Aim: To calculate statistical power with given Sample Size (Z test): Difference between two independent sample proportions

Formula Used

N = Sample Size in first group = (N1).

P₁ = Proportion of success in first group (Out of 1) (e .g. 25% = 0.25).

P₂ = Proportion of success in second group (Out of 1) (e .g. 25% = 0.25).

r= Sample size in first group : Sample Size in second group = N2 / N1

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

Φ(x)=P(Z ≤ x). It is the cumulative distribution function (CDF) of normal distribution. Simply, it is the area of the standard normal curve towards left side of x.

Example:

An investigator wanted to conduct a study to test whether proportions of successful candidates differ significantly in genders. He conducted a study by including 200 boys and girls each, which revealed that proportions of successful candidates were 80% in boys and 85% in girls. How much was the power to detect the significant difference between these two proortions, at confidence level of 95 % (alpha = 5%)?

Solution:

Here

P₁ = 80% so number of successful outcomes = S1 = 160, P₂ = 85 so number of successful outcomes = S2 = 170, confidence level = 95%, N₁=200, N₂=200, tails = 2 ("significantly different")

After putting these values, we get power = 26.07%