x and the dependent variate by y.
• The value of b is called the regression coefficient of y
upon
x. Similarly, we can obtain the regression of x upon y.
©Rohit Bhaskar

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