Understanding ANOVA the APL way

ABSTRACT

Statistics text books expound the collection of techniques known as analysis of variance by using mathematical formulae. The term analysis of variance is something of a misnomer, since any analysis follows a primary exercise of partitioning sums of squares, which is entirely a matter of computation and data reorganization of the sort which APL is particularly adept at. The crux of the analysis stage then consists of making choices between what is often a bewilderingly large range of subtly different sums of squares partitions. The primitive function enclose with axis maps naturally into the data manipulations involved in sums of squares partitions for arrays. To the casual reader the latter are obscured rather clarified by the use of mathematical formulae alone. This paper explores the relationships between APL functions and ANOVA, and goes on to illustrate how these can be used in the context of a designed experiment.

REFERENCES

• 1: E 1 -1 G. Barrie Wetherill, Intermediate Statistical Methods, Chapman and tlall, 1981
• 2: Design and Analysis of E~periments, Douglas C. Monlgomery, 3rd. edn., John Wiley & Sons, 1991

INDEX TERMS

Primary Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: APL

Additional Classification:
  G. Mathematics of Computing
  G.3 PROBABILITY AND STATISTICS
      Subjects: Statistical computing

General Terms:
Languages