Power of a Statistical Test

The power of a statistical test refers to the probability of rejecting the null hypothesis when the alternative hypothesis is true if the test is used.

Notes:

• In general, the power of a test depends on what makes the alternative hypothesis true. For example, when testing
  
  H₀: p <= 0.5    versus    H₁: p > 0.5,
  the power depends on the value of the population proportion p which makes the above H₁ true. Here, H₁ is true if p is any value between 0.5 and 1. To determine the power of the test for this case, you need to specify the particular value of p under the alternative hypothesis that is of interest to you. For any specific alternative of interest, we have
  
  Power = 1 - P(Type II error)
  for that alternative. Thus, a test with high power is desirable since this implies a correspondingly small chance of making Type II error when the test is used.