37o POPULAR SCIENCE MONTHLY. 



to a discussion of college grades. The literature is very scanty. I can 

 only refer to two papers*, both of which are slight. 



Grades are usually assigned on a scale of 100, some institutions, 

 as Harvard and Columbia, reporting only the five groups into which 

 the men are divided. The starting point in all grades is the fact that 

 the written papers or the results of the term's work can be arranged 

 more or less accurately in the order of merit, f The assignment of 

 quantitative grades to a qualitative series or its division into groups 

 is usually done in an arbitrary manner, and, so far as I am aware, no 

 attempt has hitherto been made to assign probable errors. It is 

 obvious that our grades should be standardized. Our colleges are in the 

 position of a grocer who should let each of his clerks give to customers 

 without weighing and without knowledge of market prices what he 

 believed to be a dollar's worth of tea. 



The simplest method of assigning grades is to arrange a hundred 

 papers as nearly as may be in the order of merit and to give the 

 poorest paper the grade 1, the next poorest the grade 2, and so on, 

 until the best paper receives the grade 100. The 100 cases would 

 not be exactly representative of the entire group with which we are 

 concerned; but if we had 100,000 cases, the error from this source in 

 giving the poorest 1,000 the grade of 1, etc. would be entirely 

 negligible. It is possible to calculate how likely it is that in a ran- 

 dom group of 100 cases we should find two, three or more men to 

 whom the lowest or any other grade should be assigned. Each in- 

 structor forms a rough estimate of the group of students with which 

 he is concerned, and can with a probable error that might be deter- 

 mined assign its place in the series to each case. 



If men are arranged in this way in the order of merit and each is 

 assigned his position in the series from 1 to 100, the differences be- 

 tween them will not be equal. If a hundred men are placed in a 

 row according to height, the line passing along the tops of their heads 

 will not be a straight line. The men in the middle of the row will 

 differ but little from one another, and the differences will become 

 continually greater towards the ends. Fig. 1 (page 366) shows the ap- 

 proximate distribution in stature of 1,052 English women, measured for 

 Professor Karl Pearson. Their average height was about 5 feet 2^ 

 inches; 18.3 per cent, of the whole number were between 62 and 63 

 inches, and one half of them were within about 1% inches of the 

 average, the probable error. The ordinates or vertical lines are pro- 



* ' American Titles and Distinctions,' W. Le Conte Stevens, The Popular 

 Science Monthly, 63: 312-320, 1903. 'The Education of Examiners,' E. B. 

 Sargent, "Nature, 70: 63-65, 1904. 



f Many instructors doubtless let the grade represent the percentage of 

 questions correctly answered. This is a possible but fallacious method in a 

 subject such as mathematics; in a subject such as psychology it is impossible. 



