When the normality assumption for a parametric test is not met, we have 2 options: we can try to find a transformation to normality for the data, or we can use the equivalent nonparametric method, which has more relaxed assumptions about the data. The inferences from transformed data do not change; however, interpretation can be challenging.
Nonparametric methods use ranks to relax the assumption and facilitate testing, but the use of ranks results in loss of information. For this reason, nonparametric methods are usually limited to hypothesis testing rather than estimation of effects.
If the data are not normally distributed, a corresponding nonparametric test can be used, such as the median test or the rank sum test (Mann–Whitney U test). The median test is based on the use of medians, and the rank sum test evaluates whether 2 independent samples are from populations with the same distribution. Confidence intervals can be calculated, but this is not as straightforward as with normally distributed data; those tests are mainly used for hypothesis testing. The results with the median test and the rank sum test to compare, for example, the ages of a hypothetical sample of orthodontic patients across the sexes are shown in Tables I and II respectively, and both tests indicate that the ages between the female and male participants differ significantly.
| Greater than the median | Sex | Total | |
|---|---|---|---|
| Female | Male | ||
| No | 33 | 5 | 38 |
| Yes | 19 | 17 | 36 |
| Total | 52 | 22 | 74 |
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