200 THE FACTORS OF THE MIND

son has inflexibly insisted do not recognize the distinction
which the ' multiple-factor equations' preserve between the
first c universal' or ' general' factor (with positive satura-
tions for every correlated variable) and the secondary
' group ' or * bipolar ' factors, specifying groups or types.
Hence, for him, if a type-factor is not specific, it must be
general. Consequently, with his procedure my secondary
iy^^-factors became general factors (in practice nearly always
calculated for certain sub-matrices only) ; and conversely,
he has maintained, at any rate in his earlier papers, that my
general factors, when procured by correlating persons,
" could only indicate types," and therefore should really
have been type-factors.1 Thus he applies (rightly on his
premisses, wrongly on mine) everything that I have said
about secondary factors to the general factors as well, and
vice versa.

Conclusions and. Corollaries.—In conclusion, let me briefly
indicate what I take to be the logical nature of the difference
between us. At bottom, I think, the difference is due, like
so many controversies in factor-analysis, to a confusion
between two logical standpoints—namely, the analysis of
c intension ' with the analysis of ' extension.' In correlat-
ing traits we are (in the first stage) comparing the attributes
or traits that define certain classes; in correlating persons

1 This appeared still more plausible because, as explained above, in
repeating our experiments, he rejected our relatively heterogeneous test-
material, and substituted pictures, etc., that were far more homogeneous :
but such a modification must inevitably tend to eliminate the general factor
with which we were primarily concerned, and to throw into relief our
' secondary type-factors.' This equality (actual or assumed) in the difficulty
of the various tests explains a peculiarity that marks so many of the tables
obtained by correlating persons. Thomson suggests that " since Stephenson
has found numerous negative correlations between persons, and since few
negative correlations are reported between tests, we seem here to have an
experimental difference between the two kinds of correlation " ([132], p. 211).
But the experimental difference arises only when the investigator works with
tests or traits that have, or are assumed to have, the same average level for
the different persons: thus in the investigations to which Thomson alludes
the ' general factor for persons' had virtually been partialed out beforehand
or at least reduced in magnitude. Under these conditions, as I have else-
where explained, a " bipolar " table of coefficients is " apt to be the first to
appear when correlating persons " ([114], p. 167, cf, [130], p. 419).