On Theories of Association 
Relationship between Blindness and Mental Defect 
for different Age Groups. 
Age Group 
lheoretical value 
UX / ux <p 
5 
•0113+ -0030 
10— 
•0100+ -0022 
15— 
■0065+ '0017 
20— 
•0061 + -0015 
25— 
•0046 ± -0009 
35— 
•0060 ± -0010 
45- 
•0053 + -0008 
55— 
■0059+ -0012 
65— 
•0028 + -0012 
75— 
- -0031 + -0014 
85— 
■0058 + -0065 
All ages 5—85 
•0066 + -0002 
Is it conceivable that, if Mr Yule had approached the problem of the relation- 
ship of blindness and mental defect from the standpoint of " the theoretical value " 
of r and found that the maximum value of the coefficients obtained was '0113, 
there would have been any talk of the high association of the two attributes ? If 
this on the Boas-Yulean scale means high association, what language would Mr Yule 
find to describe a Boas-Yulean coefficient of "96 ? Instead of replying to this criticism 
of Heron, Mr Yule states that this series of values confirms his view that the 
association decreases with age ! If the reader looks at the diagram below, he will 
see the mean value of the Boas- Yulean coefficient with twice the probable error 
of each age sample set off either side of it. He will note (i) that there is only one 
age 75 — 80 where the deviation from the average value becomes significant ; 
(ii) that from age 15 to age 60, the polygon is practically horizontal and agrees 
with the mean ; (iii) the "high" values ("01 order!) occur in childhood, especially 
ages 5 — 10, where diagnosis of mental defect is doubtful, and the low values at 65 
and onwards (where they are even contradicted by age 85 onwards !), just the ages 
when senile decay and old age cataract may lead the recorder of a census return to 
almost any statement as to mental derangement and blindness. We feel fairly 
confident that the unbiased statistician with this result before him could only con- 
Hence o-,.'- = ^ jl + - nil') ('"2 - 1*2') _ - 5) — t + h ^75 ( m i ~ m i) ("h ~ "'2') j 
= 1 { 1 - r* + (r + i r») X M - J r» (x* + tf) > , 
•67449 1 
or p.e. of /•= — {1 - /■- + (r + %r s ) \fx - J;- 2 (X 2 + /x 2 )[a ) 
where x = \/— , - a./— and P=\/—, \ ~ \/ — • 
V to/ \ mi V mo V »i2 
This form agrees with that obtained by Yule and verified by Greenwood, but our deduction of it 
appears to be the natural method and shows its relation to the general formula for the probable error 
of r. 
