For small and moderate sample sizes, the equal variances version of the test provides an exact test of the equality of the two population means. Just as one reflexively asks about randomization, blinding, and controls when evaluating a study design, it should become second-nature to ask about normality and equal variances when preparing to use Student's t test. Formal analysis and simulations offer the following guidelines describing extent to which the assumptions of normality and equal population variances be violated without affecting the validity of Student's test for independent samples. The worst situation occurs when one sample has both a much larger variance and a much smaller sample size than the other. Serious distortion of the P value can occur when the skewness of the two populations is different.
Outliers can distort the mean difference and the t statistic.
They tend to inflate the variance and depress the value and corresponding statistical significance of the t statistic. These preliminary tests often detect differences too small to affect Student's t test. Since the test is such a convenient way to compare two populations, it should not be abandoned without good cause. Important violations of the requirements will be detectable to the naked eye without a formal significance test. The best approach is to transform the data to a scale in which the conditions are satisfied.