Aim: To Calculate Sample Size required to test whether a sample proportion is significantly different than a known / hypothesized proportion.

Formula Used

For two tailed hypothesis

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For one tailed hypothesis

P₁ = Estimated sample proportion.

P₂ = Hypothesised proportion against which sample proportion is compared.

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:

A new therapy is to be tested to find whether proportion of successful outcome with this therapy is significantly different than an hypothesised value of 60%. The test therapy is expected to give success rate of 65%. How much sample size shall be required at confidence level of 95% and power of 80%.

Solution:

Here

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

After putting these values, we get required sample size in each group = 712.

Example 2:

A new therapy is to be tested to find whether proportion of successful outcome with this therapy is significantly more than an hypothesised value of 60%. The test therapy is expected to give success rate of 65%. How much sample size shall be required at confidence level of 95% and power of 80%.

Solution:

Here

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

After putting these values, we get required sample size  = 563.