Aim: To Calculate Sample Size required when your aim is to estimate difference between two sample proportions with specified precision.

Formula Used

P₁ = Estimated first sample proportion.

P₂ = Estimated second sample proportion.

r = Ratio of Sample Sizes in two groups (N2:N1).

Z _1-α/2 = the standard normal deviate corresponding the confidence level

ε = Precision

Example 1:

Two therapies are to be tested with an aim to estimate the difference between proportions of successful outcome in these therapies. The expected success rates are 60% and 65%. Ivestigators wants that this expected difference of 5% is to be estimated with an absolute precision of 2. How much sample size shall be required at confidence level of 95% (equal sample size in two groups).

Solution:

Here

P₁ = 65%, P₂ = 60%, confidence level = 95%, ε =2, r=1

After putting these values, we get required sample size in each group = 4490.