About
The power of a test sometimes, less formally, refers to the probability of rejecting the null when it is not correct, the chance that your experiment is right.
A test's power is influenced by the choice of significance level for the test, the size of the effect being measured, and the amount of data available.
A hypothesis test may fail to reject the null, for example, if a true difference exists between two populations being compared by a t-test but the effect is small and the sample size is too small to distinguish the effect from random chance.
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Example
Many clinical trials, for instance, have low statistical power to detect differences in adverse effects of treatments, since such effects may be rare and the number of affected patients small.