Nonparametric statistics

Nonparametric statistics is a branch of statistics that is not based solely on parameterized families of probability distributions. Nonparametric statistics differs from parametric statistics in that the former does not assume that the structure of a data-generating process has a known form. Nonparametric models differ from their parametric counterparts in that the former are characterized by a set of parameters of fixed dimension, regardless of the number of observations.

Overview

Nonparametric methods are widely used for studying populations that take on a ranked order (such as movie reviews receiving one to four stars). The use of nonparametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences. In terms of levels of measurement, nonparametric methods result in ordinal data.

As nonparametric methods make fewer assumptions, their applicability is much wider than the corresponding parametric methods. In particular, they may be applied in situations where less is known about the application in question. Also, due to the reliance on fewer assumptions, nonparametric methods are more robust.

Nonparametric models

Nonparametric models differ from parametric models in that the model structure is not specified a priori but is instead determined from data. The term nonparametric is not meant to imply that such models completely lack parameters but that the number and nature of the parameters are flexible and not fixed in advance.

A histogram is a simple nonparametric estimate of a probability distribution. Kernel density estimates are a more sophisticated way of doing the same thing, but also require a bandwidth to be chosen.

Nonparametric tests

Nonparametric tests are a subset of statistical tests. They do not rely on assumptions that the data are drawn from a given probability distribution. As such, they are sometimes referred to as distribution-free tests. The best-known nonparametric test is the Mann–Whitney U test, which can test whether two independent samples were drawn from a population with the same distribution.

See also

• Parametric statistics
• Descriptive statistics
• Statistical hypothesis testing
• Mann–Whitney U test