Aim: To Calculate Sample Size required to test whether two sample proportions are significantly different.

Formula Used

For two tailed hypothesis

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For one tailed hypothesis

P₁ = Estimated first sample proportion.

P₂ = Estimated second sample proportion.

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

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

β = 1 – Power (Out of 1) (e.g. 80% = 0.8)

Z _1-β = the standard normal deviate corresponding to 1- β.

Example 1:

Two therapies are to be tested to find whether proportions of successful outcome in these therapies are significantly different. The expected success rates are 60% and 65%. How much sample size shall be required at confidence level of 95% and power of 80% (equal sample size in two groups).

Solution:

Here

P₁ = 65%, P₂ = 60%, confidence level = 95%, power = 80%, two tailed ("significantly different"), r=1

After putting these values, we get required sample size in each group = 1468.

Example 2:

Two therapies are to be tested to find whether proportions of successful outcome with second therapy is significantly more than that with first therapy. The expected success rates are 60% and 65%. How much sample size shall be required at confidence level of 95% and power of 80% (equal sample size in two groups).

Solution:

Here

P₁ = 65%, P₂ = 60%, confidence level = 95%, power = 80%, one tailed ("significantly more"), r=1

After putting these values, we get required sample size in each group = 1156.