268 
On Theories of Association 
There is indeed no comparison between the stability of tetrachoric r t and Q in 
an illustration which Mr Yule himself has selected to indicate the badness of 
tetrachoric r t ! Mr Yule's coefficient of association, we are told by the statisticians 
of the Royal Statistical Society, will be used for Mendelian problems as soon as 
the Mendelians know a little algebra, but here in the very case of Mendelian 
data we find, as a mere coefficient of association, the r t of the despised Gaussian 
theory is immensely superior to the Yulean coefficient*. Judged algebraically : 
Average value of (Q — mean Q)/(probable error of Q) = 2"34, 
Average value of (r t — mean r,)/(probable error of r t ) = "57, 
or Q is four times as unstable as tetrachoric r,. 
(C) Severity of Small-Pox and Strength of Vaccination Immunity. 
Sixteen cases can be worked out for tetrachoric r t and Q for this material, and 
there is a great variation in both r t and Qf. 
Haemorrhagie 
and Confluent 
Confluent 
and Abundant 
Abundant ■ 
and Sparse 
Sparse and 
Very Sparse 
At 10 
r t =1±1 
§=1± '0000 
r t = -3602 ±-0911 
§=•7892 ±-1296 
r t = -2857 ±-0614 
§=•5415+ -1036 
r t = -2226+ -0626 
§= -4319 ± -1036 
At m 
r t = -2905+ -0598 
§=•5711 ±-1079 
r t = -3694+ -0281 
§= "5411 ± -0413 
r t = -3484+ -0249 
§=■4469 ±-0303 
r t = -2500+ -0293 
§=-3444± -0369 
At 45 
r ( = -2187+ -0556 
§ = -4111 ± -0890 
r,= -4169+ "0309 
§ = -5714 ± -0326 
r t = -3961 ± -0275 
§=■5474+ -0351 
r t = -2578+ -0332 
§=•4143 ±-0569 
Between Jf5 and 
Unvaccinated 
r t = -0426+ -0770 
§=-1009± -1772 
r t = -5121+ -0363 
§=•7220 ±-0322 
^=■6022 + -0287 
§=-8599± -0308 
r t = -5381 + -0349 
§=■8862 ±-0524 
In the form in which Table XXII is given on our p. 254, all values of Q and r t 
are negative. 
This table gives us the following results : 
Weighted Mean 
Weighted 
Standard Deviation 
Tetrachoric r t 
Association § 
•3827 
•5902 
•1211 
■1737 
* It is needless to say we should never have thought of applying either of these coefficients to 
theoretical Mendelian data ; we hold that the correct method was the method applied to this very 
case by one of us ab initio, namely that of product-moment r. 
f There can be little doubt that the extreme variations are due to 9 out of the 16 divisions giving 
a quadrant of minimum frequency with less than l°/ 0 of frequency in it. 
