ANALYSIS OF ILLUSTRATIVE GROUP 397

exceedingly simple. Accordingly, partly to make the
principle plain and partly because the identity of the results
has been questioned, it will be worth while to exhibit it
in a specific instance. Incidentally, the process will supply
us with a far clearer notion of what the so-called saturation
coefficient for persons really means.

What is implied in the procedure I am proposing may perhaps
best be understood as follows. Let us recollect that, when we
were following the old method of correlating traits with a view to
discovering specific factors and types, the great difficulty that
always confronted us from the outset was to eliminate the differ-
ences in average or general emotionality. The recognized statistical
device was to apply partial correlation ; this was equivalent to
estimating each person's general emotionality by a weighted average
of his measurements for the separate emotional traits, and deducting
this estimate. Now, in statistical work it is a familiar^ experience
that a weighted average seldom differs greatly or even significantly
from an ordinary or unweighted average ; and when we turn to
correlate persons, we regularly begin by deducting the unweighted
average for each person from his several measurements before we
convert them to terms of the standard deviation.

Let us therefore make this step explicit. Ignoring any suggest-
ions for weighting, let us accept the plain average of each person as
a fair assessment of his general emotionality, and eliminate all
individual variation in that respect by the simple process of sub-
traction. Table III gives the result of this elimination, the
remainders or residuals being reduced to standard measure. At
this point the computer might go on to cross-multiply all the
columns, each with each, and so obtain correlations between persons
as before. This, however, is not required. Instead he is asked to
regard these standardized residuals as forming approximate
measurements for each person in the second or more specific
factor which remains after his general emotionality has been
deducted and is responsible for the classification into temperamental
types.1 Accordingly, to obtain an indication of each ideal type

i Actually, it may be said, the measurements must include not only errors,
but also measurements of any further factor, for we have only eliminated
the first: to eliminate the third and later factors we should have to apply the
method of least squares, which alone yields uncorrelated saturations. Here,
however, we are content to suppose (as is assumed by the summation method
of factor-analysis applied by Spearman, Thurstone, Stephenson, and others)
that the influence of the further factors will virtually cancel out when the
figures are averaged.