498 Dr. F. Galton. Note to the Memoir by 



unless the coefficients of variation be constant for local races, it is 

 impossible that the coefficients of correlation can be constant for 

 indices. In other words, the hypothesis of the constancy for local 

 races of correlation, and that of the constancy for local races of 

 variation, stand on exactly the same footing. 



The conclusions of this paper although applied to organic correla- 

 tion are equally valid so far as concerns the use of indices in judging 

 the correlation of either physical or economic phenomena. It was, 

 indeed, a difficulty arising from my discussion of personal judgments 

 a spurious correlation between the judgments of different observers 

 which first drew my attention to the matter. 



Note, January 13, 1897. The result described by Professor 

 Pearson evidently affects the value of the correlation coefficients 

 determined by me in Grangon arid Carcinus (' Boy. Soc. Proc.,' vols. 

 51 and 54), because I have always expressed the size of the organs 

 measured in terms of body length. 



In order to show the effect of this, I have lately performed, at 

 Professor Pearson's suggestion, the following experiment : It happens 

 that my measures of Plymouth shrimps are recorded in a book, in 

 the order in which they were measured, and therefore at random as 

 regards carapace length or other characters. I constructed from 

 these records 420 " spurious " shrimps, in the following way : the 

 total length of the first shrimp in the book was associated with the 

 carapace length of the tenth shrimp and the " post-spinous length " 

 of the twentieth, and so throughout. Evidently these three measures 

 were associated at random, and we might expect that these spurious 

 shrimps would show no organic correlation ; but when the cara- 

 pace lengths and " post-spinous lengths " of these spurious shrimps 

 were divided by the body length, and the correlation between the 

 resulting indices was determined, the value of r was found to be 0'38, 

 the value for real shrimps being 0*81, or the correlation due to the 

 use of indices forms 47 per cent, of the observed value. 



W. F. B. WELDON. 



" Note to the Memoir by Professor Karl Pearson, F.R.S., on 

 Spurious Correlation." By FRANCIS GALTON, F.R.S. Re- 

 ceived January 4, Read February 18, 1897. 



I send this note to serve as a kind of appendix to the memoir of 

 Professor K. Pearson, believing that it may be useful in enabling 

 others to realise the genesis of spurious correlation. It is important 

 though rather difficult to do so, because the results arrived at in the 

 memoir, which are of serious interest to practical statisticians, hav( 

 at first sight a somewhat paradoxical appearance. 



