WORKING METHODS FOR COMPUTERS 461

Table IV reproduces the intercorrelations actually observed.
With only 6 tests, the correlation table should be completely ex-
plicable in terms of

r = |{ ^n + i) — V&M^i) = 3 factors.1

A. SIMPLE SUMMATION METHOD

I shall repeat the working instructions in full, partly for con-
venience of reference and partly because of certain special difficulties
that an actual problem inevitably entails.

(i) First Factor

Formula : Saturation coefficient ras — — \ as before.

vff*

1. Find the total intercorrelation of each test (2*19, 1-48, etc.),
by adding each column of observed coefficients.

2. With the aid of these totals rearrange the table so as to exhibit
the general trend or pattern as clearly as possible. The guiding
principles are, first, to bring correlations of the same size as near
together as possible, and secondly to keep the changes of size along
the rows or columns moving in the same direction and in parallel
directions, as smoothly and as continuously as possible. Here, if
the student begins by attempting to arrange the figures given above
in plain hierarchical order, he will at once discover that this
simpler pattern is disturbed by the low correlations between the
verbal group of tests and the manual group. Consequently,
although all the correlations are positive, we have to recognize at
least two high points of correlation instead of one, namely, at the
bottom right-hand corner as well as at the top left. This in turn
indicates that the totals should be arranged so as first to descend
and then to rise again.

We take the totals for (i) Composition, Reading, and Spelling,
in descending order, and those for (2) Handwork, Writing, and
Drawing, in ascending order. The rearrangement brings out an
effect that I have described as * cyclic overlap ' : z the correlations
near the leading diagonal tend to be higher than simple hierarchical
arrangement would require, and they also tend to rise, not only

1 This formula follows from the considerations set out on the preceding page : for
proof, see p. 109.

1 Loc. ctt., p, 59. If the student finds some difficulty in making a satisfactory
rearrangement, he may be content with a first approximation to begin with. Later
we shall see from the completed totals (last line but one) that it would have been
better to place Drawing at the end instead of Writing ; and this is confirmed by the
totals of the residuals (Table IV),