Following K. Pearson to test the general linear hypothesis

Lynn Roy LaMotte ()
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Lynn Roy LaMotte: School of Public Health

Statistical Papers, 2020, vol. 61, issue 1, No 4, 83 pages

Abstract: Abstract The numerator sum of squares in the conventional F-statistic for testing a linear hypothesis in a general linear model can be viewed as following the heuristic that K. Pearson used in his seminal 1900 paper. That is, find a statistic $$\varvec{U}$$U that has expected value $$\varvec{0}$$0 under the null hypothesis and form from it $$\varvec{U}^{\prime }[\mathrm {Var}(\varvec{U})]^{-1}\varvec{U}$$U′[Var(U)]-1U, which, if $$\varvec{U}$$U is approximately normal, can be approximated as a chi-squared random variable. The class considered here comprises all such statistics based on linear statistics that have expected value $$\varvec{0}$$0 under the null hypothesis. Dominance relations among this class in terms of power are examined, and a complete subclass is described.

Keywords: Power; F-tests; Linear models; 62J05; 62F03; 62H15 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00362-017-0924-6

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