ANALYSIS OF ILLUSTRATIVE GROUP 399

itself, all that is necessary is to average a sufficiently large series of
such residuals for an appropriate selection of persons. To measure
the ideal extravert, we could average the figures for the half who
appear to verge in that direction (here A to F) ; to measure the
ideal introvert, we could average figures for the other half, who
appear to verge in the opposite direction (here G to L). This, in
effect, is the procedure followed by those who prefer to deal with
the two groups separately. If, however, we assume that intro-
version is the exact antithesis of extraversion, we may reach a
much better measurement for both by taking all the figures for the
group, first reflecting or reversing the signs for those belonging to
the second sub-group. The column of averages or sums thus
calculated will represent the theoretical measurements for the ideal
extravert type. The simple totals are appended in the last column
but one of Table III, and are reduced to ordinary standard measure
in the last column of all. To obtain analogous measurements for
the ideal introvert we have merely to reverse the signs.

At this point the theorist may be tempted to urge that we are
basing our figures for the type largely on persons who do not really
represent it. If the types were sharply separated, he will say, the
procedure might pass : but if a large number in the group are more
or less intermediate between the two, ought we not to omit them
altogether or at least give them a very low weight ? Before we
reply to this objection, however, let us accept the results provision-
ally, and see how closely (or how remotely) the different persons
actually correlate with them.

Taking each person in turn, then, we correlate his
residual marks with, the sums or averages of all the residual
marks, calculated as shown in Table III. The correlation
thus obtained should express the degree to which each
person approximates to the extraverted type. How far
do the figures obtained by this simple method agree with
those obtained by the previous and far more lengthy
procedure ? The correlations are given at the foot of
Table III. It will be seen that each correlation is not merely
an approximation to, it is identical with, the saturation co-
efficient for the same person as reached, by the more elaborate
method of inter con elating all the persons and, allying a
factor-analysis by the summation method?

2 To exhibit the exact arithmetical identity I have carried the calculations
to far more decimal places than the data would otherwise warrant. The