EXAMINATION SCORES The main aim of an examination is to place a set of candidates in a relative order of merit. It has a prescribed range, between a zero which marks ability below the minimum which the exam ination is designed to test, and a maximum which marks an ability greater than the examination papers can legitimately assess. Be tween these limits the examiner used to award marks, now he scores points. The precise system of scoring should be suitable to the purpose of the examination ; a system of symbols a + , a, a — ; i3+, (3, 13 etc., serves for some examinations, notably at Oxford, but it is usual to score by numbers with o as the zero limit and ioo as the maximum. It is desirable when an examina tion is repeated annually that the pass-level shall be constant throughout the series. When the numbers of candidates are small on each occasion, the constancy of the pass-level must be main tained by the examiner and it is usual to fix 40% or 50% as the pass-level, and to leave the examiner the task of ensuring that the pass-level for successive years represents the same level of ability. This is an onerous task and calls for a measure of ripe experience and sound judgment, coupled with a somewhat rare ability in setting suitable examination papers. When the candi dates at each examination run into thousands, a more objective method may be substituted for the subjective judgment of the examiner. The pass-level may be fixed at such a point on the scale that X% always pass. X may be fixed at 50 or 6o, or even 85, to suit the purposes of the examination.
Scores are arranged so that candidates are spread between o and ioo in such a fashion that if x candidates score a% then x candidates, an equal number, also score (ioo—a) % and that about 40% of the candidates score between 41% and 59%. A curve of distribution of the candidates then resembles the lines of a broad-brimmed cocked hat. Such a distribution happens readily in arithmetic, but to ensure it in English and kindred sub jects needs more careful examining. The form in which the spread of the marks finally falls depends upon the examination paper and the schedule of marks prepared by the examiner, and is, therefore, largely within his control.
When an examination includes many papers, it is usual to record passes on the single papers with some form of allowance for can didates who do exceptionally well on one or more papers and just miss passing on others. This requires that the several examiners shall so arrange that their pass-marks measure similar degrees of ability. Subjectively, this is difficult, objectively (should time allow) this equality between different papers may be determined by the regulation that the pass-mark per paper shall be that mark which will secure that Y% of the candidates who took the paper shall pass.
In competitive examinations, where there are several papers, the scores are usually added together, with or without allowances for exceptional ability displayed on one or more papers. In cer tain cases candidates have to score a certain number of marks, so to say, "below the line," as in some civil service examinations, before they are credited with any marks at all. When the papers are marked by a, 9, etc., final positions are determined either by the number of as or by the general impressions of the can didates' work.
Borderline Cases.—In close relation to the treatment of examination scores lies the necessary consideration of those can didates who nearly or only just succeed ; these candidates are frequently designated as borderline candidates. In most exam inations borderline candidates receive special attention, careful consideration being given to their work as a whole and systematic allowances made on principles prescribed by previous experience. The method of scoring differences facilitates the consideration of borderline cases.
Closely allied with the consideration of borderline cases is the necessity in competitive admission examinations of young pupils (say boys and girls of II +) of giving them an age allowance. Usually the age allowance is determined by rule of thumb methods which secure that the numbers of successes shall be evenly distributed in each month of the age group.
Finally, in such examinations some definite allowance is made for the teacher's judgment on the relative merits of the candidates whom he submits. In these and other specially appropriate ways, means are taken to secure fair treatment to all candidates.
The Organization and Conduct of Examinations.—The organization of examinations so that each candidate shall be treated in precisely the same way as every other candidate, in creases in complexity with the number of candidates examined. The greatest precautions are taken to ensure the secrecy of the examination papers before and during the examination, and to isolate the individual candidates in the examination room. Both the seating arrangements and the supervision should be adequate to remove all temptation of copying. The hygienic conditions and the time of year and day should be such as to reduce the strain to a minimum. The examination time-table should tend to minimize the effects of mental fatigue.
Marking the Scripts.—The chief examiner usually sets the papers of questions and marks some of the scripts; the assistant examiners mark scripts. The preliminary stages in marking are usually occupied with the determination of a schedule of marks. All markers read a sample batch of scripts and then meet to dis cuss what the particular batch of candidates have done with the particular paper. The chief examiner has provided a provisional schedule of marking, and this schedule is modified in the light of the experience gained from reading the samples of scripts. The marking thus tends to be objective and to become merely a grading of the candidates against each other. The markers in conference determine upon a revised schedule of marks which is strictly followed thereafter ; they disperse and, later, supply the chief examiner with samples of their marking. Markers, being human and being required to work under pressure against a time limit, inevitably err; many of their vagaries occur in mechanical mat ters such as totalling marks. The marking of simple questions is merely a matter of eyesight. When the questions are more complex, or are of the kind which require essay-type answers, marking becomes more difficult ; human judgment in these cases does not always act consistently, and inconsistencies of marking are inevitable. It is a function of the chief examiner to standardize the work of several examiners engaged on the same paper.
The Pass-mark.—In competitive examinations there is no pass-mark, the number of awards is predetermined. In university and professional qualifying examinations, where marking is by figures and not impressions, a pass-mark is fixed to separate those who pass from those who fail. In some cases the pass-mark is 50% of the maximum, in others it may be 3o% or 70%. Refer ence has already been made to the unavoidable incidence of chance in the relationship between the candidates and the ques tions. There is also an inevitable incidence of chance in the re lationship between the candidates and the markers. In both these cases the incidence of chance tends to be concentrated upon the candidates of average ability, so that of any set of candidates the markers may decide on the relative merits of the best fourth and of the worst fourth with comparative certainty, but their de cisions concerning the middle half are much affected by luck.
Consequently, the pass-mark should always occur in such a posi tion as to leave the middle half definitely as "passes" or "fail ures"; this means that the examination papers should be either so difficult, or so easy, that the "pass-mark" falls on the slope of the cocked-hat curve which shows the spread of the marks. If the curve is a symmetrical cocked hat, the pass-mark should not be 5o%, but less than 4o% or more than 6o%. If the pass mark is 5o%, then the curve should be a "skewed" cocked hat. In other words the relation between the difficulty of the examina tion papers and the pass-mark should be such that the borderline candidates are few in number.
The fixation of the pass-mark is the business of the examin ing authority. It is urged that the pass-mark for a practical examination should be higher since candidates either can or can not perform the manipulative operations tested. Such a con tention implies that the test is a first-class sample of all the manipulative operations which might be tested. In the exam ination for teachers' certificates the pass-mark is very low, for most of the candidates have been specially selected and specially trained and, on these counts, are theoretically qualified for a certificate, and the examination result is merely a confirmation of the goodness of the previous selection and the training. It may reasonably be urged that the general school examination should be conducted similarly. Secondary scholars tend to be specially selected ; they are specially trained or taught in approved schools by registered teachers on an approved curriculum, so that the examination should be so arranged and the pass-mark should be so low that a large majority of these scholars should pass the examination at the conclusion of their course. So liberal a view of the situation runs counter to the university tradition so definitely that it is only by slow degrees that the general school examination system is being reformed. It is, of course, handicapped, as we have seen, by the two somewhat incompatible examinations, matriculation and leaving-school certificate being linked together, yet to divide them is difficult on the score of expense and of duplication of examinations, which is bad alike for pupil and teacher.
Checking the Scores.—A system of checking the scores is inevitable. Mechanical inaccuracies are readily discovered ; in consistent marking may be detected. A staff of experienced checkers is required and their efforts must be concentrated upon the scripts of candidates on or near the borderline.