Why Welchs test is Type I error robust

The comparison of two means is one of the most commonly applied statistical procedures in psychology. The independent samples t-test corrected for unequal variances is commonly known as Welchs test, and is widely considered to be a robust alternative to the independent samples t-test. The properties...

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Vydáno v:	Tutorials in quantitative methods for psychology Ročník 12; číslo 1; s. 30 - 38
Hlavní autoři:	Derrick, B., White, P.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Université d'Ottawa 01.01.2016
Témata:	Behrens-Fisher problem Equality of means Independent samples t-test Welchs approximation Welchs test
ISSN:	1913-4126, 1913-4126
On-line přístup:	Získat plný text
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Shrnutí:	The comparison of two means is one of the most commonly applied statistical procedures in psychology. The independent samples t-test corrected for unequal variances is commonly known as Welchs test, and is widely considered to be a robust alternative to the independent samples t-test. The properties of Welchs test that make it Type I error robust are examined. The degrees of freedom used in Welchs test are a random variable, the distributions of which are examined using simulation. It is shown how the distribution for the degrees of freedom is dependent on the sample sizes and the variances of the samples. The impact of sample variances on the degrees of freedom, the resultant critical value and the test statistic is considered, and hence gives an insight into why Welchs test is Type I error robust under normality.
ISSN:	1913-4126 1913-4126
DOI:	10.20982/tqmp.12.1.p030