Type I and type II errors
concepts from statistical hypothesis testing
Type I error, or a false positive, is the incorrect rejection of a true null hypothesis in statistical hypothesis testing. A type II error, or a false negative, is the incorrect acceptance of a false null hypothesis.
An analysis commits a Type I error when some baseline assumption is incorrectly rejected because of new, misleading information. Meanwhile, a Type II error is made when such an assumption is maintained, due to flawed or insufficient data, when better measurements would have shown it to be untrue. For example, in the context of medical testing, if we consider the null hypothesis to be "This patient does not have the disease," a diagnosis that the disease is present when it is not is a Type I error, while a diagnosis that the patient does not have the disease when it is present would be a Type II error. The manner in which a null hypothesis frames contextually default expectations influences the specific ways in which type I errors and type II errors manifest, and this varies by context and application. Generally the risk of such errors cannot be entirely eliminated, only traded-off between the two types, by for example changing the significance threshold.
Knowledge of type I errors and type II errors is applied widely in fields of medical science, biometrics and computer science. Minimising these errors is an object of study within statistical theory, though complete elimination of either is impossible when relevant outcomes are not determined by known, observable, causal processes.
Definition
Statistical background
In statistical test theory, the notion of a statistical error is an integral part of hypothesis testing.
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