This document discusses sample size estimation and determination. It defines key terms like population, statistic, parameter, sampling error, and confidence interval. It explains that sample size determination is calculating the number of subjects needed in a study to make inferences about a reference population. An appropriate sample size allows for valid analysis and the desired level of accuracy. The sample should be representative of the population and large enough to minimize errors and bias. Both too large and too small samples have disadvantages. Common methods for calculating sample size are using formulas, ready-made tables, nomograms, and computer software. Formulas are provided for estimating proportions, differences in proportions, means, and differences in means.

1. Sample Size Estimation
Mr Sathish Rajamani
Associate Professor,
Ved Nursing College, Panipat
Introduction
Quantitative researchers need to pay attention to the number of participants needed to achieve
statistical conclusion validity. A procedure called power analysis (Cohen, 1988) cab be used
to estimate sample size needs.
Sampling Fundamentals
 Universe / Population: ‘Universe’ refers to the total of the items or units in any field
of inquiry, whereas the term ‘population’ refers to the total of items about which
information is desired.
 Statistic(s) and parameter(s): A statistic is a characteristic of a sample, whereas a
parameter is a characteristic of a population.
 Sampling Error: The error that arises as a result of taking a sample from a
population rather than using the whole population is known as sampling error.
 Confidence Interval: the range of values within which a population parameter is
estimated to lie, at a specified probability. (e.g., 95% CI).
 Sampling Distribution: A sampling distribution is a statistic obtained through a large
number of samples drawn from a specific population.
 Sample Size: This is the sub-population to be studied in order to make an inference to
a reference population.
What is Sample Size Determination?
Sample size determination is the mathematical estimation of the number of subjects /
units to be included in a study.
Why to Determine the Sample Size in a Study?
 To allow for appropriate analysis
 To provide the desired level of accuracy
 To allow validity of significance test
Attributes of a Good Sample
To extrapolate the inference of the sample to the population, the sample should be.

2.  A representative of the population
 Should be a large enough
If a sample is too large
 Good Precision
 Less Errors and Less Bias
But
 Waste of money, time and resources
 Not Cost-effective
If a sample is too small
 Inaccurate results
 More source of bias
 Power of the study comes down
 Study fails to give the meaningful information
 Waste of resources on a inaccurate study
Methods to Calculate Sample Size
There are four methods used in estimating the sample size.
1. Use of formulae
2. Ready Made Table
3. Nomograms
4. Computer Software
Use of Formula’s
1. Calculating Proportion
This is used in cases when we are trying to find proportions.
E.g. for studies like
1. Estimation of prevalence of tuberculosis in Panipat city 2018
2. Prevalence of extra pyramid side - effects as a complication of anti-psychotic
drugs.
N = 4PQ/d2
Where,
P = Prevalence from Previous Studies
Q = 100 – P
d = allowable error ( 5 – 20% of P)

3. 2. Calculating difference in proportion
This is used when we measure the significance of difference between two proportions.
E.g. for studies like
1. Diagnostic supremacy of CT chest V/s X-ray chest in tuberculosis patients
2. Success rate of streptomycin V/s kanamycin in cure of MDR – TB
N = 15.7 x ꝑ x Q
(P1 – P2)2
Where
P1 and P2 are the proportions of the two groups.
ꝑ is the average of P1 and P2
100- ꝑ
3. Calculating the Mean
This formula is used in quantitative studies where we are estimating the mean of the
study group.
E.g. for studies like
Estimation of mean age of diagnosis of tuberculosis in Panipat Study
N = 4σ2 / d2
Where,
σ (Sigma) is the standard deviation as in similar studies done previously
d = allowable error (5 – 20% of σ)
4. Calculating difference in Means
This is used in studies where we are calculating the difference achieved quantitatively
during the study.
E.g. for studies like
Average weight gain in patients of tuberculosis before and after DOTS programme
N = 15.7 (σ1 x σ2) / d
2
Where,
σ1and σ2 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, σ1= σ2 = σ

4. Use of readymade Table for Sample Size Calculation
Sample size determination table are available in readymade to estimate the size of the
sample in a study.
Use of Nomogram for Sample Size Calculation
Altman’s nomogram is a very clever graphical method for calculating sample sizes.
Use of Computer Software for Sample Size Calculation and Power Analysis
The following software can be used to calculate sample size and Power.
 Epi – Info
 nQuerry
 Power & Precision
 SPSS
 STATA
Conclusion
Sample size determination is one of the most essential components of every research.
The larger the sample size, the higher the degree of accuracy, but this is limit by the
availability of resources.
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