THE STATISTICAL STUDY OF VARIATION 55 
high, it indicates they are in some way closely related, and, if it amounts 
to unity it shows that one is the cause of the other or else both are the 
result of the same causes. The importance of biological soundness as 
a requisite to reliability in the correlation coefficient must not be over- 
looked, e.g., see Harris on physical conformation of cows and milk 
yield. Pearl reminds us that statistical knowledge of correlation is 
precise only in the same limited sense that similar knowledge of type 
and deviation from type is precise, viz., as applied to the particular 
group or groups in the particular instance in time. However, this ability 
to describe groups in terms of the groups’ own attributes is extremely 
useful in the practical conduct of scientific experiments. Love and 
Leighty point out that correlations may be classified as fluctuating and 
stable, ‘‘these divisions being based on the behavior of the relationship 
of the characters concerned when variation occurs in environmental con- 
ditions, such as exist in different years, or in different locations. As the 
names indicate, the correlations of the first class may be made to vary 
considerably by changes in conditions, while those of the second. class 
remain of about the same value or are stable in character.”” The prac- 
tical value of knowledge of correlation is great, especially when one char- 
acter is easily seen or readily measured and the other is not. - Although 
it is difficult for the mind to grasp the relation which exists between two 
groups of data on several hundred or thousand individuals, yet when the 
relation between those data is expressed in a single number as a corre- 
lation coefficient the difficulty disappears. 
Regression.—The correlation between parents and offspring when 
used as a measure of inheritance—Galton thought his measure of somatic 
resemblance was a measure of inheritance—is usually known as regression. 
If in an allogamous species parents and offspring be compared with respect 
to the same character, it is found that the means of the offspring are 
nearer the mean of the general population of parents than they are to the 
mid-value of their own parents. In other words, extreme parents do not 
produce progeny as extreme as themselves. Galton believed this re- 
gression toward the mean of the general population to be due to “pull” 
of a mediocre back ancestry. He expressed a mathematical law, good 
under certain conditions, that is directly opposed to biological facts. 
It expresses the truth, that, if from a general population of mixed heritage 
in which there is continual crossing, extremes are selected as parents, 
there will be regression toward the mean of the general population; and 
continued selection will be necessary therefore to improve the race. 
But this regression is not due to the pull of a back ancestry; it is due to 
the fact that individuals whose somatic appearance places them in diverse 
classes in the frequency distribution are themselves gametically different 
and will breed differently. Circumstances may come about by which the 
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