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  2. Power (statistics) - Wikipedia

    en.wikipedia.org/wiki/Power_(statistics)

    Illustration of the power of a statistical test, for a two sided test, through the probability distribution of the test statistic under the null and alternative hypothesis. α is shown as the blue area , the probability of rejection under null, while the red area shows power, 1 − β , the probability of correctly rejecting under the alternative.

  3. Uniformly most powerful test - Wikipedia

    en.wikipedia.org/wiki/Uniformly_most_powerful_test

    In statistical hypothesis testing, a uniformly most powerful (UMP) test is a hypothesis test which has the greatest power among all possible tests of a given size α. For example, according to the Neyman–Pearson lemma , the likelihood-ratio test is UMP for testing simple (point) hypotheses.

  4. Statistical hypothesis test - Wikipedia

    en.wikipedia.org/wiki/Statistical_hypothesis_test

    An example of Neyman–Pearson hypothesis testing (or null hypothesis statistical significance testing) can be made by a change to the radioactive suitcase example. If the "suitcase" is actually a shielded container for the transportation of radioactive material, then a test might be used to select among three hypotheses: no radioactive source ...

  5. Neyman–Pearson lemma - Wikipedia

    en.wikipedia.org/wiki/Neyman–Pearson_lemma

    Neyman–Pearson lemma [5] — Existence:. If a hypothesis test satisfies condition, then it is a uniformly most powerful (UMP) test in the set of level tests.. Uniqueness: If there exists a hypothesis test that satisfies condition, with >, then every UMP test in the set of level tests satisfies condition with the same .

  6. Type I and type II errors - Wikipedia

    en.wikipedia.org/wiki/Type_I_and_type_II_errors

    The consistent application by statisticians of Neyman and Pearson's convention of representing "the hypothesis to be tested" (or "the hypothesis to be nullified") with the expression H 0 has led to circumstances where many understand the term "the null hypothesis" as meaning "the nil hypothesis" – a statement that the results in question have ...

  7. Sign test - Wikipedia

    en.wikipedia.org/wiki/Sign_test

    alternative =indicates the alternative hypothesis and must be one of "two.sided", "greater" or "less" conf.level = confidence level for the returned confidence interval. Examples of the sign test using the R function binom.test The sign test example from Zar [5] compared the length of hind legs and forelegs of deer. The hind leg was longer than ...

  8. One- and two-tailed tests - Wikipedia

    en.wikipedia.org/wiki/One-_and_two-tailed_tests

    A two-tailed test is appropriate if the estimated value is greater or less than a certain range of values, for example, whether a test taker may score above or below a specific range of scores. This method is used for null hypothesis testing and if the estimated value exists in the critical areas, the alternative hypothesis is accepted over the ...

  9. Likelihood-ratio test - Wikipedia

    en.wikipedia.org/wiki/Likelihood-ratio_test

    In statistics, the likelihood-ratio test is a hypothesis test that involves comparing the goodness of fit of two competing statistical models, typically one found by maximization over the entire parameter space and another found after imposing some constraint, based on the ratio of their likelihoods.