4*4

APPENDIX I

Thus, with the above table, we first estimate and check the values for
£R1V 2y?M, . . ., 272^, as follows:

TABLE XII

[ 5-76]
3-60
1-44
10-80

3*6°
[2<25]
•90
675

1*44
•90
[•36]
270

Total .
10-80
675
270
20-25 = 4-5*

Quotient
2-40
1-50
-60

Square .
s-76
2-25
.36

The saturation coefficient for (say) the first test is then :

__ i*89'V/20'25

Tle ^ 20-25 - (S-T^Ti^+i-l?)
= -90 as before.

(3) GENERAL-FACTOR METHOD

Suppose now that the discontinuities in the tables of observed
correlations had not seemed quite so obvious, and that we had
decided to apply the more usual * general-factor method * instead :
what results should we have obtained f

' I shall leave the reader to carry out, as an exercise for himself,
the detailed calculations according to the instructions given above,1
He will find satisfactory results are reached if he fills the diagonal
with the values for the ' communalities* supplied by the group-factor
analysis. Table XI, A and B, give the final figures, viz, the satura-
tions obtained by simple and by weighted summation respectively.
As before, the peculiarity of the simple-summation method is
that the totals of the bipolar saturations add up to exactly zero,
and of the weighted summation method that the bipolar columns are
uncorrelated both with each other and with the column for the

l The only novel feature arises in the treatment of the residuals obtained after the
nrst or general factor has been eliminated. In this case it is impossible, by means of
negative weighting, to convert all the negative residuals into positive. As before,
the choice of tests to be negatively weighted is determined by the general pattern
and checked by the signs of the resulting saturation coefficients* Here the computer
who followed the usual rules alone (reversing tests with most negatives or largest
tS^Lu*e \ ls) mif^ b* temPuted to give the 5th test an opposite staa to the others
Sv^S? ^UF£-' an(? P^haps the 8th an opposite sign to the others in the last
SnSL 3^i i -s wo,ul<^vidently spoil the pattern. It may be that such results
as this partly explain why those who follow Thurstone's modification of the summa-
tion method have supposed that its results must be meaningless until rotated.