Recognized HTML document

Statistical Investigations   389

case to mark from the mean or median. It is not quite clear in this case why there should not be negative marks for those who fell short of mediocrity. Galton then provides marks for each rank above 50°/° or again for the deviate. In the latter case the full number of marks is supposed to be reached by a grade 99.99. Next he draws up a table in which the total marks for physical efficiency are assumed to be 10 and are supposed to be assigned in different proportions to rank and to absolute achievement, i.e. to, deviate from mediocrity. His table (B. A. R. p. 476) is as follows

 Percentage of marks assigned to Rank Rank Deviate 50° 55° 75° 95° 99° 99-99...0 100 0 0 1.0 5.0 9.0 9.8 10.0 50 50 0 0.7 3.5 6.9 8.4 10.0 33.3 66.6 0 0.6 3.0 6.2 8.0 10.0 25 75 0 0.5 2.7 5.8 7.7 10.0 0 100 0 0.4 2.0 4.8 7.0 10.0

It is clear that Galton is compounding what every schoolmaster has to consider, namely: "place in class" with "marks in examination," or indeed "place" and "marks in examination." If the distribution were normal the marks would be readily deducible from "place in examination. Considering what wide differences occur between the top individuals-for example in the old Cambridge Mathematical Tripos system-and what slight differences between mediocre individuals, one is inclined to doubt the legitimacy of marking by rank. This point was recognised, I think, by Galton later when he endeavoured to estimate the average differences between individuals arranged according to rank. However the table is suggestive and we leave it to the consideration of the educationalist.

Galton supposes the chief physical measurements to have been reduced for the class under examination to percentile scales, such as in the table on our p. 376. He gives a rather clear diagram of the absolute values for males and females at each rank for seven characters on p. 291. In some of the characters it would be desirable for rapid and safe interpolation to insert a few more values of the deviate.

boys. Their average difference in judgment was 8.75 °/, of the maximum marks. Nineteen of the boys were subsequently examined in English Essay, and the essays submitted to two independent examiners. The average difference was now 16-7'/. of the maximum marks. The experiments seem to have been undertaken at Galton's suggestion and are used by him as an argument that physical test marks can be as accurately determined as marks for literary work. Some years ago the present writer reported on the marking statistics of the London Matriculation Examination. He was startled to find that the relative personal equation of examiners in history, languages and literature was very greatly larger than the relative personal equation of examiners in branches of science; and that no systematic method of correcting for this personal equation bad been adopted. Thus a candidate's chance of passing depended largely on the examiner to whom his paper was allotted! It would appear therefore that the choice of an English essay for comparison of marking differences was rather unfortunate.

1 See Nature, Vol. XL, pp. 650 and 651.