Neyman-Pearson lemma

In statistics, the Neyman-Pearson lemma states that when doing 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.