Type II Error

Type II error refers to the probability of not rejecting a false null hypothesis in hypothesis testing; it is denoted by a Greek symbol β. For instance, a hypothesis test is set up to examine the presence of bias in a new standardized test. The null hypothesis states that there is no bias. If there is indeed bias in the test, not rejecting the null hypothesis means failure to confirm the suspected bias.

The concept of Type II error was conceived by Jerzy Neyman and Egon Pearson who developed a mathematical framework later known as Neyman–Pearson lemma to quantify Type II error in hypothesis testing. They considered decision behavior in the significance test and theorized Type I error (false positive) and Type II error (false negative).

Type II error is commonly associated with false negative in decision making because hypothesis testing resembles dichotomous decision making—a positive or negative decision in the end. A no answer means not rejecting the null hypothesis. If the null hypothesis is false, not rejecting it will fail to confirm a researcher’s theory stated in the alternative hypothesis—this constitutes an error of the second kind or Type II error. A close analogue of Type II error can be found in a criminal trial that can render a verdict of guilty or not guilty. A guilty verdict corresponds to a positive decision and a not guilty verdict to a negative decision. When the suspect who indeed committed the crime is acquitted, the verdict of not guilty would be considered a travesty of justice. In this case, the decision is “false negative”—it lets go a real criminal.

Type II error is related to Type I error and statistical power. The latter represents the probability of rejecting a false null hypothesis. As rejecting a false null hypothesis is an event complementary to not rejecting a false null, statistical power can be expressed as one minus Type II error, that is, 1 − β. Thus, increasing statistical power will lower the Type II error in hypothesis testing. In addition, Type II error has an inverse relationship with Type I error. As Type I error goes down, Type II error goes up. The Type I error rate is traditionally limited to 5%, the significance level in hypothesis testing. If the significance level is lowered to 1%, it will be more difficult to reject the null hypothesis. Consequently, the Type II error rate will increase.

See also Significance; Type I Error; Type III Error