P-, Q-, AND R-TECHNIQUES 173

i. The Disparity of Units of Measurement.—His main criticism *
is based on the fact that the units of measurement for different
tests are generally incommensurable. But that objection, as it
seems to me, comes from taking the word c test' too literally. For
purposes of expounding the alternative method it is no doubt
convenient to draw a sharp contrast between c persons ' and £ tests.'
Yet, after all, what we correlate when we ' correlate tests' are
measurements for certain persons' traits; and what we correlate
when we * correlate persons ' are in theory measurements for the
same traits in the same persons. The only difficulty, therefore, is
to select traits and to find units which shall be consistent with the
particular form of statistical analysis in view. After all, most
examiners, I imagine, would be quite as ready to compare the same
examiner's marks for different school subjects (or c tests ') as they
would be to compare different examiners' marks for the same
subject; and every teacher is continually contrasting the different
abilities of one and the same individual: ' John is much better at
Latin than he is at French'; * Joan did not do so well in the
arithmetic tests as she did in reading and dictation.' If, to take
Thomson's own instances of incommensurable measurements
(p. 201), the marks obtained in an * analogies test' were insuperably
disparate from those obtained in a ' dotting test' (i.e. if marks for
such tests could not possibly be transmuted into commensurable
units) how could we ever cross-multiply the figures to obtain the
product-moment correlation between those tests ?

But, it may be said, in correlating a couple of tests we begin by
averaging marks for the same test, whereas in correlating persons we
must first average marks from a number of different tests. How
can we average such figures if the units of measurement are dis-
similar ? As a matter of fact, the answer is still the same; and
Thomson himself really supplies it in an earlier chapter of his book
([132], pp. 114 f.). There he proposes to find a weighted average
for four such heterogeneous tests as picture completion, geometrical
analogies, a reading test, and the Stanford-Binet test: his method
is—first "we reduce the scores to standard measure" (p. 116).
Once the arbitrary measurements furnished by the tests have been
changed to standard measure, we can average the different tests
with or without an additional weighting. That is all that is required
for correlating by persons. This or its equivalent was, indeed, the
plan suggested in my Memorandum for the Examinations Inquiry
Council, namely, " first to reduce the crude scores to terms of the

1 With his discussion of an important side-issue—the so-called reciprocity
principle—I shall deal in Part III.