ABSTRACT
Introductory statistics textbooks in psychology and education typically recommend that parametric tests such as t and F be replaced by nonparametric alternatives under three conditions: (a) when the assumption of normality is violated, (b) when the assumption of homogeneity of variance is violated, and (c) when the scale of measurement is an ordinal scale and not an interval scale. However, there is disagreement among authors as to how severe a violation has to be before a parametric test should be replaced. Many authors consider parametric tests to be robust and do not recommend alternatives unless one of the first two violations just mentioned is quite severe. Others believe that the bulk of data in psychology and social sciences is best analyzed using nonparametric methods. Perhaps a majority of textbook writers convey the impression that parametric tests are preferable when assumptions are fulfilled to a good approximation, because parametric tests are thought to be more powerful than their nonparametric counterparts under normal theory.
