Sir,
I copy the following from the letter of your Oxford Correspondent, published February 1:
“The results of the certificate examination were less satisfactory than in the previous year. In 1880 certificates were obtained by 475 out of 700 candidates, or 67” (should be 68) “per cent; but in 1881 by only 366 out of 731—i. e., by only 50 per cent. The chief failure seems to have been in elementary mathematics, in which subject 455 candidates out of 692 passed in 1881, as compared with 585 out of 666 in 1880. This being one of the essential subjects for Responsions at Oxford and Part 1 of the Previous Examination at Cambridge, it is not surprising that, while in 1880 362 certificates would have exempted from Responsions and 332 from Part 1 of the Previous Examination, in 1881 the numbers of such certificates were 240 and 239 respectively. Some light is perhaps thrown by these results upon a recent Responsions examination in which more than half the candidates were “plucked.” The assertions made after the publication of the certificate list last summer, that the large proportion of failures was due to a sudden raising of the standard, are disposed of by the statement in this report that the great majority of failures in mathematics were due to ignorance of the first two books of Euclid—in other words, to inadequate preperation, and neglect of the elementary parts of the work by teachers and taught.”
In justice to the writer, I have quoted this passage in full; but the only two points to which I wish to draw attention are—first, the fact that in the Responsions of last term more than half the candidates were “plucked”; secondly, that he offers as a sufficient explanation of this phenomenon the hypothesis that it was due to “inadequate preperation, and neglect of the elementary parts of the work by teachers and taught.” It does not seem to have occurred to him that such neglect, so sudden and so widely spread as his statistics seem to show, would be a phenomenon quite as surprising, and quite as much needing to be accounted for, as the one he disposes of so summarily.
As a teleologist, your correspondent is, perhaps, a trifle too easily satisfied—the kind of man who, on experiencing a sudden sharp pain in the back of his head, and finding himself prostrate on the pavement, would merely remark, while scrambling to his feet—“I have no doubt received a blow from behind”; and so would continue his journey, serenely conscious that all was now fully explained.
As a statistician, it would seem that he has yet much to learn—notably the fact that, when candidates can go in for two examinations and can pass in either but not in both, if he deals (as he does here) with total numbers only, he is counting many of the failures twice, while each success can be counted only once.
To get the true percentage of those who passed last term we must ascertain how many candidates there would have been and how many of these would have passed if the previous examination had not taken place. For the total number of candidates we add together the two lists () and deduct those common to both (81), who would otherwise be counted twice, and also those (55) who appear in the first list but had not matriculated before Responsions (). To get the total number who passed, we add together those who passed in the two lists () and deduct those (15) who passed in the first list but had not matriculated before Responsions (). Thus, the true percentage is 63. The average percentage, from Michaelmas, 1873, to Michaelmas, 1881, was 64.
We see, then, that the true answer to the question raised by your correspondent, “How are we to account for this phenomenon?” is simply that there is no phenomenon to be accounted for.
Charles L. Dodgson.
Christ Church, Oxford, February 2, 1882.