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