Correlation and Application of Statistics to Problems of Heredity 51 



races*, which have been often discussed from early times up to the present day, both by artists 

 and by anthropologists. The fact that the average ratio between the stature and the cubit is as 

 100 to 37 1 or thereabouts does not give the slightest information about the nearness witli which 

 they vary together. It would be an altogether erroneous inference to suppose their average 

 proportion to be maintained so that where the cubit was, say, one-twentieth longer than the 

 average cubit, the stature might be expected to be one-twentieth greater than the average 

 stature, and conversely. Such a supposition is easily shown to be contradicted both by fact 

 and theory." (loc. cil. pp. 135-6.) 



Let us now describe Galton's procedure. In the first place Galton does 

 not use means, he uses throughout medians, both for his marginal totals and 

 his arrays. Further he does not use standard deviations, he makes use of 

 the quartile measurements. Thus if Q lf M and Q 3 be the measurements at 

 first, second and third quartile divisions, he takes M as his median and 

 '. CJ.i — Qi) as his measure of variation. Thus his results, unlike our modern 

 treatment, depend essentially on assuming that all his data follow a normal 

 (or "curve of errors") distribution J. If M c be the median of any character c 

 and b M c the median of an array of this character for a given value b of a second 

 character c', then Galton plots: 



J£.-M. tQ b-M, 



In other words he reduces the deviation of an array median from the popu- 

 lation median to its unit of variation obtained from the quartiles, and plots 

 this to the deviation of the second character from its median reduced like- 

 wise to its own unit of variation. Then he plots: 



„Ms-M„, a-M„ 



to 



where a is a value of the first character and a M & the median of the corre- 

 sponding array of the second character, and thus gets a second series of points. 

 He takes six or seven values of a and of b, plots two sets of six or seven 

 points and notes that the first and second series of points are nearly on 

 one and the same straight line§. He draws this straight line as closely as 

 he can to the points and through the median, and reads off its slope. This 

 slope is Galton's measure of co-relation. If we take the mean deviation of c' 

 for a given value of c, Galton calls c the " Subject" and c' the "Relative," but 

 perhaps it would be best to call the latter the "Co-relative." Galton's data 

 consisted of about 350 males of 21 years and upwards, of whom the majority 

 were young students, measured in his Laboratory in 1888. He deals with 



* [The variation in the ratio of stature to cubit does, however, provide a means of determining 

 the correlation. K.P.] 



t [Rather 100 to 27 or thereabouts on Galton's numbers, i.e. 67 - 20" for stature and 18 - 05" 

 for cubit. K.P.] 



\ In the table given on p. 52 for the correlation of Stature and Left Cubit it is very difficult 

 to see any approximation to normality in the distribution of stature. 



§ In order to get the same straight line, if c be the subject and c the co-relative, and the 

 " subject " axis horizontal, then it is needful when c is subject and c co-relative to plot c 

 along the same axis as was used in the first case for c. In other words the character axes must 

 be interchanged. 



7—2 



