WORKING METHODS FOR COMPUTERS

453

B. WEIGHTED SUMMATION METHOD I ras = - * -

y 2 S rtffi + 2rig

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