Type I and Type II Errors

Type I And Type II Errors

In statistics, a type I error (or error of the first kind) is the incorrect rejection of a true null hypothesis. A type II error (or error of the second kind) is the failure to reject a false null hypothesis. A type I error is a false positive. Usually a type I error leads one to conclude that a thing or relationship exists when really it doesn't, for example, that a patient has a disease being tested for when really the patient does not have the disease, or that a medical treatment cures a disease when really it doesn't. A type II error is a false negative. Examples of type II errors would be a blood test failing to detect the disease it was designed to detect, in a patient who really has the disease; or a clinical trial of a medical treatment failing to show that the treatment works when really it does. When comparing two means, concluding the means were different when in reality they were not different would be a Type I error; concluding the means were not different when in reality they were different would be a Type II error.

All statistical hypothesis tests have a probability of making type I and type II errors. For example, all blood tests for a disease will falsely detect the disease in some proportion of people who don't have it, and will fail to detect the disease in some proportion of people who do have it. A test's probability of making a type I error is denoted by α. A test's probability of making a type II error is denoted by β.

These terms are also used in a more general way by social scientists and others to refer to flaws in reasoning. This article is specifically devoted to the statistical meanings of those terms and the technical issues of the statistical errors that those terms describe.