**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.

Read more about Type I And Type II Errors: Statistical Test Theory, Informal Interpretation, Consequences, Etymology, Various Proposals For Further Extension, Usage Examples, See Also

### Other articles related to "type i and type ii errors":

**Type I And Type II Errors**- See Also

... Statistics portal Detection theory Egon Pearson False positive paradox Family-wise error rate Information retrieval performance measures Neyman-Pearson lemma Null hypothesis Prosecutor's fallacy Prozone phenomenon Receiver operating characteristic Sensitivity and specificity Statisticians' and engineers' cross-reference of statistical terms Testing hypotheses suggested by the data. ...

### Famous quotes containing the words errors and/or type:

“Their *errors* have been weighed and found to have been dust in the balance; if their sins were as scarlet, they are now white as snow: they have been washed in the blood of the mediator and the redeemer, Time.”

—Percy Bysshe Shelley (1792–1822)

“How is freedom measured, in individuals as in nations? By the resistance which has to be overcome, by the effort it costs to stay aloft. One would have to seek the highest *type* of free man where the greatest resistance is constantly being overcome: five steps from tyranny, near the threshold of the danger of servitude.”

—Friedrich Nietzsche (1844–1900)