406 



SCIENCE 



[N. S. Vol. XXXVI. No. 926 



class, if it is too easy or too difBeult, a 

 skewed distribution may result even if tlie 

 scholarship of the class is actually normally 

 distributed. In the above investigation, as 

 the number of examinations increased there 

 was a closer approach toward the normal 

 type of distribution and when nine tests had 

 been given the actual distribution was prac- 

 tically identical with that of the normal type. 

 This was also true for the elementary classes 

 in chemistry. In general it is the writer's 

 experience that as the methods of examina- 

 tion are refined and as the number of stu- 

 dents and the number of tests is increased 

 there is a closer and closer approach toward 

 the normal curve. Mathematically speaking, 

 the normal curve seems to be the limit which, 

 with refinement of method and the elimina- 

 tion of accidental variations, tests of general 

 intelligence approach. It is to be remem- 

 bered that these students were university 

 freshmen and sophomores upon whom the ef- 

 fects of high school selection have been opera- 

 tive. It is possible that if all the high-school 

 classmates of these students had continued 

 and taken the same course in the university 

 the average accomplishment of the whole 

 class might have been somewhat less, yet it is 

 not likely that the distribution would have 

 been different. 



That some mental tests are not normally 

 distributed need be no cause for criticism 

 when we recall that the essential factor in 

 grading is uniformity. What a particular 

 grade will eventually signify will depend 

 upon how successfully or unsuccessfully the 

 students who are characterized by this grade 

 meet the demands of higher institutions or 

 the demands of the world at large. It wiU 

 not depend upon whether the grade is found 

 below or above some hypothetical accomplish- 

 ment of the population at large. 



There is another question which might be 

 asked, namely: How many of the ten grades 

 awarded by Reed College represent distin- 

 guishable degrees of scholarship? At the 

 University of Missouri only five different 

 grades are awarded, and from working with 



the records of these students the writer is in- 

 inclined to believe that students who are only 

 a little above or below the average in some 

 courses tend to approach closer to the average 

 when the grades in their other courses are 

 taken into account. If this is a fact then it 

 is possible that the Reed College grades 5, 6, 

 7, do not represent different degrees of scholar- 

 ship. There is no way of determining this at 

 the University of Missouri, but Reed College 

 has the data for making this investigation. 

 If three series were to be formed as follows : 



Series I. — Students whose grades are be- 

 tween and including the limits 4^6. (Those 

 students who have no grade higher than 4 nor 

 a grade lower than 6.) 



Series II. — The same for the grade limits 

 5-7. 



Series III. — The same for the grade limits 

 6-8. 



If after credit units are considered the aver- 

 ages of these three series are not respectively 

 5, G, 7, but approach more closely to each 

 other, say 5^, 6.0, 6J, this would show that the 

 grades 5, 6, 7, do not represent distinguish- 

 able degrees of scholarship. It would, no 

 doubt, be of considerable interest to school ad- 

 ministrators to have a report from Reed Col- 

 lege on this point. 



In conclusion we may summarize the argu- 

 ments in this paper as follows : 



Such mental tests as are significant for de- 

 termining school grades approach the form 

 of the distribution of the normal curve. The 

 deviations from the normal curve may be con- 

 siderable, but some of the deviation is due to 

 factors other than those of scholarship. Wiere 

 the deviation is due to a number of interre- 

 lated causes it is difiicult to assign a value to 

 the effect of a single one of them. In the in- 

 terest of uniformity in grading it is essential 

 that the form according to which the grades 

 are distributed be the same for the differ- 

 ent schools. Since the normal curve is a 

 purely theoretical invention closely approx- 

 imating the actual conditions and is at the 

 same time not hampered by empirical con- 

 siderations, its mathematical simplicity and 



