INHERITANCE OF WAXY ENDOSPERM IN MAIZE. 67 
dividual ears of a given family? Both theories require that this be 
true and that the correlation between any given pair of characters 
remain constant. 
In this bulletin there is evidence to show that at least in the second 
generation the correlations observed are for the most part explained 
by assuming a gametic series of 3-1-1-3. 
METHOD OF MEASURING CORRELATIONS. 
It has been the common practice to test the “ goodness of fit” of 
couplings by contrasting the observed series with the calculated series 
and trusting to the eye to detect the agreement. 
The danger of this method has been effectively pointed out by 
Collins (4), who proposed using Yule’s coefficient of association with 
its probable error as a quantitative method of making the compari- 
sons. For the higher degrees of coupling the coefficient of associa- 
tion with its probable error does not afford a satisfactory method of 
comparison, since the differences between the higher couplings, when 
* measured by the coefficient of association, are extremely small. 
With couplings of this nature and where more than two coupled 
characters occur, a method proposed by Pearson (13) can be used. 
By the use of Elderton’s tables (9) the method is very simple. Cau- 
tion, however, should be observed in applying this method as a 
measure of correlation where the characters are departing from the 
Mendelian expected ratios. This method does not distinguish be- 
tween departures from the Mendelian proportions and differences in 
the way the characters are combined. Since the behavior of the in- 
dividual characters from a Mendelian standpoint need not affect their 
association with each other, we are not concerned with any discrepan- 
cies between the observed and expected percentages of these charac- 
ters, desiring only to know whether the characters under discussion 
are correlated or associated in a given proportion. It is obvious, 
then, that to measure the “ goodness of fit” of the observed associa- 
tion to the theoretical association by the use of Pearson’s formula 
(13) and Elderton’s tables we must first eliminate any differences 
between the observed proportion of the individual characters and the 
Mendelian expected ratios, otherwise an injustice will be done to the 
agreement of the observed with the theoretical association. 
Mr. G. Udney Yule has recognized this difficulty in applying Pear- 
son’s formula to testing the “goodness of fit” of a coupling ratio 
where the Mendelian ratios of the characters are skew, and in a letter 
to Mr. Collins suggested another method (15, pp. 585-590). 
This method very satisfactorily corrects the material to the proper 
Mendelian proportions without altering the degree of association, 
but it seems to offer little advantage in cases of a low degree of 
