Sfdfitttiral /nncgtif/afiotiH 377 



At this point in liis paper Gallon draws attention to a "Common Error 

 in Statistics'," which he says has not hitherto attracted attention. It occurs 

 ill a classification, such as "G5 — " for stature, vvhicli is assumed to mean 

 65 inches ami less thnii GO inches. Ho points out that the centre of this 

 group is usually taken as 65"5 inches, but that this is most often erroneous, 

 and that the true centre of the group (if we arrange the gro'T uniformly 

 over its range) may differ very considerably from this. The true centre 

 depends on the fineness of our readings. If, for example, we read stature to 

 the nearest half-inch only, then all measurements in excess of 64'5 would be 

 included in G5, and all measurements in excess of 65'5 in G6. The former 

 would all appear in "65 — " and the latter would not. Thus the centre of 

 "65 — " would be actually the centre of the range 645 to 65*5 or 65 and not 

 65 •5. In other words, there would be half an inch error in the resulting 

 mean. Most tyros in statistics are now aware of this point, i.e. that the 

 centre of a subrange depends upon the fineness or coarseness of the readings. 

 It is, therefore, startling to think that Galton was the first to point out this 

 pittall even as late as 18841 



I The next paragraphs are of some historical interest. Galton is seeking 

 to find a relation between various characteristics, and considering the old 

 idea of the ratios of anatomical measurements as constants. He notes that in 

 certain cases these ratios are not constant (p. 281). Galton also gives rough 

 gi'owth curves for vital capacity, but has missed the point of contraflexure 

 in the neighbourhood of puberty, which his own data treated more in detail 

 exhibit. These are cases of what we should now term skew regression. Galton, 

 we notice, had not yet reached in 1884 the full conception of correlation. He 

 gives (p. 285) what we should now term a coiTelation table between vital 

 capacity and strength of squeeze for 522 males of ages 23, 24 and 25. He says 

 that he was surj>rised to find no close relation between these two characters. 



"The iinport-ance of a large breathing capacity to a man who expends force rapidly, aa to a 

 runner or mountain climber, is undoubted, but for a strain of short duration it seems com- 

 paratively non-essential." (p. 284.) 



He reaches his conclusion by comparing the means for strength of squeeze 

 corresponding to vital capacities of 150 and 300 cubic inches. He says there 

 is a difference of 17 lbs. But without a measure of the variabilities we could 

 not deduce any measure of the association of the two characters. Now-a- 

 days we should say that the coefficient of correlation was certainly not 

 negligible : it is '40 ± 02 from his table; but we are able to express the in- 

 tensity of the association in this simple manner, only because Galton later 

 taught us how to do it'. 



Some data are given for the leliitlonship of right and left sides. Thus 

 Galton found the left hand to he about G /^ weaker than the right. The 

 right and left eyes on the average had equal keenness of sight. Galton 



' See p. 280 of the present paper. Galton also contributed a paper on the same point to 

 the Jubilee Ydwm of the Statistical Society, June 22-24, 1885, p. 261. 



^ Gallon's wording is rather vague, but I think there is more correlation than his phrase 

 would suggest. 



p o II 48 



