CRITICISMS OF METHODS 381

remains so dependent on an arbitrary choice. This difference of
zero point, or (as it may be called) of average level, operates as a
general factor, and has to be eliminated, either statistically by what
is virtually partial correlation (crude or precise), or experimentally
by selecting a sample in which the averages are approximately the
same for every individual. In my article I chose the latter. My
chief reason was that, by avoiding differences in the irrelevant
' general factor ' from the outset, and working with a relatively
homogeneous population, the graded differences of type would stand
out more conspicuously.

Stephenson does not apparently criticize this choice : for he
himself has proposed it as being " the simpler case to examine." l
In his subsequent calculations, too, he commonly treats the general
factor for persons, introduced by differences between the averages
for the traits, as non-existent or at any rate as negligible. Each
mental type, he believes, is so sharply differentiated from the rest
that, with his modified technique, he can proceed at once to extract
the relevant type-factors, without needing to eliminate a general

1 [97]> P* 34-8- Here, in his own account of Q-technique, he proposed first
to reduce the scores to deviations about the means of the columns and then to
reduce the new deviations to deviations about the means of the rows. He
then assumed, for purposes of a simplified exposition, that -with such a mode
of calculation it was " possible, although unlikely," that a set of scores
could be obtained which " will satisfy both conditions (3) and (4.) *' (viz.
Exij = o and Sxq — o), i.e. that the marks for each person and for each

* 3

test should simultaneously add up to zero. This was, in fact, the mode of

* standardization ' I had described in suggesting an analysis by covariances,
though it differs from the mode of standardization ultimately preferred by
Stephenson (Psychometrika, loc. cit. sup.).

The supposed difficulty to which Stephenson here alludes has been
raised by more than one research student (e.g. by Miss Knowles in her

* Studies of Temperamental Traits by Q-Technique s)> Obviously it is
" possible " to write down an arbitrary set of figures which will satisfy both
conditions (3) and (4.); but, they ask, is not such a result " unlikely," except
for a " few very special sets of figures " ? Suppose we take an actual set of
measurements and £ standardize' the figures by columns, so as to satisfy
equation (3) ; we then proceed to restandardize the figures by rows; to do
this, we subtract a different figure from each figure down the column: surely,
it is argued, except for rare and unlikely cases, this must upset the original
standardization which made that column add up to zero. Stephenson him-
self makes a somewhat similar point. The reply, of course, is that the
column of averages subtracted themselves necessarily add up to zero : con-
sequently, although the individual figures in each column are changed, the
total of the column remains unchanged. The result, therefore, is not
" unlikely " j it is an inevitable result of the mode of calculation described.