P-, Q-, AND R-TECHNIQUES 181

I have in front of me a mark-sheet giving marks gained by all the
boys in a certain school in all the subjects taught at that school.
The headmistress tells me she is interested in the way two subjects
vary together, particularly the way composition seems to depend on
reading. How, she asks, can one predict the mark in composition
for any child from his mark in reading ? To solve her problem I
must correlate the two tests, and compute the appropriate regression
equation. But now, she tells me, she is also interested in the way
the marks for two pupils often correspond : Richard, the mentally
defective, like Hugh, his normal twin, is much better in manual
subjects than in verbal, and worst of all at arithmetic. How (we
may suppose her to inquire) can she predict Richard's probable
mark in any test from Hugh's ? To solve this second problem I
must now correlate the two persons. Moreover, I claim (and here
I differ from Stephenson) that this can be done quite legitimately
with the same set of data. Provided the two types of problem are
kept distinct, I see no * inconsistency' or * confusion' in changing
the standpoint, transposing the labels, and treating the former
variables as constants, and the former constants as variables. The
incidence of the word * any' indicates which of the two classifica-
tions is taken for the moment as providing the ' variables,' and the
transverse classification then represents the * population * or
universe. If I seek to express any value of a given test-performance
as a function of another given test-performance, then the two tests
are the * variables ' (dependent and independent respectively) and
the aggregate of the values for the different children make up the
* population.' If I seek to express any value of a given child's
test-performances as a function of some other given child's test-per-
formances, then the persons are the ' variables ' and the aggregate
of the values of their performances in the different tests must now
be called the * population.'

I do not deny that, if we are to use the same twofold table for the
two different problems, then that table must first fulfil certain
conditions. As I myself have insisted, several attempts to apply
correlation to c persons' have been invalidated, because these
preliminary conditions have been disregarded. The point most
easily overlooked by the psychologist is that his set of tests or traits
are merely a sample of the total' population ' of traits belonging to
the same class, just as his group of persons are merely a sample of
the total population of persons belonging to the same class. But an
invalid application does not invalidate the procedure itself. The
situation is identical with that which occurs in the analysis of
variance. Some tables can be analysed for one criterion only ;