Overview: Analysis of Variance

The functions described in this chapter are for commonly-used experimental designs. Typically, responses are stored in the input vector y in a pattern that takes advantage of the balanced design structure. Consequently, the full set of model subscripts is not needed to identify each response. The functions assume the usual pattern, which requires that the last model subscript change most rapidly, followed by the model subscript next in line, and so forth, with the first subscript changing at the slowest rate. This pattern is referred to as lexicographical ordering.

The IMSL_ANOVA1 function allows missing responses if confidence interval information is not requested. NaN (Not a Number) is the missing value code used by these functions. Use IMSL_MACHINE to retrieve NaN. Any element of y that is missing must be set to NaN. Other functions described in this chapter do not allow missing responses because the functions generally deal with balanced designs.

As a diagnostic tool for determination of the validity of a model, functions in this chapter typically perform a test for lack of fit when n (n > 1) responses are available in each cell of the experimental design. Functions in Chapter 14, "Regression" are used for analysis of generalizations of the models treated in this chapter. In particular, Chapter 2: Regression, also provides functions for the general linear model.