"Distribution-Free": A Misleading Term

Our third warning [in Chapter 21] concerns the term "distribution-free," a label that is sometimes used instead of the term "nonparametric." As a consequence of these terms being used as if they were synonyms, many applied researchers are under the assumption that nonparametric tests work equally well no matter what the shape of the population distribution(s). This is not true for the two reasons we have touched upon earlier. On the one hand, the power of each and every nonparametric test varies depending upon the shape of the population distribution(s). On the other hand, the proper meaning of a rejected null hypothesis is frequently influenced by what is known about the distributional shape of the populations.

(From Chapter 21, p. 674)

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Schuyler W. Huck
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