Power of a Test

The power of a statistical test is defined as the probability of correctly rejecting a false null hypothesis. Power is therefore defined as: 1 - β, where β is the Type II error probability. A test with a low power is of little worth, although the level of significance α may be high (the results are inconclusive since the null hypothesis is true only with a low probability).

Note that for a given set-up of an experiment, the power of a test and the level of significance are related to each other: decreasing the level of significance α (which is favorable, since the probability of making an error when rejecting the null hypothesis is lowered) also decreases the power of a test (which is bad, since the probability of making a type II error increases). Thus, without changing the experiment, we have to make a compromise between a low level of significance and the high power of the test.