314 
On Theories of Association 
Pearson's criterion gives the following results : 
I. P = 003 
II. P = -ooo 
III. P = -113 
IV. P = -036 
The odds against the first series arising from material following the theory are 
332 to 1 ; the second series is impossible on the theory ; the odds against the third 
series are about 8 to 1 ; and against the fourth series are about 27 to 1. The com- 
bined odds against even the three series (I, III and IV) representing the theory 
are very large indeed. Dr Pearl actually tells us that " the investigator is usually 
expected to reject abnormal material" (p. 256). And he prides himself on not having 
done so*, and asks us to form a judgment not on the summary but on the detailed 
data in the body of the paper. We have done so, and the criterion gives still worse 
results. We agree with Dr Pearl that " the high producing hen, somewhat like 
the race horse, is a rather finely strung, delicate mechanism, which can be easily 
upset, and prevented from giving full normal expression to its inherited capacity 
in respect to fecundity " (loc. cit. p. 255). But surely this is only to admit that 
the character chosen was wholly unfit to test the theory upon at all ? It does not 
justify rejecting the only scientific test of "goodness of fit," and then concluding 
from nothing other than general impression that "the cumulative probability 
that the hypothesis applied represents at least a reasonable approximation to 
the true interpretation of the results becomes very great" (loc. cit. p. 257). If 
"cumulative probability" signifies anything at all, it means the theory of 
probability applied to the series to deduce combined odds against the total 
results and these are hopelessly against Dr Pearl. Further we cannot go until 
Dr Pearl publishes his record, which is not yet before us, although he has 
published his own interpretation of it in a great variety of journals. 
APPENDIX III. 
On the Equation to the Surface of Constant Q. 
If the limits to the frequency range in the variate a; be ft and a', and in the 
variate y be b and b' , then in the notation of p. 184 
" "But in view of the rather hysterical attacks upon geneticists and their method of work in this 
country, if for no other reasons, it seems best to follow the plan of publishing all the data." We 
would remind Dr Pearl that this is exactly what he has not done. We require the quantitative record 
of every individual hen and its ancestry as far as is known before we can fully test the validity 
of his results. 
