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Miscellanea 
"plastic" enough for his observations. But this, the logical application of the method, is not 
what Dr Pearl adopts although he has commenced his paper by emphasising the "'ever-growing 
need for adequate and clearly understood tests for the statistical significance of differences 
between observed results and expectation* " and cited in this respect the and the y/mpq tests 
both of which are criteria of goodness of fit of observed results as a sample of the results to be 
expected from an indefinitely large and rigidly proportioned theoretical population. 
What Dr Pearl actually does had better be stated in his own words (italics his): "The pro- 
posal which I wish to make for the expression of a Mendclian result is that the expectation be 
expressed as the qvarlile limits of each class of frequency in a second sample of the same size as the 
observed sample].'" 
Now it is very difficult to understand this sentence, for we are not told what the "expectation" 
is. If it is the Mendelian expectation, then why is the Mendelian expectation the second sample 
and not the first sample ? And further why should its size be the same as that of the observation 
and not indefinitely large? 
If we seek enlightenment in the working of the illustrations provided we can find it on 
pp. 150-151. Here to begin with we have the observations of F. L. Piatt on the mating of Blue 
Andalusian fowls set out. There are 58 offspring of the mating Blue x Blue of which almost 
7 % instead of being the white, blue or black of Mendelian theory are "dark red." These 
"mutations," "errois of record" or "what nots" are thrown in with the blacks and classed as 
"pigmented not blue" (elastic observations!). Dr Pearl now assumes a, first sample of 58 to be 
given in the actual Mendelian proportions of 1 : 2 : I, i.e., 14-5 : 29 : 14-5, and he then uses (i) and 
(ii) to obtain the mean = 14-9833 and cr = 4-6364 for testing the actual data. 
Now what is the real significance of this procedure? Clearly he has made the Mendelian 
theory absolutely plastic. He has taken it not as the rigid law of the population sampled, but 
as the variable distribution of a very small first sample of 58 from a population of which the 
actual law is absolutely unknown or rather merely suggested by a very small sample. The smaller 
the observed series, the weaker will be the theory. The artifice is clear when it is clearly 
expressed, but no biologist with the average biologist's knowledge of mathematics would realise 
what Dr Pearl has done and he would thus run the danger of accepting Dr Pearl's test as a 
valid one. Suppose the sampled population to contain 1000 blue balls, 800 green balls, 500 red 
balls and 10 yellow balls. A sample of 50 would as a rule produce no yellow balls, say it pro- 
duced 22 blue, 17 green and 11 red. This would be used to represent the "Mendelian" ratio 
22 : 17 : II but later samples of 50 might occasionally produce yellow balls. These it is true 
would not appear in the "Mendelian theory" of 22:17:11, but would give no indefinite 
improbability, because the Mendelian theory has been shifted from being the rigid law of an 
indefinitely large population, to being the chance distribution of a sample, of just the same size 
as the observations themselves. Its accuracy or weight fluctuates with the observations themselves, 
and the "goodness of fit" test suggested by this process becomes no test whatever of the accord- 
ance of theory and observation, for the theory is made to have just the same weight as the 
observations, and the fewer the observed data, the greater ceteris paribus will be the HkeUhood 
of accordance between the two samples. 
Shortly Dr Pearl's method is entirely fallacious, as any trained mathematician would have 
informed Dr Pearl had he sought advice before publication. It is most regrettable that such 
extensions of biometric theory should be lightly published, without any due sense of responsibility, 
not solely in biological but in psychological journals. It can only bring biometry into contempt 
as a science if, professing a mathematical foundation, it yet shows in its manifestations most 
inadequate mathematical reasoning. 
* Loc. cit., p. 144. The italics are mine. f Loc. cit., p. 148. 
CAMBRIDGE : PlilNTED BY J. B. PFACE, M.A., AT THE UNIVERSITY PRESS. 
