304 MR. G. UDNY YULE ON THE ASSOCIATION 



thesis, but other explanations are here possible. The fact that the association 

 decreases throughout life, as far as we can judge from present material, while 

 defectiveness also decreases in later childhood (cf, below, p. 310) is against it. 

 Thus I do not think we can accept the hypothesis without wider evidence ; I have 

 mentioned it as it occurred to me, and would probably occur to others, as covering 

 certain of the facts presented. 



58. The foregoing figures of Tables I. -III. show that all the defects dealt with by 

 Dr. WARNER are associated to a high degree, though this degree varies somewhat in 

 different groups of material. The question now arises, can we investigate further 

 the nature of the association between A and B or B and C ? Suppose the hypothesis 

 to be put forward, for example, that low nutrition was the cause of both defects in 

 development and nerve signs, and that we only found the latter occurring together 

 because they were both generally present in cases of low nutrition ; could this 

 hypothesis be tested ? It could be proved at once by forming the partial coefficient 

 |AB|y|. If this were small the hypothesis would be confirmed, as we would be 

 shown that on excluding all cases of C, A and B ceased to be associated. If, on the 

 other hand, | AB | y \ were still large, even though slightly smaller than | AB | , the 

 hypothesis could only be partially true or be a partial explanation. 



The partial coefficients in undefective or negative universes thus play the same 

 sort of part in checking interpretations as partial coefficients of correlation. Partial 

 associations in positive or mixed universes give further information ; if, for instance, 

 | AB | C | , | AB | D | , | AB | CD | , &c., be aU of the same order of magnitude as | AB , it 

 is evident that the presence of B continues to be a bad symptom to render A more 

 likely even when C, D, &c., are already present. If, on the other hand, these 

 associations are small, or zero within the limits of probable error, the piling up of 

 symptom on symptom, or defect on defect, ceases to make the case any worse. 



59. Now in the present case we have four defects to handle. These give 6 total 

 coefficients ; 1 2 first-order coefficients with negative and 1 2 with positive universes ; 

 6 second-order coefficients with wholly negative, 12 with partially positive, and 

 6 with wholly positive universes or 54 altogether (excluding what I have called 

 " group coefficients "). I did not think it worth while to calculate all these, and 

 have confined myself to the total and second-order partial coefficients. These are 

 given in Table IV. for boys and Table V. for girls. As well as working out the 

 associations for children of all ages, I have divided each sex into three groups : 

 Infants, Standards I. to III., and Standards IV. to Extra VII. (material in Report, 

 Table 21). This serves for two purposes: first, to check signs, &c., as given in the 

 " all ages" column ; secondly, to give some idea of change of association with age, a 

 purpose for which no other material is available in the Report.* 



* A table is given (Table 22 of the Report) showing the frequency of defective groups, but the number 

 of undefective children (a/8y<5) is not given, nor the number of children observed at each age. This makes 

 the figures useless for discussing the associations of defects in normal children. The importance of the 



