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Definition 2024

Neyman-Pearson_lemma

Neyman-Pearson lemma

English

Proper noun

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