Statistics in a Nutshell, 2nd Edition

Chapter 13. Nonparametric Statistics

The basis of inferential statistics is parameter estimation, estimation of the parameters of a population from information gained from a random sample presumed to have been drawn from that population. Many of the most common statistical techniques rely on the underlying distribution being of a particular type, such as the normal distribution, for inferences made from the relevant statistical tests to be valid; hence, these techniques are called parametric statistics. What about scenarios in which you know or suspect that the population does not meet the assumptions for a particular statistical test? In these cases, a different set of statistical techniques, known as nonparametric statistics, can be used. These techniques are often known as distribution-free statistics because they make few or no assumptions about the underlying distribution of the data; some prefer the term “distribution-free-er” because some nonparametric tests do require assumptions about the population distribution, although those assumptions are generally less stringent than those made by common parametric tests.

Nonparametric statistics are often applied to data sets in which data has been collected as ranks rather than as raw scores, or rank data is substituted for raw scores due to concerns about the distribution of the raw data. Rank data by definition is ordinal, as discussed in Chapter 1, and should not be analyzed using procedures meant for interval- and ratio-level ...