Statistics Toolbox

Robust and Nonparametric Methods

As mentioned in the previous sections, regression and analysis of variance procedures depend on certain assumptions, such as a normal distribution for the error term. Sometimes such an assumption is not warranted. For example, if the distribution of the errors is asymmetric or prone to extreme outliers, that is a violation of the assumption of normal errors.

The Statistics Toolbox has a robust regression function that is useful when there may be outliers. Robust methods are designed to be relatively insensitive to large changes in a small part of the data.

The Statistics Toolbox also has nonparametric versions of the one-way and two-way analysis of variance functions. Unlike classical tests, nonparametric tests make only mild assumptions about the data, and are appropriate when the distribution of the data is not normal. On the other hand, they are less powerful than classical methods for normally distributed data.

The following sections describe the robust regression and nonparametric functions in greater detail:

• Robust Regression
• Kruskal-Wallis Test
• Friedman's Test

Both of the nonparametric functions described here can return a stats structure that you can use as input to the multcompare function to perform multiple comparisons.

Note    See for information on another type of nonparametric regression.

Example: Generalized Linear Models

Robust Regression