Welch's t test
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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.
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[edit] Formulas for t, ν
Welch's t-test defines the statistic t by the following formula:
where , and Ni are the ith sample mean, sample variance and sample size, respectively. Unlike in Student's t-test, the denominator is not based on a pooled variance estimate.
The degrees of freedom ν associated with this variance estimate is approximated using the Welch-Satterthwaite equation:
Here νi is Ni − 1, the degrees of freedom associated with the ith variance estimate.
[edit] Statistical test
Once t and ν 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.
[edit] See also
[edit] References
- Welch, B. L. (1947), “The generalization of "student's" problem when several different population variances are involved”, Biometrika 34: 28-35
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