Aim: To calculate statistcal power gained with given Sample Size required to test whether a sample mean is significantly different than a known / hypothesized mean.

Formula Used

For two tailed hypothesis

μ_T = Estimated sample mean.

μ_H = Hypothesised mean against which sample mean is compared.

SD = Estimated standard deviation in sample.

N = Sample Size

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 1:

A new antihypertensive drug is tested to find whether mean reduction in SBP with this test drug is significantly different than an hypothesised value of 25. The study was conducted with a sampe size of 30 hypertensives, and it has shown a mean reduction of SBP by 28 mm of Hg with SD of 6. How much was the power of the study to detect whether mean reduction in SBP by this drug is significantly different than a hypothesised value of 25, at confidence level of 95%.

Solution:

Here

μ_T = 28, μ_H = 25, SD = 6, confidence level = 95%, N = 30, two tailed ("significantly different")

After putting these values, we get power = 78.19%.

Example 2:

A new antihypertensive drug is tested to find whether mean reduction in SBP with this test drug is significantly different than an hypothesised value of 25. The study was conducted with a sampe size of 30 hypertensives, and it has shown a mean reduction of SBP by 28 mm of Hg with SD of 6. How much was the power of the study to detect whether mean reduction in SBP by this drug is significantly more than a hypothesised value of 25, at confidence level of 95%.

Solution:

Here

μ_T = 28, μ_H = 25, SD = 6, confidence level = 95%, N = 30, one tailed ("significantly more").

After putting these values, we get power = 86.30%.