Neyman-Pearson lemma

(statistics) A lemma stating 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 𝛬(x)=(L(𝜃₀∣x))/(L(𝜃₁∣x))≤𝜂 where P(𝛬(X)≤𝜂∣H_0)=𝛼 is the most powerful test of size α for a threshold η.