W. Brown 
359 
the values were as follows : — 
Correlations luith Age {ranh 
Geom. 0-19^ 
Alg. 0-19X 
Arith. 0-04 
A 0-21X 
B 0-11 
0 0-06 
D 0-05 
E -0'02 
F 0-02 
G -0-12 
H 0-18>^ 
I 0-19X 
•7 7 38 
P.E. for zero correlation = — — - = 0"09. 
The only values greater than twice the probable error, and therefore possibly 
appreciable, are those marked with a cross. The corresponding values, using marks, 
are : — 
Geom. 0-06, Alg. 0■23^ A 0-09, H 0•19^ I 0-07, 
"67449 
P.E. for zero correlation = — ; — , = 0'075. 
\/«3 
In the .second case, therefore, only Alg. and H are affected appreciably. Owing 
to the discrepancies between marks and ranks, only the coefficients obtained from 
marks were corrected. The formula used was, of course, the partial correlation 
coefficient fy^ for constant age*, viz. 
V(l-r,/)(l-r,/) 
Thus, for Geom. Alg., putting Geom. 1, Alg. 2, Age 3, 
rvi-rnr,. -66-0 x -23 -66 
= 68. 
' V(l-jy)(l-r,r) -0-^)(l--23=) -973 
The second main disturbing factor was the arrangement of the boys in sets 
or forms. The boys of the higher sets miglit have been expected to do better in 
every part of the work than those of the lower sets, because they had covered more 
of the syllabus than the others. Instead, however, of calculating correlation 
coefficients between order of form and each of the series of measurements, the 
"correlation ratio," -q, was evaluated^. In carrying out the correction, t] is 
substituted instead of r in the partial correlation coefficient. 
The values of t] obtained were the following : — 
Correlation Ratios, " Form " and Cliaracter. 
Geom. 
•71 
D 
•57 
Arith. 
■59 
E 
•73 
Alg. 
•87 
F 
•59 
A 
•59 
G 
•65 
B 
•28 
H 
•76 
C 
•66 
I 
•80 
Ago ^41 
The fact that t) for age is -41 while the correlation between age and total marks 
is nil seems to show that the effect of diffei'ence of form in the other series is due 
* See, e.g., G. Udny Yule : "On the Theory of CorrelatioD," Journal of the Royal Statistical 
Society, Vol. lx. Part iv. Dec. 1897, p. 833. 
t See Karl Pearson: Biometric Series ii, Drapers' Company Research Memoirs, pp. fl £f. For an 
example of the method, see Appendix II. 
46—2 
