Generalized p-value: Difference between revisions

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In [[statistics]], a '''generalized ''p''-value''' is an extended version of the classical [[p-value|''p''-value]], which except in a limited number of applications, provides only approximate solutions.

Conventional statistical methods do not provide exact solutions to many statistical problems, such as those arising in [[mixed model]]s and [[MANOVA]], especially when the problem involves a number of [[nuisance parameter]]s. As a result, practitioners often resort to approximate statistical methods or [[Asymptotic theory (statistics)|asymptotic statistical methods]] that are valid only when the sample size is large. With small samples, such methods often have poor performance.<ref name=WE/> Use of approximate and asymptotic methods may lead to misleading conclusions or may fail to detect truly [[Statistical significance|significant]] results from [[experiment]]s.

Tests based on generalized ''p''-values are exact statistical methods in that they are based on exact probability statements. While conventional statistical methods do not provide exact solutions to such problems as testing [[variance components]] or [[ANOVA]] under unequal variances, exact tests for such problems can be obtained based on generalized ''p''-values.<ref name=WE>Weerahandi (1995)</ref><ref name=TW>Tsui & Weerahandi (1989)</ref>