<P> Welch's t - test can also be calculated for ranked data and might then be named Welch's U-test . </P> <P> Once t and ν (\ displaystyle \ nu) 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 alternative hypothesis that one of the population means is greater than or equal to the other (using a one - tailed test). The approximate degrees of freedom is rounded down to the nearest integer . </P> <P> Welch's t - test is more robust than Student's t - test and maintains type I error rates close to nominal for unequal variances and for unequal sample sizes under normality . Furthermore, the power of Welch's t - test comes close to that of Student's t - test, even when the population variances are equal and sample sizes are balanced . Welch's t - test can be generalized to more than 2 - samples, which is more robust than one - way analysis of variance (ANOVA). </P> <P> It is not recommended to pre-test for equal variances and then choose between Student's t - test or Welch's t - test . Rather, Welch's t - test can be applied directly and without any substantial disadvantages to Student's t - test as noted above . Welch's t - test remains robust for skewed distributions and large sample sizes . Reliability decreases for skewed distributions and smaller samples, where one could possibly perform Welch's t - test on ranked data . </P>

What is the main consideration for conducting a student’s t-test or welch's t-test
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