The Neyman-Pearson Lemma characterizes the most powerful statistical test for choosing between two simple hypotheses at a fixed significance level, showing that the optimal test rejects the null hypothesis exactly when the likelihood ratio between the two hypotheses exceeds a fixed threshold. Proved by Jerzy Neyman and Egon Pearson, it is a foundational result of the theory of statistical hypothesis testing.
Facts
StatementFor testing a simple null hypothesis against a simple alternative at a fixed significance level, the likelihood ratio test is the uniformly most powerful test, meaning no other test at the same significance level has greater power against the alternative. Jerzy Neyman and Egon Pearson introduced the result in a paper published in 1933. 2 Classification
Statement Form Connections
Sources
1. Wikipedia: Neyman-Pearson lemma
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
Their seminal 1933 paper, which includes the Neyman-Pearson lemma showed not only the existence of tests with the most power that retain a prespecified level of type I error ( α ), but also provided a way to construct such tests.
2. Neyman-Pearson Lemma (Wikipedia)
Wikimedia Foundationlead section, first paragraphQuote, lead section, first paragraph
In statistics, the Neyman-Pearson lemma describes the existence and uniqueness of the likelihood ratio as a uniformly most powerful test in certain contexts. It was introduced by Jerzy Neyman and Egon Pearson in a paper in 1933.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.