Most inferential statistics assume normal distributions. Although these statistical tests work well even if the assumption of normality is violated, extreme deviations from normality can distort the results. Usually the effect of violating the assumption of normality is to decrease the Type I error rate. although this may sound like a good thing, it often is accompanied by a substantial decrease in power. Moreover, in some situations the Type I error rate is increased.

There is a collection of tests called distribution-free tests that do not make any assumptions about the distribution from which the numbers were sampled. Thus the name, "distribution-free." The main advantage of distribution-free tests is that they provide more power than traditional tests when the samples are from highly-skewed distributions. Since alternative means of dealing with skewed distributions such as taking logarithms or square roots of the data are available, distribution-free tests have not achieved a high level of popularity. Distribution-free tests are nonetheless a worthwhile alternative. Moreover, computer analysis has made possible new and promising variations of these tests.