Neyman-Pearson lemma

In statistics, the Neyman-Pearson lemma states that when performing a hypothesis test between two point hypotheses H₀: θ=θ₀ and H₁: θ=θ₁, then the likelihood-ratio test which rejects H₀ in favour of H₁ when

<math>\Lambda(x)=\frac{ L( \theta _{0} \mid x)}{ L (\theta _{1} \mid x)} \leq k \mbox{ where } Pr(\Lambda(X)\leq k|H_0)=\alpha</math>

is the most powerful test of size α. The lemma is named for Jerzy Neyman and Egon Pearson. In practice, most of the time, the likelihood-ratio itself is not actually used in the test. Instead one computes the ratio to see how the key statistic 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)

External links

• cnx.org -- Neyman-Pearson criterion