multidimensionality of the mental abilities.
Spearman's theory has been called a two-factor method or theory. The two factors involved in it
are, first, a general factor common to all of the tests or variables, and second, a factor that is
specific for each test or variable. It is less ambiguous to refer to this method as a single-factor
method, because it deals with only one common or general factor. If there are five tests with a
single common factor and a specific for each test, then the method involves the assumption of
one common and five specific factors, or six factors in all. We shall refer to his method less
ambiguously as a single-factor method.
We must distinguish between Spearman's method of analyzing the intercorrelations of a set of
variables for a single common factor and his theory that intelligence is such a common factor
which he calls "g". If we start with a given table of intercorrelations it is possible by Spearman's
method, and also by other methods, to investigate whether the given coefficients can be
described in terms of a single common factor plus specifics and chance errors. If the answer is
in the affirmative, then we can describe the correlations as the effect of (1) a common factor,
(2) a factor specific to each test, and (3) chance errors. In factor theory, the last two are
combined because they are both unique to each test. Hence the analysis yields a summation of
a common factor and a factor unique to each test. About this aspect of the single-factor method
there should be no debate, because it is straight and simple logic.
But there can be debate as to whether we should describe the tests by a single factor even
though one factor is sufficient. It is in a sense an epistemological issue. Even though a set of
intercorrelations can be described in terms of a single factor, it is possible, if you like, to
describe the same correlations in terms of two or three or ten or any number of factors.
The situation is analogous to a similar problem in physical science. If a particle moves, we
designate the movement by an arrow-head, a vector, in the direction of motion, but if it suits our
convenience we put two arrowheads or more so that the observed motion may be expressed in
terms that we have already been thinking about, such as the x, y, and z axes. Whether an
observed acceleration is to be described in terms of one force, or two forces, or three forces,
that are parallel to the x, y, and z axes, is entirely a matter of convenience for us. In exactly the
same manner we may postulate two or more factors in a correlation problem instead of one,
even when one factor would be sufficient. To ask whether there "really" are several factors
when one is sufficient, is as indeterminate as to ask how many accelerations there "really" are
that cause a particle to move. If the situation is such that one factor is not adequate while two
factors would be adequate, then we may think of two factors, but we may state the problem in
terms of more than two factors if our habits or the immediate context makes that more
convenient.
Spearman believes that intelligence can be thought of as a factor that is common to all the
activities that are usually called intelligent. The best evidence for a conspicuous and central
intellective factor is that if you make a list of stunts, as varied as you please, which all satisfy
the common sense criterion that the subjects must be smart, clever, intelligent, to do the stunts
well, and that good performance does not depend primarily upon muscular strength or skill or
upon other non-intellectual powers, then the inter-stunt correlations will all be positive. It is quite
difficult to find a pair of stunts, both of which call for what would be called intelligence, as
judged by common sense, which have a negative correlation. This is really all that is necessary
to prove that what is generally called intelligence can be regarded as a factor that is
conspicuously common to a very wide variety of activities. Spearman's hypothesis, that it is
some sort of energy, is not crucial to the hypothesis that it is a common factor in intellectual
activities.
There is a frequently discussed difficulty about which more has been written than necessary. It
has been customary to postulate a single common factor (Spearman's "g") and to make the
additional but unnecessary assumption that there must be nothing else that is common to any
pair of tests. Then the tetrad criterion is applied and it usually happens that a pair of tests in the
battery has something else in common besides the most conspicuous single common factor.