WORKING METHODS FOR COMPUTERS

453

B. weighted summation method I r_as = - * -
y	2 S rtffi + 2r_ig
TABLE II
weighted intercorrelations and calculation of saturation
coefficients

Multipliers. | Products. | Total.
•90 | 729 | •648 | •567 | -486 | -405 |
•80 | •576 | -512 | -448 | •384 | •320 |
70 | •441 | •392 | •343 | •294 | •245 |
-60 | •3H | •288 | •252 | •216 | •180 |
•50 | -225 | •200 | -175 | •150 | •125 |
Totals 3-50 | 2-295 | 2-040 | 1785 | 1-530 | 1-275 | 8-925 -r 3-50 = 2-55
Sat. Coeffs.* | •90 | •80 | 70 | •60 | •50 | 3*5°
Squares | •81 | •64 | •49 | .36 | -25 | 2-55 (checks)
_rv .	Total of Products       8-925
Divisor = -= — - — ~~. .   .. . ,.~~ — = — ^-? = 2-55.
Total of Multipliers      3-500
etc, ;  2nd row :   -80 X 72 = ^576, etc.) ;  the products are shown
in the body of Table II.
3.	Add each column of products to obtain its total (2-295, 2-040,
etc*).
4.	Add the totals of the columns to obtain their grand total
-
5.	Add the trial multipliers or weights (saturation coefficients)
to obtain their total (3-50).
 6.	Divide the grand total of weighted correlations (8-925) by the
total of the weights  (3-50), obtaining the quotient 2-55.    This
should give the total of the variance contributed by the first factor.
 7.	Divide each weighted total by this quotient (2-295 ~ 2-55 =
'90, etc.),   The quotients so obtained give revised estimates for the
saturation coefficients as obtained by weighted summation.   They
should be approximately equal to the trial multipliers with, which we
started (-90, -80, etc.).    If not, the revised saturation coefficients
must be taken as trial weights, and the whole process repeated.
 8.	Square the final revised saturation coefficients.   The sum of the
squares (2-55) should give the total variance contributed by the
first factor and therefore be equal to the quotient obtained above in