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Power of a Test

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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.


Consider a z-test of H0: μ = μ0 against the alternative H1: μ > μ0.

The decision criterion is to reject H0 if Z > zα

Now the power of the test can be calculated for any value under the alternative, H1, say μ1.

Power = P(Reject H0/H0 is not true) = P(Reject H0/H1 is true)
            = P(Z > zα / μ = μ1)
which is the area to the right of zα under the normal distribution curve with mean μ1.

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.

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