
Why Welchs test is Type I error robust
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Doi:
10.20982/tqmp.12.1.p030
Derrick, B.
, White, P.
3038
Keywords:
Independent samples ttest
, Welchs test
, Welchs approximation
, BehrensFisher problem
, Equality of means
(no sample data)
(no appendix)
The comparison of two means is one of the most commonly applied statistical procedures in psychology. The independent samples ttest corrected for unequal variances is commonly known as Welchs test, and is widely considered to be a robust alternative to the independent samples ttest. 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.
