Tiers of Ability, Part 2

Continued from Part 1

 

    In his book Hereditary Genius, Francis Galton provides an excellent illustration of this phenomenon with data from the Cambridge Mathematical Tripos.  There were two degrees in the old Cambridge system, an honours degree and a pass degree.  In the original Tripos, which ran from 1748 - 1909, the honours students were ranked based on how many points they scored on the exam.  The highest scorers were called Wranglers and those below them Optimes, while the very highest scorer was called the Senior Wrangler.  The candidate who scored lowest, but still managed to perform at the honours level was called the Wooden Spoon.  Here is what Galton has to say about the matter:       

 "There can hardly be a surer evidence of the enormous difference between the intellectual capacity of men, than the prodigious differences in the numbers of marks obtained by those who gain mathematical honours at Cambridge. I therefore crave permission to speak at some length upon this subject, although the details are dry and of little general interest. There are between 400 and 450 students who take their degrees in each year, and of these, about 100 succeed in gaining honours in mathematics, and are ranged by the examiners in strict order of merit.

About the first forty of those who take mathematical honours are distinguished by the title of wranglers, and it is a decidedly creditable thing to be even a low wrangler; it will secure a fellowship in a small college. It must be carefully borne in mind that the distinction of being the first in this list of honours, or what is called the senior wrangler of the year, means a vast deal more than being the foremost mathematician of 400 or 450 men taken at hap-hazard. No doubt the large bulk of Cambridge men are taken almost at hap-hazard. A boy is intended by his parents for some profession; if that profession be either the Church or the Bar, it used to be almost requisite, and it is still important, that he should be sent to Cambridge or Oxford. These youths may justly be considered as having been taken at hap-hazard. But there are many others who have fairly won their way to the Universities, and are therefore selected from an enormous area. Fully one-half of the wranglers have been boys of note at their respective schools, and, conversely, almost all boys of note at schools find their way to the Universities. Hence it is that among their comparatively small number of students, the Universities include the highest youthful scholastic ability of all England. The senior wrangler, in each successive year, is the chief of these as regards mathematics, and this, the highest distinction, is, or was, continually won by youths who had no mathematical training of importance before they went to Cambridge.

... 

The examination lasts five and a half hours a day for eight days. All the answers are carefully marked by the examiners, who add up the marks at the end and range the candidates in strict order of merit. The fairness and thoroughness of Cambridge examinations have never had a breath of suspicion cast upon them.

Unfortunately for my purposes, the marks are not published. They are not even assigned on a uniform system, since each examiner is permitted to employ his own scale of marks; but whatever scale he uses, the results as to proportional merit are the same. I am indebted to a Cambridge examiner for a copy of his marks in respect to two examinations, in which the scales of marks were so alike as to make it easy, by a slight proportional adjustment, to compare the two together. This was, to a certain degree, a confidential communication, so that it would be improper for me to publish anything that would identify the years to which these marks refer. I simply give them as groups of figures, sufficient to show the enormous differences of merit. The lowest man in the list of honours gains less than 300 marks; the lowest wrangler gains about 1,500 marks; and the senior wrangler, in one of the lists now before me, gained more than 7,500 marks. Consequently, the lowest wrangler has more than five times the merit of the lowest junior optime, and less than one-fifth the merit of the senior wrangler.

The results of two years are thrown into a single table.

The total number of marks obtainable in each year was 17,000.

 

The precise number of marks obtained by the senior wrangler in the more remarkable of these two years was 7,634; by the second wrangler in the same year, 4,123; and by the lowest man in the list of honours, only 237. Consequently, the senior wrangler obtained nearly twice as many marks as the second wrangler, and more than thirty-two times as many as the lowest man. I have received from another examiner the marks of a year in which the senior wrangler was conspicuously eminent.

He obtained 9,422 marks, whilst the second in the same year—whose merits were by no means inferior to those of second wranglers in general—obtained only 5,642. The man at the bottom of the same honour list had only 309 marks, or one-thirtieth the number of the senior wrangler.

...

The mathematical powers of the last man on the list of honours, which are so low when compared with those of a senior wrangler, are mediocre, or even above mediocrity, when compared with the gifts of Englishmen generally. Though the examination places 100 honour men above him, it puts no less than 300 “poll men” below him. Even if we go so far as to allow that 200 out of the 300 refuse to work hard enough to get honours, there will remain 100 who, even if they worked hard, could not get them. "

    From the table, we see that the scores are indeed positively skewed.  One amusing story about the Tripos is that William Thompson, later Lord Kelvin was universally acknowledged as the best in his year at Cambridge, so when the Tripos results were posted, he asked one of the college servants, "Go see who is the second Wrangler."  The servant did so and then responded, "You are, sir."  Someone else had beaten him.