NATURE OF THE FACTORIAL TECHNIQUE 75

of course, that the test-results are expressed in comparable
units.

But the actual details of the calculations need not trouble
us for the moment. My point is that, whether we are con-
cerned with primary or secondary factors, the factor itself
always appears at the end in the character of an average or
sum, that is (prima facie, at any rate), as a synthetic rather
than an analytic result: and the purpose of the so-called
' analysis? is simply to find the best possible ways of grouping
the available tests so as to represent thisgeneralcharacteristic
or that, and the best possible weights to give to each test,
when we require something more than a rough approxima-
tion. It is during this preliminary sorting that the pro-
cedure takes on a more technical and, as we shall see, more
controversial appearance,

Factors as Patterns.—The simplest weights available
are + I, o, and — I. If we introduce no further differ-
entiation, we can still treat our factors as averages to be
obtained,by simple addition.

Consider, for example, the following set of traits extracted from a
rating-scheme, where pupils of school-leaving age were marked on
a standardized bipolar scale for a list of characteristics, including
the chief school subjects and McDougall's * primary emotions.'

Traits.
Factors.

General Intelligence.
General Emotionality.
Introversion.
Cheerfulness.

English Composition Problem Arithmetic .
+ 1
0 O
O O
O 0

Sociability Anger Tenderness
O 0
o
+ 1
— I — I
— I

Fear
• o
+ i
+ I
— I

In a previous investigation on vocational guidance it had been found
that the four f key qualities' which (a) were of greatest practical
importance, and (b) accounted for the greatest amount of variance
in a set of character-studies sent in by teachers, social workers, and
works' managers, were the ' general' factors of intelligence and