What is Statistical Power?

Statistical Power of any test of statistical significance is defined as the probability that it will reject a false null hypothesis. Statistical power is inversely related to beta or the probability of making a Type II error. The power is a function of the possible distributions, often determined by a parameter, under the alternative hypothesis. As the power increases, there are decreasing chances of a Type II error, which are also referred to as the false negative rate (β) since the power is equal to 1−β, again, under the alternative hypothesis. A similar concept is Type I error or the level of a test under the null hypothesis. Power analysis can be used to calculate the minimum sample size required so that one can be reasonably likely to detect an effect of a given size. For example: “how many times do I need to toss a coin to conclude it is rigged?” Power analysis can also be used to calculate the minimum effect size that is likely to be detected in a study using a given sample size. In addition, the concept of power is used to make comparisons between different statistical testing procedures: for example, between a parametric and a nonparametric test of the same hypothesis.

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