270 
On Theories of Association 
Therefore Q exhibits an increase of about 33°/ 0 'on the variability of tetrachoric r t . 
If we take the probable error test 
. , .r ( - weighted mean r t _ , _ . 
Average value of : — n = lr.oo, 
° probable error 
a i f Q — weighted mean Q , „ - _ 
Average value ot — = lo\L9. 
° probable error 
Thus Q represents an increase of 40°/ o on the variability of r t . 
(E) Correlation of Hair and Eye Colours. Livi's Dataf. 
The table is : 
Eye-Colour. 
53 
O 
o 
O 
Blue 
Grey 
Brown 
Black 
Totals 
Blond 
9083 
8187 
7031 
217 
24518 
Red 
343 
518 
819 
37 
1717 
Brown 
17829 
39467 
117522 
4945 
179763 
Black 
3627 
13433 
54883 
20919 
92862 
Totals . . . 
30882 
61605 
180255 
26118 
298860 
This table gives the following nine comparative results ; 
Blue-Grey 
Grey-Brown 
Brown-Black 
Blond-Red 
r t = -5307+ -0026 
§=•7442 ±-0023 
r t = -5074+ -0023* 
§=•7129 ± 0023 
rj=-4392+ -0054* 
Q= -8422 ± -0067 
Red-Brown 
r t = -5239+ -0030 
Q= -7356 ± -0023 
/(= -5255+ -0023* 
V=-7263± -0023 
r t = -4332+ -0048* 
§=•8294 ±-0067 
Brown-Black ... 
r t = -3601 + -0025 
§=■5791 ±-0041 
r t = -3240+ -0020 
Q= -4393 ± -0026 
r t = -6449+ -0020 
§= '8365 ± -0016 
Now it is of interest to compare the values of r, found by fourfold tables with 
those obtained by other methods. Mr Yule has nothing but the method of 
pseudo-ranks to apply to the table in its detailed form. This gives a Yulean 
•3680; the value found by corrected mean square contingency is '5189; the 
weighted mean of the nine tetraclioric r t values is '4842, much nearer to the 
contingency value. Indeed the Yulean, if corrected for ranks becomes '3953, and if 
corrected for class-index correlations becomes "5051, i.e. differs quite insignificantly 
f Antropometria militare, Part I. p. 62. 
* Mr Yule's values do not agree to the second decimal place with ours in these cases. 
