Does your data violate t test assumptions?

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If the populations from which data to be analyzed by a t test were sampled violate one or more of the t test assumptions, the results of the analysis may be incorrect or misleading. For example, if the assumption of independence is violated, then the two-sample unpaired t test is simply not appropriate, although another test (perhaps the paired t test) may be appropriate. If the assumption of normality is violated, or outliers are present, then the t test may not be the most powerful test available, and this could mean the difference between detecting a true difference or not. A nonparametric test or employing a transformation may result in a more powerful test. If the population variances are unequal, the Welch-Satterthwaite t test provides means of performing a t test adjusted for the inequality of the variances. Often, the effect of an assumption violation on the t test result depends on the extent of the violation (such as the how unequal the population variances are, or how skewed one or the other population distribution is). Some small violations may have little practical effect on the analysis, while other violations may render the t test result uselessly incorrect or uninterpretable. In particular, small or unbalanced sample sizes can increase vulnerability to assumption violations.

Potential assumption violations include:



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