May 19, 1904] 



NATURE 



^l 



THE EDUCATION OF EXAMINERS.' 

 "T^HE subject that I have chosen for my presidential 

 ■'- address may at first sight seem far from inviting. 

 Yet, in spite of the unusual title of my paper, 1 undertake 

 to say that most of you present here to-day will follow 

 the results which 1 shall lay before you with ease, and 

 will find a growing interest in certain ideas which cannot 

 but prove novel to those of you who have not before thought 

 of examiners as belonging to the human race, and there- 

 fore capable of education. 



In a sense we are all examiners. We note and tabulate 

 events and their causes. We distribute mankind into 

 ethnological groups, or compare them as industrial workers. 

 We ascertain their wants and their means of satisfying 

 those wants. We examine and record the growth of 

 custom, the physical and mental development of the human 

 being, the changes in the mind itself and the order of 

 such changes, the progress and decay of language, the 

 distribution of wealth, the progress of society. Even the 

 laws of statistics are submitted to examination. 



Thus, side by side with the advance of theory in con- 

 nection with all the sciences that fall under this section 

 (archa;ology, education, mental science, philology, political 

 economy, sociology, statistics), goes the scrutiny of results. 

 It is justifiable, therefore, to think that an examination 

 of methods of examination, even in connection with only 

 one of those subjects, will throw a light upon such methods 

 in general. I propose to-day to consider that small part 

 of education which consists in the testing of the results of 

 study by written papers. 



You will perhaps wonder how it is that 1 have taken 

 such an interest in the doings of examiners. The ' fact 

 is that I am one of the few persons who have been for a 

 lengthy period in the position of an examiner of examiners. 

 In the position which I held in the Civil-Service Commission 

 for nearly fifteen years, it was my daily task to consider 

 the character of the papers set by some of the highest 

 dignitaries at Cxford and Cambridge, arid other universi- 

 ties, to candidates for appointments in the English Civil 

 Service. I had, moreover, to investigate the marking of 

 the written answers of candidates, and to say whether the 

 general results appeared to me to be fair and -trustworthy. 



Of course, it will be understood that there are good as 

 well as bad examiners. If the methods of good examiners 

 are compared together, it will be found- that they tend to 

 uniformity, and that their results have certain character- 

 istics in common. Whereas the methods and results of bad 

 examiners differ froin one another in every conceivable way. 



But how are these results to be shown? It is not possible 

 to obtain such information by running the eye down the 

 totals awarded to candidates in the mark-sheets. Patient 

 study will no doubt do something, but, where figures occur 

 irregularly, it is hard to appreciate their import without 

 definite classification. 



In these days of the almost universal use of " squared " 

 paper, all that is required is to find the percentages of 

 candidates obtaining marks between the limits named, and 

 to mark them off by counting the squares, say five candi-" 

 dates to a square. If the maximum in the subject is not" 

 100, then it is only necessary to reduce the marks to that' 

 scale. By joining the top points of the vertical lines, which 

 we call ordinates, the characteristic curve of the examiner 

 is obtained, or, what is even more satisfactory, if black' 

 columns are raised on the bases o to 10, 11 to 20, &c., to 

 show the number of candidates within these limits of marks,' 

 the result is a number of stepping-stones, shown in silhouette, 

 and rising and falling in general harlnony with the curve. 



Difficulties presented themselves to me as soon as 

 I began to plot the results of exaini'ners from their mark- 

 sheets. Until this had been done it was impossible to 

 analyse the character of the marking, even after hours of 

 study of the mark-sheets themselves. But as soon as the 

 graphical representation had been arrived at, the whole 

 matter was simplified. It was only necessary to determine 

 whether there was any Special form of curve to which the 

 many varieties that have been placed before you ought to 

 tend, or whether each subject, and even each examiner, 

 1 .\bndged from an address delivered before Section D of the South 

 African Association for the .Advancement of Science on April 5 hy Mr. 

 E. IJ. Sargant, Education Adviser to Lord Milner. 



NO. 1803, VOL. 70] 



might be properly represented by a different curve. I very 

 soon became convinced that there was a tendency among 

 the best examiners in many subjects to obtain results which 

 gave the graphical form of a gendarme's hat (Fig. 2). 



This form is one which is recognised by mathematicians 

 as belonging to the so-called curve of " errors." I can 

 best illustrate what is meant by this curve by supposing 

 that some person in this room, experienced in the use of 

 fire-arms, were asked to fire shots at a paper target on 

 which a vertical straight line had been drawn as the mark 

 to be aimed at. After a large number of shots had been 

 fired, you would find that the holes in the target were 

 arranged in about equal 

 numbers on either side of 

 the line, and that very few 

 had actually hit the mark. 

 If the distance of each shot 

 from the centre line were 

 measured and entered on a 

 table, we should find so 

 many falling within one 

 inch of the line, so many 

 between one inch and two 

 inches, and so on. The 

 curve now placed before 

 you (Fig. i) is produced by 

 showing the number of 

 shots falling within one 

 inch on one side as a' 

 column of proportionate 

 height erected on a base 

 reaching one inch from the 

 centre line. Similarly the 

 column showing the 

 number between one and 

 two inches is drawn on a 

 base between one and two 

 inches from the centre line, ' 

 a-nd so on. 



Now I show you a 

 second curve (Fig. 2), in 



which the pistol has been put into the hands df an in- 

 experienced person. You will at once perceive that these 

 two curves are familiar to you. The curve of the good shot 

 resen^bles the curve of the bad examiner, and the curve of 

 the bad shot the curve of the good examiner. ' I think you 

 will spare-me giving you the mathematical equation of this 

 curve, although many of the theorems gnd problems con- 

 nected with it are extremely interesting. In preparing my 

 paper to-day I have had to consider some of these questions 

 from a mathematical point of view, and in doing so I have 

 had the inestimable assistance of Miss Fawcett. I do not, 

 however, propose to weary you with the rtiaithfematical 

 treatment of the subject, but one result deserves consider- 

 ation, because it is at the root of all the properties of this 

 curve. If we allow the two sets of shots to be fired at one 

 target, and classify them as before (dividing each total by 

 two, since the number of shots is doubled), we shall obtain 

 a curve of the same family as the component curves. How- 

 ever many times the pro- 

 cess is 'repeated, each 

 iTiarksman will repeat his 

 identical curve — on the 

 supposition that he does 

 not improve owing to 

 practice^and of course the 

 resultant curve due to 

 both sets will be repeated. 



Instead of taking only 

 two performers with the 

 pistol of unequal merit, 

 we may bring within our 

 view a considerable 

 number in an ascending 

 or descending scale of 

 accuracy, and trace upon one sheet a series of these curves. 

 Here is such a series (Fig. 3). 



In each of these curves it should be noticed that the 

 extreme portions never touch the base line, but they 

 approach closer and closer to that line, so that the area 

 enclosed in each case between it and the curve in question 



