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Help on Sample Size Calculation



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Importance of Sample Size

A researcher needs to know the number of subjects required in a study. In order to do so one should know about the size of treatment effects and also the variability. Researcher use binomial distribution for binary outcomes and normal distribution for continuous distribution.


The measures required for sample size calculation (One or Two group) are as follows:


1. Type I Error


1. Type II Error


1. Power is the complement of Type II error =1 - B .


1. Variances under the null hypothesis (σ0) and alternative hypothesis (σ1).


1. Means under the null hypothesis (σ0) and alternative hypothesis(σ1)


1. Sample sizes in two groups n0 and n1 .


A controversy arises while choosing the alternative hypothesis. According to some, the study is not required if the value of the alternative hypothesis is known. Also difference in opinion arises in deciding the null and alternative hypothesis.


The critical value defining the boundary between rejection and acceptance region must be similar for both null and alternative hypothesis.


Manipulate Required Sample Size

One should answer some questions for determining the sample size. They are as follows:


The population size: It's Best Estimate :

One should know the best estimate of the population size instead of the exact size of population. The formula for computing sample size is remains unaffected if an inaccurate population size is used. We do not use the population size if the population size is very large.


Best estimate of the rate in the population

Based on the null hypothesis one should also make a best estimate of the rate in the population in terms of percentage.


Maximum acceptable difference

It refers to the maximum difference (in percentage) that one accepts between true population and sample rates.


Desired confidence level

This tells the level of confidence one have that the true population rate will fall within the acceptable difference. It is similar to the confidence that one should have in his findings.


Sample Size Calculation Power

Power Calculation

Calculation of Sample Size

1. To calculate sample size when we need to compare two population means:


n= 2*[{z((1-α)/2)+ z(1-β)}]^2/ {(μ0-μ1)/σ}^2


2. Using the coefficient of variation:


n =16(CV )^2/(lnμ0 - lnμ1)^2


CV represents the coeffcient of variation


3. For calculating sample size for a survey one should not take into consideration the finite population correction


4. Calculation for poisson distribution:


Let θ0 and θ1 be the means of the two populations. Then the required number of observations per sample is n = 4/(√θ0 -√θ1)^2


The situations where unequal Sample Sizes arises:

Sometimes we need to deal with unequal sample sizes. An example can be cited in this regard. Example: in epidemiological studies more controls are available than cases. Let there be n subject in each group, however for one of the groups only (n0 < n) are available. Now we may be interested to know the number of subjects (kn0) in the second group so that we get equal precision as for the n in each group.


For a two sample situation with the above assumptions, select

k =n/(2n0 - n)

Sample Size Calculation Proportion

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