Karl Pearson and David Heron 
309 
so far as we are aware he has not warned students of the extreme danger of his Q 
in these cases. The non-applicability of tetrachoric r t to cases in which one of the 
quadrants has zero or small relative frequency is, on the above and on other 
grounds, well-known to those who habitually work with it, and the rule has long 
been to avoid where possible all such extreme dichotomies. This point has been 
largely disregarded by Mr Yule in his criticism of tetrachoric methods. 
APPENDIX II. 
On the Test of Goodness of Fit of Observation to Theory 
in Mendelian Experiments. 
An objection to the y 2 , P, test of goodness of fit, has recently been raised with 
somewhat unconscious humour by certain ardent Mendelians. A simple illustration 
may be taken. Suppose the mating to be 
(DR) x (DD) = 50 % (DR) + 50 % (DD). 
For example, let there be 1000 offspring and let 480 of these be recognised by 
later experiment as (DR)'s and 520 as (DD)'s. Then the standard deviation is 
V1000 x ^ x 1 = 15-8 
and the observed deviation is 20, and P = about - 90, or the fit is quite good. 
But suppose the observations are 
480 (DR)'s 519 (DD)'s and 1 (RR) 
i.e. Observation : 480 519 1 
Theory: 500 500 0 
. , „ (observation — theory) 2 
Clearly y 2 = S- r— —^ = 00, 
J A theory 
and P = 0, or the probability of observation being a random deviation from theory 
is zero, there is absolute badness of fit. Hence either theory or observation is at 
fault. It is not, however, the theory of "goodness of fit" which fails in such a 
case, but the Mendelian theory which wants mending. If we put a black balls, 
b white balls and c red balls in a bag, the theory will tell us whether any sample 
of black, white and red balls can be reasonably considered as a random extract 
from that bag. But if we are presented with a series of black, white, red, and 
green balls and asked what is the probability that these were drawn from that bag, 
we must assert that it is zero, however concordant with theory the results for the 
black, white and red balls alone may be. There are only two courses open to the 
