16 ETHEL M. ELDERTON 



This view might be confirmed possibly by noting that the less easy measurements, 

 those on hand and wrist, gave lower results than the joint measurements. But 

 on further inspection of the table we notice that it is the female-female series which 

 diverges so much from our previous results. The eight cases in which a male was one 

 of the pair, and presumably worked the spanner, give a mean of - 270, agreeing 

 excellently with the - 267 of our much larger first series. It is the pairs of female 

 cousins, with their excessive variabilities, which give an intensity of resemblance 

 equal to that of a sibship, and raising the average from - 270 to "336. 



To test the matter further the following steps were taken. A formula has been 

 given by Pearson* which is based on normal distribution of frequency and gives the 

 correlation coefficient in terms of the sum, S(x — y), of the positive differences of 

 correlated variates which have the same mean and s.D. Now this is precisely the 

 case of the 106 cousin pairs if we treat them as a symmetrical distribution of 212 

 pairs. The formula is : 



,.-1 y{ s ( x -y)Y 



Applied to the data for the joint of the little finger in pairs of female cousins, we find 

 r = '5578, while found by the product moment method the answer is "5579, a very 

 close agreement. But it will be clear that if the measurer had a personal equation of 

 the nature of a constant error for each pair, it would drop out in the difference x — y 

 for that pair. Hence the formula above is convenient to use when such an error for 

 the individual pair is suspected to exist, and the variability cr can be found from 

 other considerations. If in this particular case we adopt : (a) the standard deviation 

 of the women in the series of male and female cousins, (b) the standard deviation 

 found for the women on the assumption that the coefficient of variation for the women 

 ought to be (what it usually is) practically the same as for the men, i.e. if we take the 

 two values 2701 and 2 - 474, we find that the above formula gives r= - 48 and "38 

 respectively. Thus indicating some considerable reduction from the value - 56. It is 

 therefore possible that an adding or subtracting of a constant difference in some of 

 the measurements is the source of the exaggerated values of the female cousins 

 resemblance. Such an error would not only have exaggerated the standard deviation, 

 but it would have resulted at once, if a wrong correction had been applied to the 

 measurements of those helpers who read at the edge, and not at the index point, of 

 the spanner. It is believed that no spanners were removed from the numbered boxes 

 until the measurements had been corrected ; but the doubt, however slight, to those 

 who had the control of the instruments, is sufficient to. make it needful to repeat as 

 soon as possible the whole series of measurements on female-female cousins. 



We are able to use this second series as a control series also for the characters, 

 hair colour, eye colour and general health. The method used was that of contingency 



* "On further methods of determining Correlation," Drapers' Research Memoirs, Biometric Series IV. 

 p. 4 et seq. (Dulau it Co., Soho Square). 



