Definition

The power of a test is defined as the probability of correctly rejecting the Null Hypothesis, i.e., rejecting the Null Hypothesis when it is false.

Power is calculated as (1- Beta), where Beta = probability of a Type II Error.

Examples

Consider a z-test of H_{0}: μ = μ_{0} against the alternative H_{1}: μ > μ_{0}.

The decision criterion is to reject H_{0} if Z > z_{α}

Now the power of the test can be calculated for any value under the alternative, H_{1}, say μ_{1}.

Power = P(Reject H_{0}/H_{0} is not true) = P(Reject H_{0}/H_{1} is true)

= P(Z > z_{α} / μ = μ_{1})

which is the area to the right of z_{α} under the normal distribution curve with mean μ_{1}.

Thus, the power can be found for any value under the alternative hypothesis. The formula for computing power depends on the type of test, sample size, effect size and the specified significance (α) level.

External Links

*Power of a Statistical Test* by MoreSteam.com -
http://www.moresteam.com/whitepapers/power-stat-test.pdf