XI] 



Introduction 



XXIX 



Illustration (i). The following distribution represents the ' tail ' of a group of 

 301 mentally defective children measured by G. Jaederholm using Binnet-Simon 

 test methods* : 



Mental Defect in Years. 





wj 







^ 





^ 



§ 



^ 

 -=)- 







s^ 



-* 



-* 



iti 



^. 



^a 



■a 



t- 







1 



I. 



1 



1 



1 



1 



1 



1 



1 



1 



3 



o 

 H 





■? 



1 



1 



1 



1 



1 



1 



1 





Frequency ... 



34 



18 



13 



3 



4 



4 



1 



1 



78 



We find, with origin at — 3'45, 



d = 1-8077 in i years and S= = 2-7258. 



Hence i/ti = 2Vc^' = -834. 



The Table (p. 26) gives us A' = 2-186 and i|r2= 2-833. Hence the mean is at 

 distance from — 3'45 on left= 2-186 x cr, and for the standard deviation 



o- = i|r„xd = 2-833x 1-8077 = 5-1212 | years = 2-5606 years, 



whence mean is at distance h = 5-597 years from — 3-45. 



Now h' = 2-186 corresponds by Table II to i (1 + a) = -98559. 



.-. n/i\r= -01441, or i\r= 7S/(-01441) = 5413. 



Thus the distribution is the tail of a population of 5413 individuals with 

 a mean at 2"15 years of mental excess, and a standard deviation of 2-56 years. 



The example is merely illustrative and of no importance in itself. 



Illustration (ii). Assuming that the correlation data follow the normal law, 

 determine indirectly the 'plural' partial correlation f of habits of mother and 

 health of baby for the limited universe of unclean homes. 



The correlations between the various characters found by tetrachoric tables are 

 Habits of mother and health of baby: j-j., = -3060, 



Habits of mother and cleanliness of home : r,3 = -7958, 

 Health of baby and cleanliness of home : Vo^ = -2578. 

 There are 947 out of 2931 homes which are not clean. Data from Bradford. 

 Here n/N = 947/2931 = "3231 = ^ (1 - a) ; 



hence a = -3538, and by Table III 



x' = x/a- = -459,049. 



* Alendelism and the Problem of Mental Defect. II. On the Continuity of Mental Defect. Dulau&Co., 

 37, Soho Square, W. 



+ Biometrika, Vol. ix. p. 289. 



