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 



