GENERAL- AND GROUP-FACTOR METHODS 315

we may be left with two sets of positive saturations which really
belong to two different test-groups : the principle of one factor, one
ability, however, leads the investigator illogically to merge these two
groups into one.

But there is a further fallacy. Since all summation-factors
except the first express merely a contrast, the choice of signs is
arbitrary. For example, in Thurstone's table the last nine tests
fall into two sharply distinguishable groups, namely, the four
* numerical tests ' and the five ' performance tests.' Thurstone's
third centroid factor, with its opposite signs, brings out the difference
quite plainly. If, however, our positive signs are to indicate, not an
abstract distinction but a concrete ability, how are we to proceed ?
Are we to allot the positive sign to the first four tests on the ground
that their coefficients are somewhat larger, and regard the factor
as essentially a * numerical' factor ? Or are we to allot the
positive sign to the last five tests on the ground that they form the
majority, and so regard the factor as essentially a c visuo-kinaesthetic'
or c performance ' factor ? Thurstone himself, it would seem, seeks
to combine both principles by giving the positive sign to that group
of tests which yields the largest total saturation, whether due to
number or to size. But the slight divergence in the two totals is, as
we have noted, due simply to the rough estimate of the communali-
ties, and the continual substitution of the largest coefficient in the
column ; with an exact estimate the totals would be equal.

Yet, arbitrary though it is, once the choice for the positive sign
has been made, that seems to determine the subsequent interpreta-
tion.1 If the saturations which are arbitrarily made negative are
small, they are likely to be ignored. If they are large, the rotation
will perhaps not entirely suppress them, but postpone them to a
later factor. A glance at the results, however, shows that with the
postponement they are very apt to lose their importance. Here, for
instance, Thurstone has chosen to give negative signs to the Oppo-
sites tests and to the Performance tests. The result is that the
obvious group-factor common to the Opposites tests is overlooked ;
and some vaguer common factor has to be found for the three
contrasted tests, in spite of the fact that they have little or nothing

1 This may not be true of Thurstone's example, since the selection of axes
is based primarily on the geometrical diagram : however, the diagram is
admittedly not decisive by itself ([84], p, 169). The circular argument
criticized in the text is quite common in research theses, where the writers
frequently draw conclusions from the 'positive saturations,5 entirely for-
getting that the allocation of the positive sign has been arbitrarily made by
themselves.