"Distribution-Free": A Misleading Term

My third warning [in Chapter 18] 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 discussed 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 18, p. 496)

 

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Schuyler W. Huck
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