OP ATTRIBUTES IN STATISTICS. 



305 



60. Comparing first the partial coefficients with negative universes, | AB | yS | , 

 Ac., with the total coefficients, we see that in every case, without exception, the 

 partial coefficient is greater than the total. Hence it cannot be true that any one ot 

 the defects noted is, or is even indicative of, a necessary connecting link between any 

 other two. That low nutrition brings on at once development defects and nerve 

 signs, or development defects and dulness, so that we find these pairs associated is, 

 for instance, a hypothesis that may be partly true but is insufficient to explain the 

 facts observed. Dr. WARNER'S hypothesis that " the connecting link between defects 

 of body and defective mental action is the coincident defect of brain which may be 

 known by observation of ' abnormal nerve-signs ' " * seems to me equally untenable ; 

 it may be so in some cases, but on the other hand the " connecting link " may be a 

 defect of brain not indicated by abnormal nerve signs, or not a defect of brain at all. 

 The demonstration of a necessary connecting link X between A and B would, it 

 seems to me, only be complete when |AB|| was shown to be small compared with 

 | AB | ; the demonstration that either X t or Xj or X 3 or X, had to be present as a 

 connecting link would only be complete if | AB | f , , s . . . , | were shown to be 

 small (zero within the limits of error). Now |AB|y8|, |AC|y88|, &c., are not small 

 but even larger than |AB|, |AC|, &c., hence CD, BD, &c., cannot be necessary even 

 as alternative connecting links or symptoms of such links in the way described 

 above ; the case must be much more complex and depend on a much greater variety 

 of conditions than those described by the four classes of defects noted. The follow- 

 ing figures show further how little the absence of nerve signs affects the chance of 

 an individual with development defects being mentally dull ; on Dr. WARNER'S 

 hypothesis (A/?D)/(A$) should be small compared with (AD)/(A) : 



Chance of individual being dull who exhibits development defects 



= (AD)/(A) 



Ditto, but no nerve signs = (A/JDV(A/3) 



Ditto, but neither nerve signs nor low nutrition = (A/3yD)/(A/3y) . . 



61. Turning next to the partial coefficients with wholly or partly defective 

 universes (i.e., associations in groups of which every member possesses either one or 

 two defects in addition to the possible two of which the associations are considered), 

 we see that the great majority are small and many even negative. The probable 

 errors are, however, high, since the material is small when we are confined to those 

 who are defective, so one cannot always lay great stress on the sign. In three cases 



omission is apparently unrecognised, as the last Report issued (1899) only gives more such figures ; this 

 seems to me waste of time and money. 



* Report, p. 13. 



VOL. CXCIV, A, 2 R 



