CORRELATIONS BETWEEN PERSONS 291

laboratory with the help of several of our research students.
Stephenson's interpretation of these results led him, as we shall see
(chap, xix), to reject the * reciprocity principle,' and to maintain
that the * type-analysis' by correlating persons could no longer be re-
garded as the * obverse ' of the older psychometric procedure, i.e.
of the factorization of correlations between traits (; Postscript' to
[96], p. 206). Indeed, so different in his opinion are the factors
obtained by correlating persons and traits that he now considers
" no analysis of a set of measurements can be considered complete
until it has been analysed both ways " ([97], p. 36I).1

With his criticisms of the principle I shall deal more fully in
a later chapter. Meanwhile, as I have already observed (p. 191), in
spite of minor changes in tests, traits, and statistical procedure, the
various c type-factors * obtained by Stephenson, whether cognitive,
temperamental, or aesthetic, appear after all to be very similar to
those already obtained with the alternative procedure. Let me add,
I do not for one moment deny that it is possible to invent a factorial
technique which will always lead to different sets of ' factors 9 when
applied to correlations between tests and between persons respec-
tively. But I see no advantage in multiplying such entities un-
necessarily. On the contrary, the difficulty about the methods of
factorial analysis hitherto proposed is that they allow us too much
liberty in selecting our final factors. And one great advantage of
the reciprocity principle, as it seems to me, is that, if we adhere to it
on grounds of economy, it may enable us to narrow down that
selection and even render it unique.

Since the foregoing paragraphs were written, Thomson's
admirable book on The Factorial Analysis of Human
Ability has appeared. In it he discusses, at some length
and with his usual combination of lucidity, impartiality,
and critical insight, what he terms the c reciprocity of tests
and persons * ([132], chaps, xiv and xix). He does not,
as Stephenson appears to do, deny that the factorization
of the two sets of correlations can ever lead to the same

1 Among the results of the researches carried out under his guidance he
cites those of J. I. Cohen. The data and methods then employed
were hardly adequate to test the issue; and the completed investigations
show a clear correspondence between the two sets of factors (a correlation
of about *9, according to his unpublished thesis. University of London
Library). P. C. Hu has applied both procedures to Stephenson's own
data, obtained with picture cards of Japanese vases; and obtains a similar
agreement.