WORKING METHODS FOR COMPUTERS 479

3. Mark off the square blocks, as shown in the table, and prolong
the lines of separation so as to partition the entire table into rect-
angular sub-matrices. Unless there is considerable overlapping, the
lines of separation will be clearly shown by the sudden rise or fall of
correlations, e.g. in rows 4 to 6 of the correlation matrix the correla-
tions rise from the 3rd column to the 4th (instead of decreasing),
and fall from the 6th to the yth much more sharply than in rows I to
3. Similarly, in rows 7 to 9 they rise from the 6th column to the
7th. We may label these sub-matrices according to the usual
notation for a partitioned matrix as follows :

n

21

^22
$32

The square blocks lying along the leading diagonal (Rn, £22,
contain correlations affected by group-factors as well as by the first
factor* Hence these blocks must be omitted from all the calculations
for the first factor. As shown at the head of this section, a slight
but obvious complication in the primary summation formula is
entailed by these omissions.

4. Add each short column in each of the oblong blocks in order to
obtain its sub-total (1*35, 1-20, etc.).

5. Add the sub-totals to obtain the total for each block :

. (2&H «= 3-60, SR^ = i-44, ZR^ « -90).

6. Find the (curtailed) totals for each column (i,e, the totals
obtained with the figures in the square diagonal blocks still omitted)
by adding the totals of the two half-columns (1-35 -f- *54 = 1-89,
etc.).

7. Calculate the divisor for the curtailed totals in each double
block from the square roots of the three block-totals, appropriately
arranged. Thus, for the total for the first column (1*89), which, is

one of the three columns making up the double block Da L

31
the divisor will be

Note that the figures inside the bracket are the totals of the two
blocks to which the curtailed column belongs, and the figure out-
side the bracket is the total for the third remaining block. We thus
obtain the following three divisors :