Neyman-Pearson lemma

Named after Jerzy Neyman and Egon Pearson.

Neyman-Pearson lemma

1. (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 ${\displaystyle \Lambda (x)={\frac {L(\theta _{0}\mid x)}{L(\theta _{1}\mid x)}}\leq \eta }$ where ${\displaystyle P(\Lambda (X)\leq \eta \mid H_{0})=\alpha }$ is the most powerful test of size α for a threshold η.