OF ATTRIBUTES IN STATISTICS. 301 



56. The differences between the associations cannot probably be, at present at all 

 events, assigned to any definite cause or any definite difference in the material 

 observed. We would expect to find differences of association in different groups, just 

 as we find differences between the correlation coefficient for different local races, 

 without our being able to say with certainty how these differences have come about. 

 In many cases the differences are certainly real, as they are large compared with the 

 probable errors of the differences three to eight times the probable errors. That 

 considerable differences exist between different classes of schools, not only in the 

 proportions of defective children but in the associations between defects, is shown by 

 Table II. (based on Table 1 9 of the Report), and consequently the divergence between 

 the results of the two investigations may be due to the different classes of schools 

 observed. Such differences between schools may in their turn be partly or wholly 

 due to differences of age or nationality between the children. The effects of age we 

 deal with below (pp. 309, et seq.) ; the differences between nationalities* are illustrated 

 by Table III. (based on Tables 27, 28 of the Report), showing the associations for 

 English, Jews, and Irish : 



57. These two tables suggested to me at first sight an apparent law that asso- 

 ciations were on the whole higher where populations were healthier or less defective. 

 If we take Table II., 4 of the 6 associations in Poor Law schools are greater than 

 those in Industrial schools ; 4 of the associations in Homes and Orphanages are 

 greater than those of the Poor Law schools, equality subsisting in one of the remain- 

 ing cases ; and 5 of the associations in Elementary schools are greater than those in 

 Homes and Orphanages, taking the schools in order of healthiness. The case is not so 

 marked for girls, and we must note that for them the Homes and Orphanages are 

 more defective than Poor Law schools. In Table III. for the boys, Jews are more 

 defective than English, and Irish than Jews ; the Jews are less associated than the 

 English in 4 cases of the 6, and the Irish less associated than the Jews in 4 cases out 

 of 6 also. But again the case breaks down for girls. English girls are more 

 defective than Jewish girls, but their associations are less in just 3 out of the 6 cases ; 

 Irish girls are more defective than English, but their associations are actually greater 

 in the majority of cases. 



If we compare in this way only those cases that are adjacent in the order of 

 defectiveness we get 



TABLE II.- 



Boys. Girls. 



Associations greater where defectiveness less in 12 cases, in 9 cases. 

 less or equal 6 



TABLE III.- 



Associations greater where defectiveness less in 8 5 ,, 

 less or equal 4 7 



* It must be noted that they were all London children 



