Beta Error

In inferential statistics, we state a null and alternative hypothesis, gather data, and compute statistics to decide whether to accept or reject the null hypothesis. Because we compute statistics on a sample in order to make decisions about a population whose parameters are unknown, there is always some probability that our decision will be incorrect. There are two ways we may be incorrect: We may reject the null hypothesis when it is true, or we may accept the null hypothesis when it is false. The first type of error is known as alpha error, or Type I error. The second type of error is known as beta error, or Type II error.

For instance, we might be comparing two groups of children to see if they differ in height: Our null hypothesis is no difference between the group means on height, while our alternative hypothesis is that there is a difference in the group means. If our sample statistics indicated that there was no significant difference between the groups, while in the population they were significantly different, we would fail to reject the null hypothesis and commit a beta error.

The probability of an beta error, also referred to as β (the Greek letter beta), is commonly set at 0.20, which is higher than that commonly used for alpha error (0.05) because the consequences of beta error are usually considered less serious than the consequences of alpha error. Statistical power is defined as 1-β; for instance, if β is 0.20, power is 1–0.20 or 0.80.