Sample size calculation

Sample Size Calculation

Dr P Raghavendra
2nd Year Post-Graduate
Dept of Community Medicine,
Siddhartha Medical College, Vijayawada

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.

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.

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.

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

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.

The usual Question

How big a
sample is a
good

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.

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

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.

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.

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.

1. Calculating Proportion

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

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

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

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 -

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

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

• This formula is used in quantitative studies
where we are estimating the mean of the
study group.
– 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


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

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

Here, = 10.
So, d = 20% of = 2.

Hence, N = (4 x 10x10) / (2 x 2)

= 100

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

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 =

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

Here, 1 = 2 = 70, d = 10

N = (15.7 x 70 x 70) / (10 x 10)
= 769

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

• When already we know the P, why should we
do the study again?

• How big should be the sample of a pilot
study?

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

Sample size calculation

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