Norman Thomson ‘Understanding ANOVA the APL Way’

Transcribed from the printed issue; not yet reviewed. Read it in the PDF of the issue, page 93

Norman is an expert and charming teacher and he began in characteristic style by saying that the consequence of devising the functions he was about to present was that he now feels that he understands ANOVA fully for the first time. The implication was also that the subject is a good deal simpler and more approachable than it has been made by professional teachers of statistics. Indeed this was the theme he was developing when he suddenly broke off to present his last slide in order to ensure that he would not run out of time before presenting his conclusions. This seemed to be an exercise in canny Scottish prescience because two minutes later the lecture was prematurely ended by a false fire alarm.

The paper contains all the functions, of course, beginning with the basic set,

Mean of a vector
Vector with mean substitution
Sum of squares about the mean
Mean polish of array — all axes
Fitted values following regression

These are then used to show how to perform:

One-way ANOVA
Two-way ANOVA
Multi-way ANOVA
Analysis of Variance following Regression

The use of the regression function is then developed in a discussion of orthogonal polynomials, regression with two-way data, multi-way ANOVA with regression and maximum decomposition of sums of squares. Finally an illustration is given of the application of the functions to experimental data.

To round it all off Norman provides a Summary of the Principal Functions,

one-way ANOVA
two-way ANOVA
multi-way (main effects)
multi-way (all effects)
multi-way interactions
1-way with linear regression
1-way with polynomial regression
2-way with polynomial regression
multi-way polynomial regression
2-way total decomposition
Balanced incomplete block designs
Latin & Youden squares

For maximum impact the following message should be projected as large as possible on the wall at stage back and the lecturer should leave the podium without further comment, allowing the audience to draw its own conclusions.

'These functions have been fully described and their use illustrated in less than ten pages. They are fully sufficient to deal with the computational needs of the many and varied exercises in one of the best known current textbooks "Design and Analysis of Experiments", Douglas C. Montgomery, 3rd edn., John Wiley & Sons, 1991'

Yet we wonder why APL is not popular with the Educational Establishment?