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

Formula Used

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

μ₁ = Mean in first group.

μ₂ = Mean in second group

SD₁ = Standard deviation in first group

SD₂ = Standard deviation in second group

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 examination scores differ significantly in genders. He conducted a study by including 50 boys and girls each, which revealed mean score of boys = 84 ± 10, and girls = 86 ± 9. How much was the power to detect the significant difference between these two means, at confidence level of 95 % (alpha = 5%)?

Solution:

Here

μ₁ = 84, μ₂ = 86, SD₁ = 10, SD₂ = 9, confidence level = 95%, N₁=50, N₂=50, tails = 2 ("significantly different")

After putting these values, we get power = 18.17%