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Question

Why do we use nonparametric tests?
Under what circumstances would you use nonparametric tests?

Answer 1

Nonparametric tests are also referred to as distribution-free tests. These tests have the obvious advantage of not requiring the assumption of normality or the assumption of homogeneity of variance. They compare medians rather than means and, as a result, if the data have one or two outliers, their influence is negated.

Parametric tests are preferred because, in general, for the same number of observations, they are more likely to lead to the rejection of a false hull hypothesis. That is, they have more power. This greater power stems from the fact that if the data have been collected at an interval or ratio level, information is lost in the conversion to ranked data (i.e., merely ordering the data from the lowest to the highest value).

Occasionally, the assumptions of the t-tests are seriously violated. In particular, if the type of data you have is ordinal in nature and not at least interval. On such occasions an alternative approach is to use nonparametric tests.

Nonparametric tests are often used in place of their parametric counterparts when certain assumptions about the underlying population are questionable. For example, when comparing two independent samples, the Wilcoxon Mann-Whitney test does not assume that the difference between the samples is normally distributed whereas its parametric counterpart, the two sample t-test does. Nonparametric tests may be, and often are, more powerful in detecting population differences when certain assumptions are not satisfied.

All tests involving ranked data, i.e. data that can be put in order, are nonparametric.

Nonparametric, or distribution free tests are so-called because the assumptions underlying their use are “fewer and weaker than those associated with parametric tests” (Siegel & Castellan, 1988, p. 34). To put it another way, nonparametric tests require few if any assumptions about the shapes of the underlying population distributions. For this reason, they are often used in place of parametric tests if/when one feels that the assumptions of the parametric test have been too grossly violated (e.g., if the distributions are too severely skewed).

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