ANOVA was developed by the English statistician, R.A. Fisher (1890-1962). Though initially dealing with agricultural data[1], this methodology has been applied to a vast array of other fields for data analysis. Despite its widespread use, some practitioners fail to recognize the need to check the validity of several key assumptions before applying an ANOVA to their data. It is the hope that thi...

Functional ANOVA models are considered in the context of generalized regression, which includes logistic regression, probit regression and Poisson regression as special cases. The multivariate predictor function is modeled as a speci ed sum of a constant term, main e ects and interaction terms. Maximum likelihood estimates are used, where the maximizations are taken over suitably chosen approxi...

A grouping or blocking of observations can be achieved by using categorical or dummy variables. Examples of categorical variables include gender, country of origin, job title and experimental treatment. This should be contrasted with ordinal variables, such as age class, highest degree attained or a score on a 5-point scale with values comprised between strongly agree and strongly disagree. The...

The author proposes some simple diagnostics for the assessment of the necessity of selected model terms in smoothing spline ANOVA models; the elimination of practically insignificant terms generally enhances the interpretability of the estimates, and sometimes may also have inferential implications. The diagnostics are derived from Kullback-Leibler geometry, and are illustrated in the settings ...

ANOVA decompositions are a standard method for describing and estimating heterogeneity among the means of a response variable across levels of multiple categorical factors. In such a decomposition, the complete set of main effects and interaction terms can be viewed as a collection of vectors, matrices and arrays that share various index sets defined by the factor levels. For many types of cate...