A General Algorithm for Analysis of Variance

Abstract

SUMMARY The general method of analysis of variance described by Wilkinson (1970) is reviewed. The implementation of an algorithm based on this method is described with particular attention to the doubly linked binary tree used to store information about the design. WILKINSON (1970) described a general analysis-of-variance method which enables a single algorithm to analyse most common experimental designs. These designs include all ortho- gonal designs (possibly with several error terms), designs with balanced confounding and other designs with a specified pattern of confounding. The normal equations are not solved directly but by sequentially sweeping a working variate which initially contains the data values. The sweep operation calculates effects for a particular term of the linear model from the working variate and uses them to modify it as described below. The algorithm has been implemented as part of the Genstat system (Wilkinson and Rogers, 1974; Nelder et al., 1975). In this paper we review the methods of analysis, explaining how the necessary sequence of sweeps is determined automatically, so that the user only defines the error and treatment terms to be included (together with the treatment combinations applied to each experimental unit). We describe some of the facilities of the program, and how they are implemented, paying