190 
On Theories of Association 
discrete quantities, and we can oidy judge what he means by this term from seeing 
the cases to which he has applied it. We shall therefore deal first with the 
discussion of the cases to which Mr Yule has applied his methods, and then 
consider their effects as applied to (a) continuous, (b) discrete variates. 
Mr Yule opens his paper by observing* that if we classify objects into two 
classes only, for example "peas into yellow-seeded and green-seeded, or the 
members of any group of mankind into male and female, the resulting data are 
of the simplest possible form." The data may be thus in the simplest possible 
form, but difficulties might occur even in such simple cases as those cited by 
Mr Yule. The classification even into yellow- and green-seeded peas is by no 
means so simple as Mr Yule suggests, and certain types of hermaphrodite in man 
might undoubtedly puzzle even Mr Yule's powers of discrimination. To under- 
stand really what Mr Yule proposes to classify we must turn to the cases to which 
he has applied his method. They are as far as we can judge from an examination 
of his writings the following: (1) Good and Bad Temper, (2) Presence and Absence 
of the Artistic Faculty, (3) Stature in Man, (4) Tallness in Plants, (5) Mental 
Dulness, (6) Low Nutrition, (7) Defects in Development involving "size, form or 
proportioning of parts," (8) Abnormal Nerve Signs, involving " abnormal actions, 
movements, and balances," (9) Mental Derangement involving imbecility and 
idiocy, (10) " Blindness," (11) Deaf-mutism, (12) Recovery and Death in the case 
of Smallpox, (13) Vaccination or non-vaccination, (14) Male and Female, (15) Cross 
and Self-Fertilisation, (16) Eye-Colour, (17) Colour of Flower, (18) Prickliness of 
Fruit. Mr Yule has probably used or suggested the use of the coefficient of 
association in other casesf. Looking through the above cases we see it is in 
the rarest instances, possibly only in (14) and (15), that Mr Yule has confined 
himself to discrete variates. He has applied his coefficient of association over 
and over again to continuously varying quantities. Temper (1), artistic faculty (2), 
stature (3), tallness (4) are all quantitatively determinable variates, even if 
difficult in some cases to measure. One man has a better or worse temper than 
another ; one man has a greater or less degree of artistic faculty ; where the 
division between presence and absence of the faculty is put, or what is called good 
or bad temper is largely matter of personal equation. But nobody doubts the 
range of such variates ; they are continuous, there is no sudden break. 
Now turn to the next four characters (5) — (8). No one who has studied the 
essential difficulty of defining what is feeble-minded will doubt the continuity of 
mental dulness. It is not a discrete character, but a continuous variate. There 
are certainly all grades of mental defect, and the groups idiot, imbecile, feeble- 
minded, " simple " are quite artificial. If the whole population were graded 
according to intelligence, the frequency curve would be continuous; no one knows 
whether it would be Gaussian or not, or whether it would be ' humpy" towards 
* Journal R. S. S., Vol. lxxv. p. 579. 
t He has apparently approved of its application, as we shall see later, to a long series of absolutely 
continuous variates by Professor Niceforo. 
