Type I and Type II Errors in Hypothesis Testing

We reject the null hypothesis or do not reject the null hypothesis based on comparing the calculated test statistic to a specified possible value or values. The comparison values we choose are based on the level of significance selected.

The probability of a Type I error in testing a hypothesis is denoted by α, also known as the levelof significance of the test.

The probability of a Type II error is denoted by β.

The power ofa test is the probability of correctly rejecting the null. When more than one test statistic is available, we should prefer the most powerful, all else equal.