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).
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