High Quality Content by WIKIPEDIA articles! In statistics, the Neyman-Pearson lemma states that when performing a hypothesis test between two point hypotheses H0: ? = ?0 and H1: ? = ?1, then the likelihood-ratio test which rejects H0 in favour of H1 when Lambda(x)=frac{ L( theta _{0} mid x)}{ L (theta _{1} mid x)} leq eta text{ where } P(Lambda(X)leq eta|H_0)=alpha is the most powerful test of size ? for a threshold ?. If the test is most powerful for all theta_1 in Theta_1, it is said to be uniformly most powerful (UMP) for alternatives in the set Theta_1 , . It is named for Jerzy Neyman and Egon Pearson. In practice, the likelihood ratio is often used directly to construct tests — see Likelihood-ratio test. However it can also be used to suggest particular test-statistics that might be of interest or to suggest simplified tests — for this one considers algebraic manipulation of the ratio to see if there are key statistics in it is related to the size of the ratio (i.e. whether a large statistic corresponds to a small ratio or to a large one).

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