Chapter 18 Distribution-Free Methods
Assumptions are the termites of relationships.
– Henry Winkler
18.1 Introduction
Most of the methods we have covered until now are based on parametric assumptions; the data are assumed to follow some well-known family of distributions, such as normal, exponential, or Poisson. Each of these distributions is indexed by one or more parameters (e.g., the normal distribution has µ and σ2), and at least one is presumed unknown and must be inferred. However, with complex experiments and messy sampling plans, the generated data might not conform to any well-known distribution. In the case where the experimenter is not sure about the underlying distribution of the data, statistical techniques that can be applied regardless of the true distribution of the data are needed. These techniques are called distribution-free or nonparametric. To quote statistician James V. Bradley (1968, p. 15):
The terms nonparametric and distribution-free are not synonymous, and neither term provides an entirely satisfactory description of the class of statistics to which they are intended to refer. . . . . Popular usage, however, has equated the terms. . . . Roughly speaking, a nonparametric test ...
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