Karl Pearson and David Heron 
213 
he starts from the held of pure logic and not from the observation and record of 
actualities. Even if the actual Mendelian differences were units, not the differences 
of continuous variation, then would be the right coefficient to use, not those 
of colligation or association*. But even here the results will be often difficult to 
interpret. In the usual case, however, of Mendelian practice, what we need is 
not the value of a correlation, but an investigation of whether observation is a 
reasonable fit to theory, i.e. we must use the ordinary "Goodness of Fit" testf. 
This point is discussed in Appendix II, as there has recently been some mis- 
interpretation of the matter. 
* We have taken the series of those symmetrical fourfold tables for which <p has always the Mendelian 
value 1/3; the values of Q range from -6 to 1. What interpretation can association give of such 
Mendelian tables? 
t The evil done by Mr Yule's preaching of association to the neglect of more general methods is 
manifest in a recent paper by G. N. Collins in The American Naturalist, Vol. xt/vi. p. 572. He gives 
such numbers as the following for flower colour and long pollen in hybrid sweet peas, taken from 
Bateson, Saunders and Punnett, Report III to the Evolution Committee, p. 9, 1906. The calculated 
Purple 
Red 
White 
Long 
Round 
Long 
Round 
Long 
Round 
Observed 
Calculated 
1 
1528 
1448-5 
106 
122-7 
. 
117 
122-7 
381 
401-5 
1199 
1220-5 
394 
407-4 
numbers are curious ; the authors do not explain adequately how they have obtained them. Assuming 
them to be correct — but of this we have doubts — the problem proposed by Mr Collins is to determine 
whether the observed "Purple" and "Red" as distributed into "Long" and "Round" are a random 
sample from the calculated values, i.e. we compare 
Observation ... I 1528 
Theory 
1448-5 
106 
122-7 
117 
122-7 
381 
401-5 
Mr Collins remarks "No method has been proposed for making definite comparisons between such 
series of numbers " (p. 572), and continues "A customary and direct method of comparing the degree 
of relationship that exists between any two characters is to compute the coefficient of correlation or 
Yule's 'coefficient of association.'" In the discussion which follows Mr Yule's "coefficient of asso- 
ciation" (1900) is used. Considering the work of Pearson and Elderton on "Criteria of Goodness 
of Fit" (Phil. Mag. Vol. l. 1900, pp. 157—175, and Biometrika, Vol. r. pp. 155—163), Mr Collins can 
hardly have gone far in statistics, for how would he have proceeded had he included the "White" 
in his series? The proper method appears to us the general one, i.e. to determine the probability 
P of the recorded divergence between observation and theory, calculating 
„ (observation - theory) 2 
X 2 = sum — — , 
theory 
and deducing P by Elderton's Tables : see our Appendix II. In this case a deviation as large as that 
observed would only occur once in twenty-one trials or the odds are 20 to 1. But we believe Messrs 
Bateson and Punnett have done themselves injustice. We do not write this in disparagement of 
Mr Collins' work; he is undoubtedly right in demanding some test for "goodness of fit" in these 
luxuriant Mendelian formulae. 
