Miscellanea 
Correlation of Rank and Examination Marks. 
303 
Examination 
Civil Service Junior Examinations : 
Liverpool Messengers, 1901 
Glasgow Messengers, 1901 ... 
Manchester Messengers, 1901 
Liverpool Postmen, 1901 
Glasgow Postmen, 1901 
Manchester Postmen, 1901 ... 
Female Learners, Post Office, Nottingham, 1900 
„ „ „ Leeds, 1900 
„ „ „ Bristol, 1900 ... 
„ „ „ IManchester, 1899 
„ „ „ Leeds, 1899 
Female Skilled Telegraphists, December, 1899 ... 
May, 1899 
Female Learners, Post Office, Birmingham, 1899 
Technical School : 
English, Second Year 
Mechanics ,, 
Metalwork ,, 
Gymnastics „ 
Machine Drawing, Second Year 
Art, Second Year 
Science ,, 
Mathematics, Second Year. . . 
English, First Year 
Mechanics „ 
Metalwork „ 
Gymnaistics ,, 
Machine Drawing, First Year 
Art, First Year 
Science ,, 
Mathematics, First Year ... 
Numbers 
27 
24 
21 
19 
21 
18 
26 
46 
33 
21 
20 
18 
17 
29 
37 
35 
38 
36 
36 
36 
33 
38 
33 
31 
33 
31 
33 
32 
30 
33 
Correlation and P.E. 
9739 ± 
9831 ± 
9323 ± 
9861 ± 
9359 ± 
9647 ± 
9416± 
9694 + 
9795 ± 
9784 ± 
9736 ± 
9684 ± 
9238 ± 
9951 + 
•0067 
•0046 
•0196 
•0043 
•0183 
•0110 
•0150 
■0060 
•0048 
•0064 
•0079 
•0099 
•0240 
•0012 
•8690 + 
•9286 ± 
•9676 ± 
•9728 ± 
•9831 ± 
■ ^9845 + 
■ •9876 ± 
■ ^9896 ± 
■ ^9957 ± 
■ •9725± 
■ •9877± 
■ ^96941 
- •9508 ± 
■ ^9838 ± 
•9905 + 
- ^9742 + 
0271 
0157 
0070 
0060 
0038 
0035 
0030 
0023 
0010 
0066 
0029 
0073 
0113 
0038 
0023 
0060 
Now taking the eight First Year examinations we have 
Correlation = - -9780 ± '0032, 
while the theoretical result is — ^9766 + ^0123. 
The diflFerence is well under tlie probable error. 
If we omitted the erratic English markings we obtain for the two cases — ^9735 and - ^9754 
both fairly good representations of — -9766. 
If we include the English results and pool both series we obtain 
Coii'elation = - -9685 + "0070 
against the theoretical result Correlation = - '9766 ± '0087, 
the difference being just below the probable error of the latter result. 
The impression formed upon my mind by these results is that the result of correlating rank 
and marks of the candidates in an examination will give a result slightly less than that to be 
anticipated by the theory of a normal distribution ; but so little less that an effective control for 
detecting erratic markings such as that of the English in the technical school returns (or possibly 
the Female Skilled Telegraphists, May 1899 of the Civil Service Examinations) may be obtained 
by this correlation. 
As a second illustration I will take the following data from a Civil Service Examination for 
Messengers. There were 10 posts to be filled and 27 candidates. The subjects were Arithmetic, 
