634 



SCIENCE 



[N. S. Vol. XXXVIII. No. 9S3 



in length from ten inches to twenty-three 

 inches. These " measurements " based on 

 visual impressions are given in Table IV. 



The validity of these measurements can be 

 readily compared with the validity of the 

 grades in Table I. by means of the coefficient 

 of variability which is computed by dividing 

 the mean variation by the average. The aver- 

 age coefficient of variability of the grades (last 

 column in Table I.) is almost identical with 

 that of the rods, .07 and .06, respectively. 

 Hence measurements made by means of a 

 mental scale are subject to the same amount 

 of inaccuracy in one field as in another. It 

 simply means that the mind can not discrimi- 

 nate any more accurately. If we are attempt- 



simply using the same scale for measuring 

 something of similar nature. 



Then it has been suggested that the grades 

 in Table I. must necessarily be inaccurate be- 

 cause these instructors did not know the stu- 

 dents who wrote the papers. But just on that 

 account they would be all the more able to 

 give an unprejudiced evaluation of the papers 

 as papers. Many teachers have the practise 

 of placing the papers so that when they pick 

 one up for grading they do not know whose 

 paper it is. If then the teacher wishes to raise 

 or lower the mark according to the diligence 

 or negligence of the student, well and good, 

 but that does not mean that the grade of the 

 paper will be any more accurate. 



ing to evaluate a paper by a scale of 100, 99, 

 98, 97, 96, 95, etc., we are attempting the im- 

 possible. The mind simply can not discrimi- 

 nate between a paper of grade 85 and another 

 one of grade 86. If the second is appreciably 

 better it more likely ought to have a grade of 

 90. The situation is analogous to asking a 

 person to estimate the width of a room in 

 inches when you should ask him to estimate it 

 in yards. Estimates in terms of large units, 

 of course, do not have greater absolute ac- 

 curacy, but they are more apt to be uniform. 

 Several criticisms have been suggested to 

 me in discussing the results presented in this 

 paper. For example, some teachers state that 

 they do not attach much importance to the 

 final examination, but grade the student largely 

 by his other work, such as themes, daily reci- 

 tations, etc., and that the situation is very dif- 

 ferent in those matters. This objection is be- 

 side the point because you are simply shifting 

 the responsibility to something else. You are 



A third suggestion is that with a fine scale 

 of marking the teacher is able to impose a 

 penalty for shiftless work and indifferent atti- 

 tude. But with a coarser scale on which the 

 steps really mean something it is possible to 

 attach a penalty of real significance. 



The second part of this paper relates to the 

 distribution of grades. How frequently should 

 each division of the scale be used when as- 

 signing marks to large groups of pupils? By 

 various psychological reasons, which I shall 

 not state here,* it can be shown that the dis- 

 tribution of grades among large groups of stu- 

 dents who have not been subject to special se- 

 lection, should follow the probability curve. 

 Thus the distribution of marks of college 

 freshmen, who, strictly speaking, are a more 

 or less select group, should, and in fact does, 

 conform to the probability curve. Fig. 1 



*See Dearboriij W. F., "School and Univereity 

 Grades," Bulletin of the University of Wisconsin, 

 No. 368. 



