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In statistics, the Neyman-Pearson lemma states 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

is the most powerful test of size α for a threshold η. If the test is most powerful for all , it is said to be uniformly most powerful (UMP).

In practice, the likelihood ratio itself is not actually used in the test. Instead one computes the ratio to see how the key statistic in it is related to the size of the ratio (i.e. whether a large statistic corresponds to a small ratio or to a large one).

Contents 1 Example 2 See also 3 References 4 External links

[edit] Example

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[edit] See also

• Statistical power
• Receiver operating characteristic

[edit] References

• Jerzy Neyman, Egon Pearson (1933). On the Problem of the Most Efficient Tests of Statistical Hypotheses. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character 231: 289-337.
• cnx.org: Neyman-Pearson criterion

[edit] External links

• MIT OpenCourseWare lecture notes: most powerful tests, uniformly most powerful tests

This page uses content from the English-language version of Wikipedia. The original article was at Neyman-Pearson lemma. The list of authors can be seen in the page history. As with Psychology Wiki, the text of Wikipedia is available under the GNU Free Documentation License.