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Following K. Pearson to test the general linear hypothesis

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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 \(\varvec{U}\) that has expected value \(\varvec{0}\) under the null hypothesis and form from it \(\varvec{U}^{\prime }[\mathrm {Var}(\varvec{U})]^{-1}\varvec{U}\), which, if \(\varvec{U}\) 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 \(\varvec{0}\) under the null hypothesis. Dominance relations among this class in terms of power are examined, and a complete subclass is described.

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  1. LSU Health - New Orleans, School of Public Health, 2020 Gravier St., New Orleans, LA, 70112, USA

    Lynn Roy LaMotte

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  1. Lynn Roy LaMotte
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Correspondence to Lynn Roy LaMotte.

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LaMotte, L.R. Following K. Pearson to test the general linear hypothesis. Stat Papers 61, 71–83 (2020). https://doi.org/10.1007/s00362-017-0924-6

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  • DOI: https://doi.org/10.1007/s00362-017-0924-6

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