310 
On Theories of Association 
experimenter who gets green balls however few in number out of a black, white 
and red ball theory : 
(i) to assert that they are anomalies due to his temporary colour-blindness, 
to mistakes in his observations, or to some misinterpretation of his results, which 
are not accurately describable in terms of his original categories, or 
(ii) to amend his original theory by inserting some green balls a posteriori 
into the bag and starting afresh to calculate his probabilities. 
The one course weakens the weight we must lay on his record or on his choice 
of categories ; the other tends to discredit his a priori theory. To adopt a third 
course and assert that we want a new test for " goodness of fit " of theory to 
observation, which shall cover such discrepancies, i.e. which shall slur over 
divergencies between a priori theory and a posteriori results, may appeal to 
our sense of human fallibility but scarcely to our appreciation of scientific logic. 
We shall be left with the suspicion that the theory is plastic and the observations 
elastic. What criterion of " goodness of fit " can the theory of probability provide 
when it is a case of applying plastic theory to elastic observations ? The answer 
surely is none whatever until the plasticity of the theory has been quantitatively 
studied, and until the errors of the record have been quantitatively stated. Either 
we must be told that the observer will mistake a red ball for a green one in 
so many per cent, of cases, or we must be told that the theory will be inaccurate 
in so many per cent, of cases. Personally we think it possible that all attempts to 
find a "good fit" of a plastic theory to elastic observations are idle. It is a con- 
sideration of the green balls, which are said not to be in the black, red and white bag 
at all, which is often the basis of marked scientific progress. That atmospheric 
nitrogen differed from pure nitrogen was just such a " green " ball ; but the plastic 
theory that air consisted of oxygen and nitrogen only had been confirmed by many 
elastic observations before Lord Rayleigh followed up his "green " ball. 
These remarks are suggested by the following paragraphs in two recent 
Mendelian publications. Dr Raymond Pearl writes* concerning Mendelian 
data : 
" A determination might be made of the ' goodness of fit ' of theory to 
observation by Pearson's method, were it not for the fact that that method 
cannot be applied to cases like the present." 
Dr Pearl says it cannot be applied because he finds green balls, where his 
theory puts only black, white and red into his bag. It is either his observation 
record or his Mendelian theory, not the mathematics of " goodness of fit," which 
needs modification. Dr Pearl continues in a footnote as follows: 
" The difficulty lies in the fact that Pearson's test depends upon a variable 
* The Journal of Experimental Zoology, Vol. xm. p. 203. 
