EXAMINATIONS, GRADES AND CREDITS. 375 



per cent, in history; 34.9 per cent, are given a grade below 50 in 

 mathematics and only 19.1 per cent, in English. It is obvious that 

 such grades should be standardized. It may be remarked incidentally 

 that it is easy to select examiners by a competitive examination. If 

 twenty candidates grade the same sets of papers, those whose grades 

 are nearest the average of all the grades are likely to be the most 

 competent examiners. 



In these cases, and in all grades with which I am acquainted, 

 there is a tendency to grade students above the average. Professor 

 Pearson finds that in estimating the health of English boys, teachers 

 place twice as many above ' normally healthy ' as below, and he seems 

 to regard it as gratifying that English boys should be more than 

 normally healthy. We look on our own students as better than the 

 average and in any case give them the benefit of the doubt. We call 

 things ' fair ' that are only average, and then the word ' fair ' comes 

 to mean average. Then we assign the grade ' fair ' to students who 

 are below the average, and a ' fair ' student comes to mean a poor 

 student. In assigning grades such words should be avoided ; we should 

 learn to think in terms of the average and probable error. 



If grades are given on a centile system, the grade should mean the 

 position of the man in his group; thus 60 should mean that in the 

 long run it is more likely than anything else that there would be 

 forty men better and fifty-nine not so good. The average probable 

 error should be determined and a probable error should be attached 

 to the grades; thus the grade 60 =fc 10 means that the chances are 

 even that there are between thirty and fifty men in the group who 

 are better. The probable error becomes smaller as we depart from 

 the average man; I estimate on the basis of a few experiments that 

 it is over 10 in the middle of the scale. If this proves to be correct 

 on the basis of more extended data, it is needless to grade more closely 

 than on a scale of 10, though the first decimal would have some 

 meaning when the grades are combined. If a hundred men are 

 divided into ten groups of 10 each, the men in the middle groups will 

 differ less from each other than those towards the ends, and if we 

 wish to let the groups represent approximately equal ranges of merit, 

 we can, as explained above, make five groups, A, B, C, D and F, 

 putting 40 men in C, 20 men in both B and D and 10 in both A 

 and F. 



The determination of the validity of the grades given to college 

 students and their standardization appear to me to be important be- 

 cause I regard it as desirable that students should be credited for the 

 work they do rather than for the number of hours that they attend 

 courses. By our present method a student who fails gets no credit 

 at all, while a student who is nearly as bad (and perhaps worse) 



