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The Essentials of Biostatistics for Physicians, Nurses, and Clinicians,
First Edition. Michael R. Chernick.
© 2011 John Wiley & Sons, Inc. Published 2011 by John Wiley & Sons, Inc.

CHAPTER 9

Nonparametric Methods

Most of the statistical methods that we have covered in this book

have involved parametric models. The bootstrap, Fisher ’ s exact test,

and the chi - square test are the exceptions. A parametric model is one

that involves probability distributions that depend on a few parameters

(usually fi ve or less). For example, when we assume a normal distribu-

tion the parameters, it depends on are the mean and variance. We then

use the data to estimate the parameters, and we base our inference on

the sampling distribution for these estimates based on the parametric

model. But in many practical situations, the parametric model may be

hard to justify, or may be found to be inappropriate when we look at

the sample data.

Nonparametric methods on the other hand only assume that the

distribution function F is continuous. Ranking the data or considering

permutations of the data are two ways to construct test statistics that are

distribution free under the null hypothesis. Distribution free mean that

the distribution of the test statistic is known exactly when the null

hypothesis is assumed, and does not depend on the form or parameters

of the original data. So, for example, the sign test has a binomial distri-

bution with p = 1/2 under the null hypothesis, and Fisher ’ s exact test has

a specifi c hypergeometric distribution when the null hypothesis is true.