FILIAL REGRESSION 315 



sexual selection. Its variability, though small, is nearly normal ; 

 that is to say, the normal curve of the frequency of error nearly 

 fits the distribution in many cases. 



As the subject is by no means easy to those unaccustomed 

 to statistical inquiry, and as we cannot within our limits explain 

 the methods which Galton followed, it may be most profitable to 

 give a few illustrative quotations from Natural Inheritance (1889). 



" If the word ' peculiarity ' be used to signify the difference 

 between the amount of any faculty possessed by a man, and 

 the average of that possessed by the population at large, then the 

 law of Regression may be described as follows. Each peculiarity 

 in a man is shared by his kinsmen, but on the average in a less 

 degree. It is reduced to a definite fraction of its amount, quite 

 independently of what its amount might.be. The fraction differs 

 in different orders of kinship, becoming smaller as they are 

 more remote " (p. 194). 



In the population with which Galton dealt the level of medi- 

 ocrity in height was 68 J inches (without shoes). The law or 

 fact of regression which the statistics revealed was that the 

 deviation of the sons from the mean of the population (P) is, on 

 the average, equal to one-third of the deviation of the parent 

 from P, and in the same direction. If P ± D = stature of 

 the parent, then P =fc ^D = stature of the son. In these in- 

 quiries it is convenient to use the concept of a mid-parent, whose 

 stature is half-way between the stature of the father and the 

 " transmuted stature " of the mother, the last phrase meaning 

 practically the stature that the mother would have if she were 

 not female, i.e. an additional inch for every foot. 



" However paradoxical it may appear at first sight, it is 

 theoretically a necessary fact, and one that is clearly confirmed 

 by observation, that the stature of the adult offspring must on 

 the whole be more mediocre than the stature of their parents, 

 that is to say, more near to the mean or mid of the general 

 population " (p. 95). 



