200 
On Theories of Association 
then to —"87. What information can the coefficient of association give us as to 
the nature of these two uncorrelated variates ? It is no doubt a measure in some 
manner of the heteroscedasticity of the arrays. But how and in what way does 
it measure this phase of want of independence by a value which varies from — 1 
to + 1 several times over ? If it in some manner measures this heteroscedasticity, 
it is only by its local values, it measures nothing of the dependence of the variates 
as a whole. Will Mr Yule tell us how to infer whether, when Q = + -87 or — "87, 
it is a measure of the relation between the means of the arrays corresponding 
to given variates, or is merely a measure of the differences in the variabilities of 
those arrays ? Will he also tell us in what manner, by a multiplicity of values, 
it measures mere heteroscedasticity ? 
Are we doing Mr Yule an injustice in taking any notice of Q at the extreme 
limits of our table, e.g. of such values as -+■ '81 or — "81 ? Well, consider the 
corresponding fourfold table : 
3 
707 
710 
77 
174,295 
174,372 
80 
175,002 
175,082 
§=+•811 
and multiply each entry by the factor 
32,527,84 3 
175,082 
we find 
= 185-78633, 
557 
131,351 
131,908 
14,300 
32,381,629 
32,395,935 
14,863 
32,512,980 
32,527,843 
Compare this with the fourfold table deduced by Mr Yule from the Census 
data of 1901 : 
Blindness. 
CD 
Present 
Absent 
Totals 
Present 
Absent 
558 
24,759 
132,096 
32,370,430 
132,654 
32,395,189 
Totals 
25,317 
32,502,526 
32,527,843 
§= + •693, 
or the following one from the same Census, again formed by Mr Yule 
Deaf-Mutism. 
Present 
Absent 
Totals 
Present 
96 
25,221 
25,317 
Absent 
15,150 
32,487,376 
32,502,526 
Totals 
15,246 
32,512,597 
32,527,843 
§=+•782 
