148 On Polychoric Coe^cients of Correlation 
Wo have thus the values of' /' found from each coluuin*. 
We now turn to Table X and calculate in exactly the same way the values of 
x',s' = % To + /• Ti T,' + ... + rp X Tp X' t; + 
for the /• peculiar to each column for that column. We thus obtain Table XIII. 
TABLE XIII. 
Values ofX'ss'for r of eadi Vertical Column. 
s' 
S = l 
s = 2 
s = 3 
s = 4 
s = 5 
s = 6 
1 
2 
3 
4 
6 
6 
7 
- -013,707,54 
-•021,315,40 
- -000,771,58 
+ -000,880,04 
+ -000,759,52 
+ -000,584,54 
+ -000,127,47 
- -044,362,34 
-•15.3,841,07 
- -008,202,77 
+ -014,176,58 
+ -013,488,41 
+ -011,211,78 
+ -002,739,83 
- -013,376,98 
- -074,192,36 
- -004,826,27 
+ ■018,829,61 
+ -024,318,82 
+ ■031,232,08 
+ ■015,206,16 
- ^002,394,74 
- ^029,418,02 
-•002,225,87 
+ •015,680,02 
+ -022,680,28 
+ -032,630,32 
+ •017,131,65 
- -000,770,04 
- -009,240,63 
- -000,633,67 
+ •005,954,01 
+ ^009,395,75 
+ •015,-526,73 
+ -010,878,46 
- ^000,212,73 
- ^006,036,02 
- -000,217,60 
+ -008,797,09 
+ •016,257,72 
+ -032,207,15 
+ ■028,515,80 
- -000,006,10 
- -000,641,41 
+ -000,030,11 
+ -001,837,83 
+ -004,194.22 
+ -011,205,66 
+ -017,104,71 
kg. 
- -963,72 
- -507,66 
- ■010,29 
+ ^303,04 
+ •425,95 
+ -789,11 
+ 1-238,75 
The values in Table XIII divided by ?!.sv/hss' froni Table XIV and summed for 
each column give, on multiplication by Njiis., the ks. of the last row of the table. 
To obtain Table XIV we must return to Equation (x), use the appropriate r for 
the column and the values in Table III of ^j,. r.p t/. Taking ax and a-y as units 
of the horizontal and vertical variates we can plot kg. in Table XIII to hg. from 
Table XII and so obtain the regression line as formed by the means of each column, 
and set against it the regression lines as found from polychoric r.p = -5034, or '5204. 
TABLE XIV. 
Values 
of for 
"ss 
columnar 
Values of 
r. 
s' 
s = l 
s = 2 
s = 3 
s=4 
s=6 
s = 7 
1 
2 
3 
4 
5 
6 
7 
1 •481,160 
•850,270 
•910,673 
1-846,116 
00 
00 
00 
•918,247 
•995,746 
1 ^075,087 
r016,776 
•866,469 
•980,885 
•454,171 
•881,901 
•946,290 
1 ^090,803 
1 ^066,432 
1-028,801 
■887,677 
■808,851 
00 
1 •319,975 
•830,945 
•856,640 
•992,395 
1 •263,099 
1 •368,315 
•366,2.58 
1^351,776 
•853,291 
•855,012 
•968,288 
r61 9,040 
•848,918 
00 
1^261,565 
•876,250 
1 ^248,823 
r018,112 
•803,917 
r316,691 
00 
00 
1^668,232 
•600,417 
•937,952 
•999,089 
1^074,517 
* The mean value of r weighted with the column totals is •SOaS which is in reasonable accord with 
(i.e. within the probable error of) the results on p. 14'2. 
