12Nonparametric Analyses

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Chapter Learning Objectives

  1. Parametric versus nonparametric analyses
  2. Chi‐square

Parametric Versus Nonparametric Analyses

All of the procedures covered in the previous three chapters are appropriately classified as inferential statistics, but the category of “inferential statistics” can also be further divided. One common division is between parametric and nonparametric inferential statistics. All of the previous inferential analyses (z‐test, t‐tests, ANOVAs, regressions, correlations) are considered parametric procedures because they either: (1) estimate a population parameter (for example, using the sample statistic [s] as an approximation of the population parameter [σ] as is done with t‐tests), or (2) are dependent on assumptions about an underlying population distribution (for example, that scores are distributed approximately normally).

Not every empirical situation is characterized by (at least) one of these above conditions, however. There are, therefore, statistical procedures that have been developed for situations where a population parameter is not estimated and no assumptions are made about underlying population distributions. This category of procedures is commonly given the label of nonparametric statistics. ...

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