WORKING METHODS FOR COMPUTERS 485

general factor, so that the weighted totals add up to zero.1 With the
former method the figures fit the observed two-place correlations
with discrepancies of less than -oi ; with the latter they yield a fit
that is even closer still. Thus the factor pattern furnished by general-
factor methods tends to be more economical or parsimonious than
the * simple structure ' furnished by the group-factor method or an
equivalent rotation. The reason is clear. Where the group-factor
method yields a factor with 6 zeros, the general-factor method will
substitute a factor with 6 negative figures (as well as the 3 positive
figures appearing in both), so that this latter is helping to do the
work of a second group-factor; and the negative figures of the
two bipolar factors will between them dispense with the need for
a third group-factor,

It is evident that the two main forms of analysis lead to virtually
the same conclusions. The results may be summed up as follows: (i)
All the nine tests are influenced by a general factor whose importance
decreases from one test to another in a definite order, the order being
the same with all three methods. (2) The nine tests can be divided
into three groups of three, each group being influenced positively by
a different factor from the rest, the division being the same with all
three methods : thus, with each method we see (i) that the last three
tests are influenced positively by a large special factor which does
not enter positively into the first six; and (ii) the middle three tests
are influenced by a smaller special factor which does not enter
positively into the first three and does not enter at all into the last
three (or hardly at all) ; moreover, since we may reverse the signs
for the last bipolar factor, we may add (iii) the first three tests are in
effect influenced positively by a still smaller special factor, which
does not influence the middle three in the same way and does not
enter at all into the last three (or hardly at all). Finally, (3) within
each group of three the influence of its special factor diminishes from
one test to another in an order which is the same with all three
methods. The chief difference between the results of the group-factor
method and those of the two general-factor methods is that the
former assumes that a non-positive influence is identical with a
complete absence of influence, the latter assumes that it may be a
negative influence and may vary in amount.

Now, if we prefer the former method of expression, but start with
a summation method of analysis, we can obviously translate our
bipolar general factors into group-factors by ' rotation of axes/
Thus, if we started (as Thurstone would do) by the simple summa-
tion method, we could * rotate ? the factors shown in Table X!A,

1 With ' weighting * defined as on p, 456, this holds of both methods.