Neyman-Pearson Lemma

The Neyman-Pearson lemma gives the mathematically most powerful method for testing a simple hypothesis against a simple alternative at a chosen significance level, showing that a test based on the ratio of the likelihoods of the two hypotheses is least likely to miss a real effect for a given rate of false positives. Jerzy Neyman and Egon Pearson, the son of Karl Pearson, developed it as part of a broader framework for hypothesis testing, published in their 1933 paper On the Problem of the Most Efficient Tests of Statistical Hypotheses. Their framework, which formalizes a null and alternative hypothesis, a significance level fixed in advance, and the statistical power of a test, became the basis of the hypothesis testing procedure most widely taught and used in applied statistics today, developed partly in response to and partly in tension with Ronald Fisher's own approach to significance testing.