Welch's t test
In statistics, Welch's t test is an adaptation of Student's t-test intended for use with two samples having possibly unequal variances. As such, it is an approximate solution to the Behrens–Fisher problem.
Welch's t-test defines the statistic t by the following formula:
The degrees of freedom, , associated with this variance estimate is approximated using the Welch-Satterthwaite equation:
Here = , the degrees of freedom associated with the th variance estimate.
Once t and have been computed, these statistics can be used with the t-distribution to test the null hypothesis that the two population means are equal (using a two-tailed test), or the null hypothesis that one of the population means is greater than or equal to the other (using a one-tailed test). In particular, the test will yield a p-value which might or might not give evidence sufficient to reject the null hypothesis.
- Further reading
- Daniel Borcard, Lecture Note Appendix: t-test with Welch correction, excerpt from Legendre, P. and D. Borcard. Statistical comparison of univariate tests of homogeneity of variances.
- Sawilowsky, Shlomo S. (2002). "Fermat, Schubert, Einstein, and Behrens–Fisher: The Probable Difference Between Two Means When σ1 ≠ σ2". Journal of Modern Applied Statistical Methods 1 (2): 461–472.
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