Nonparametric Statistics

Characteristics of Nonparametric Statistics

There are alternative statistical tests that make fewer assumptions concerning the data being examined. These techniques have been called distribution free-er (because many are not entirely free of distributional assumptions) or nonparametric tests. Common assumptions for nonparametric tests include the following:

• Like parametric tests, nonparametric tests assume independence of randomly selected observations except when the data are paired.
• Unlike parametric tests, the distribution of values for the dependent variable is not limited to the bellshaped normal distribution; skewed and unusual distributions are easily accommodated with nonparametric tests.
• When comparing two or more groups using rank tests, the distribution of values within each group should have similar shapes except for their central tendency (e.g., medians).
• There are no restrictions as to the scale of measurement of the dependent variable. Categorical and rankordered (ordinal) outcome variables are acceptable.
• The major focus of analysis in nonparametric statistics is on either the rank ordering or frequencies of data; hypotheses, therefore, are most often posed regarding ranks, medians, or frequencies of data.
• The sample sizes are often smaller (e.g., n ≤ 20).

Types of Nonparametric Tests

There are a wide variety of nonparametric statistical tests that are available in user-friendly computer packages for use in epidemiology. Table 1 summarizes the most commonly used nonparametric tests, their purposes, the type of data suitable for their use, and their parametric equivalents, if any. The following is a brief overview of these statistics. For more details on these and other nonparametric tests as well as instructions on how to generate these statistics in various statistical packages, the interested reader is [Page 737][Page 738][Page 739][Page 740]referred to the texts on nonparametric statistics cited at the end of this entry.

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