This document discusses sample size calculation and provides formulas for determining appropriate sample sizes for different types of studies. It explains that sampling involves studying a subset of a population to make inferences about the whole population. The key types of studies covered are: 1) calculating a proportion, 2) calculating the difference between two proportions, 3) calculating a mean, and 4) calculating the difference between two means. Formulas for determining sample sizes for each of these study types are presented along with examples and exercises to demonstrate how to apply the formulas.

1. Sample Size Calculation
Dr P Raghavendra
2nd Year Post-Graduate
Dept of Community Medicine,
Siddhartha Medical College, Vijayawada

2. What is Sampling?
• A sample is a part of the population under
study.
• In most situations, it might not be possible to
study an entire population.
• We typically draw a subset of people drawn
from a larger population and then use
inferential statistics to make an inference from
the sample and apply it to the whole
population.

3. What is sampling?
• We try to study the characters of the
population by measuring them from a smaller
number of subjects.
• Sample is expected to be the MIRROR of the
population.
• Cook sees only a handful of rice to check if it is
cooked or not.

4. Attributes of a good sample
To extrapolate the inference of the sample to
the population, the sample should be:
• A representative of the population.
• Should be large enough.

5. If sample is too large…
Good precision
Less errors
Less bias
But,
Wastage of time, money and resources
Resources could be as well be deviated to
other projects.
Not cost-effective

6. If sample is too small…
Inaccurate results.
More source of bias.
Power of the study comes down.
Study fails to give meaningful information.
Waste of resources on a inaccurate study.
Ethical issues about recruiting patients into a
meaningless study.

7. The usual Question
How big a
sample is a
good

8. How big should a sample be?
• Formulae are present.
• The forthcoming formulae are tailor-made for
a power of 80% and a Confidence Interval of
95%. (Acceptable levels)
• Power of the study is the ability to detect the
true significance.
• 95% CI means 5% of erroneous significance.

9. Types of studies
• Based on what we are measuring, there are 4
types of studies:
1. Calculating the proportion
Qualitative
2. Calculating the difference of
proportions
3. Calculating the mean
Quantitative
4.Calculating the difference in means

10. Qualitative v/s Quantitative
• Qualitative are those which can be answered
as YES or NO, Male or Female, etc.
• We can only measure their numbers,
eg: Number of males, Number of MDR-TB
cases among TB patients, etc.
• A set of qualitative data can be expressed as
proportions. Eg: Prevalence, success rate.

11. Qualitative v/s Quantitative
• Quantitative are those which can be measured
in numbers, like Blood pressure, Age, etc.
• A set of quantitative date can be expressed in
mean and its standard deviation.
• Mean is the average of all variables in the
data.
• Standard deviation is a measure of the
distribution of variables around the mean.

12. 1. Calculating Proportion
• This is used in cases where we are trying to
find proportions.
• Eg: for studies like:-
– Estimation of prevalence of tuberculosis in
Vijayawada city in 2012.
– Prevalence of malignant hyperthermia as a
complication of enflurane administration.

13. 1. Calculating Proportion
N= 4PQ/d 2
Where,
• P = Prevalence (from previous studies)
• Q = 100 – P
• d = allowable error (5-20% of P)

14. Exercise - 1
• Calculate the sample size required to find out
the proportion of children receiving BCG
vaccination if the BCG coverage of that area in
previous studies was 80%.
• Sol: P = 80; Q = 100-P = 20; d= 20% 0f P = 16.
N= 4PQ/d2
= 4x80x20
16x16
= 25

15. 2. Calculating Difference in proportion
• This is used when we measure the significance
of difference between two proportions.
• Eg: For studies like:-
– Diagnostic supremacy of CT Chest v/s X-ray chest
in pulmonary tuberculosis.
– Success rate of Streptomycin v/s Kanamycin in
cure of MDR-TB

16. 2. Calculating Difference in proportion
N= 15.7 x x Q
(P1-P2 )2
Where,
• P1 and P2 are the proportions of the 2 groups
• is the average of P1 and P2
• Q is 100 -

17. Exercise - 2
• A new treatment regimen for Tuberculosis was
planned. The success rates of DOTS was 75%.
The success rate of the new treatment in a
pilot study was 85%. Calculate the sample size
for a study to compare the success rates of the
two regimen.
Hint: N= 15.7 x x Q
(P1-P2 )2

18. Solution to exercise - 2
Here, P1 = 75; P2 = 85%; = 80
Q = 100 - = 20; P1-P2 = 10
Hence N = (15.7 x 80 x 20) / (10 x 10)
= 251

19. 3. Calculating the mean
• This formula is used in quantitative studies
where we are estimating the mean of the
study group.
• Eg: For studies like:-
– Estimation of mean age at diagnosis of
tuberculosis in Vijayawada city
– Bacteriological index at the initiation of DOTS in
TB patients attending DOTS centre of
GGH, Vijayawada
– Mean time of onset of action of Sevoflurane

20. 3. Calculating the mean
N= 4 2/d2
Where,
• (Sigma) is the Standard deviation as in
similar studies done previously
• d = allowable error (5-20% of )

21. Exercise - 3
• We are planning to do a study regarding Age
of onset of smoking practice among youth in
rural Vijayawada. A previous such study done
in Andhra Pradesh gave a mean age at onset
as 25 years with a standard deviation of 10
years. Calculate the sample size required to do
the planned study.
Hint: N= 4 2/d2

22. Solution to exercise - 3
Here, = 10.
So, d = 20% of = 2.
Hence, N = (4 x 10x10) / (2 x 2)
= 100

23. 4. Calculating Difference in Means
• This is used in studies where we are
calculating the difference achieved
quantitatively during the study.
• Eg: For studies like:-
– Average weight gain in patients of tuberculosis
before and after DOTS.
– Mean fall in Blood pressure due to propofol
infusion.

24. 4. Calculating Difference in Means
N = 15.7 ( x 2
1 2)/d
Where,
• 1 and 2 are the standard deviations of the 2
study groups,
• d is the smallest meaningful difference that
can be measured.
In before-after type of studies, 1 = 2 =

25. Exercise - 4
• Determine the sample size required to detect
an increase of 10 cells/cu.mm in CD4 counts of
HIV patients those receiving HAART, assuming
the standard deviation of CD4 counts to be 70
cells/cu.mm.
Hint: N = 15.7 ( 1x 2)/d2

26. Solution to exercise - 4
Here, 1 = 2 = 70, d = 10
N = (15.7 x 70 x 70) / (10 x 10)
= 769

27. Frequently asked questions
• Where can we get the values of or P?

28. Frequently asked questions
• When already we know the P, why should we
do the study again?

29. Frequently asked questions
• How big should be the sample of a pilot
study?

30. Frequently asked questions
• What should we do if we are not getting
enough cases or if the sample size is bigger
than the total number of cases?

31. Any Questions or
Doubts??