Note that, in statistics, the term “error” does not mean somebody did something wrong. It refers to
variability. An “error” occurs because the sampling variability caused a sample statistic that led us to the
wrong decision. The errors have names that are rather unspectacular: If the (null) hypothesis is true, and
we mistakenly reject it, it is a Type I error . If the hypothesis is false, and we mistakenly fail to reject it,
it is a Type II error . We note that the probability of a Type I error is equal to α, the significance level.
(This is because a P -value < α causes us to reject H 0 . If H 0 is true, and we decide to reject it because
we got an unusual sample, we have made a Type I error). We call the probability of a Type II error β .
Filling in the table with this information, we have:
The cell in the lower right-hand corner is important. The probability of correctly rejecting a false
hypothesis (in favor of the alternative) is called the power of the test . The power of the test equals 1 – β
. Finally, then, our decision table looks like this: