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OPTIMAL TESTS OF SIGNIFICANCE
Author(s) -
Robinson J.
Publication year - 1979
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1979.tb01147.x
Subject(s) - test statistic , null hypothesis , one and two tailed tests , p value , statistics , statistical hypothesis testing , pearson's chi squared test , alternative hypothesis , mathematics , statistic , statistical significance
Summary To perform a test of significance of a null hypothesis, a test statistic is chosen which is expected to be small if the hypothesis is false. Then the significance level of the test for an observed sample is the probability that the test statistic, under the assumptions of the hypothesis, is as small, or smaller than, its observed value. A “good” test statistic is taken to be one which is stochastically small when the null hypothesis is false. Optimal test statistics are defined using this criterion and the relationship of these methods to the Neyman‐Pearson theory of hypothesis testing is considered.