Background
Statistical tests use data from samples to assess, or make inferences about, a population. In the concrete setting of a two-sample comparison, the goal is to assess whether the mean values of some attribute obtained for individuals in two sub-populations differ. For example, to test the null hypothesis that the mean scores of men and women on a test do not differ, samples of men and women are drawn, the test is administered to them, and the mean score of one group is compared to that of the other group using a statistical test such as the two-sample z-test. The power of the test is the probability that the test will find a statistically significant difference between men and women, as a function of the size of the true difference between those two populations. Note that power is the probability of finding a difference that does exist, as opposed to the likelihood of declaring a difference that does not exist (which is known as a Type I error, or "false positive").
Read more about this topic: Statistical Power
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