K. Tkakson and A. Lkk 



367 



collections ot' data. I inay have bcen unfortuiiiito in my choicc of the foroann as 

 niore ditficult of inoasiuviiiont, or iiiore subject tliaii span to growtli iTifliiciiRcs, V)ut 

 the resulls i'nr the forrann ilivfi-go cousidei'ably uunc fVinn nurmalily lliaii those 

 Ibr staturc or .«paii. 1 i;ivc my c-niicliisions inv the lliree cascs 1 liavr iiivustigatud. 

 These are as foilows: 



Korcann in I'athcrs: 14 Ljroiips, t^- =:!,')• 1,S, P = -0()(), 

 „ in Daughtcrs: 14 gnaips, i^- = o3'5I, 7' = (JOS, 



in Si>ns: I ö groups, ^'- = 3()-70, P=m7. 



Tiic inipi'ohability of tlu' norniiil distribution is, howcvcr, in all tlicse oases 

 chieHy diio to a Httlu hinip of "outJicrs" at the " giant " cnd of tlic <bsnil)iitioii. 

 Therc are four fathers with excessive forearnis, foiir daughter's with the like and 

 four sons also Those twelve cases cainiot, I feel sure, be in the bidk iliie to 

 slips of nicasniTiriciit, thcy may bu (lue to some anomalous grovvth or to a 

 rever.sion to au excessive radius. If vve remove theui \ve find roughly : P = "45 

 für fathers, = 21 for sons and = "18 for daughters, i e. \ve obtaiu an excellent normal 

 curve fit in the first case, and quite fair ones in the other two. We are therefore 

 forced to the concltisiou that forearm in the bulk follcjws fairly ehisely a normal 

 distribution, but there appears to exist in man a small abnormal groiip with 

 excessive forearms, of less than "5 per cent. The following is the table of observed 

 and theoretical results for forearm in f ithers : 



Forearm in Fathers. 1050 Gases. Mean = 18"-31, Standard Deviation ="-968. 



This is shown in Diagram VI. The mere graphical inspection of such a 

 result as this would hardly lead us to give proper weight to the abnormal 

 group of outliers, which carry P from -4.') to -OOO. To some it might seem a 

 good fit, but the traincd eye sees at once defeets and P = -000 shows how great 

 they are*. 



* It is almost in vain that one enters a protest against the mere Rraphical representation of goodness 

 of fit, DOW that we have an exact measure of it. As typical case.s in which qnite recently argunients are 

 based on mere graphical appreciation, I would refer to an articie by Thorndylie on "Fertility in Man" 

 {Populär Science Muntkhj, Vol. 03, pp. 64 and 84) wherein the skewness of fertility distributions is 

 denied on graphical appreciation of eurves, which are analytically skew by odds of the iirder of a 

 1000 to 11 Anotlier transgressor is Johannseu, who in his recent work Veher Erhlichkeil in Popu- 

 lationen und in reinen Linien, asserts on mere graphical appreciation that certain data are normal and 

 other non-normal and bases argunients on these assertions, wbereas the eye alone cannot possibly 

 juclge whether or no his distributions follow the normal law. If biologists use biometric methods, 

 they must be reminded that no vague appreciation will answer biometric problems, they must study 

 suifioient matliematics to apply the necessary tests and eriteria on which alone biometric arguments can 

 be safely based. 



47—2 



