SETTING & MAINTAINING EXAM STANDARDS Raja C. Bandaranayake

NORM- & CRITERION-REFERENCED STANDARDS Absolute Not related to peer performance Standard set prior to exam Referenced to a defined level of performance NORM-REFERENCED Relative Based on peer-performance Varies with each group Cut-off point not related to competence

NEDELSKY (1954) METHOD: Example Consider N judges and n MCQ items of 1 in 5 type Judge A identifies 2 options in item 1 as those which a minimally competent examinee should eliminate as incorrect. MPL for that item for Judge A [MPLA1] = 1/(5-2) = 1/3 Similarly, in item 2 he identifies 3 options, giving an MPLA2 = 1/(5-3) = 1/2 He repeats this process for each item. The exam MPL for Judge A [MPLA] = MPLA1 +MPLA2 + MPLA3 + ………….MPLAn Similarly, Judge B’s MPL [MPLB] is determined The MPL for the exam (= cut-off score) is: (MPLA + MPLB + MPLC +….MPLN) / N

ANGOFF (1971) METHOD Example N judges consider 100 minimally competent examinees taking an MCQ exam of n items. Judge A estimates that, of these examinees, 50 should answer item 1 correctly, 20 item 2 correctly, 70 item 3 correctly, and so on to item n. The MPL for Judge A [MPLA] = (0.5 + 0.2 + 0.7 + . xn) / n X 100 = (say) A%. Similarly, for Judges B, C, D, E, …..N, the MPLs would be B%, C%, D%, E% ……N%, respectively. The MPL (cut-off score) for the exam is: (A% + B% + C% + D% + E% +....N%) / N

EBEL (1972) METHOD Example Assume that Judge A assigns items in a 200-item MCQ test to the cells of a “relevance-by-difficulty” matrix, as follows. He then estimates the percentage of items in each cell of the matrix that a minimally competent examinee should be able to answer correctly (as indicated within the cell). Each cell also includes the products of these two values. EASY MEDIUM HARD ESSENTIAL 15 x 100% = 1500 25 x 80% =2000 10 x 60% = 600 IMPORTANT 20 x 80% = 1600 40 x 60% =2400 20 x 50% =1000 ACCEPTABLE 10 x 50% = 500 25 x 40% = 1000 5 x 10% = 50 QUESTIONABLE 10 x 30% = 300 15 x 20% = 300 5 x 0% = 0

EBEL (1972) METHOD - contd. Example The MPL for Judge A [MPLA] is then: (1500 + 1600 + 500 + 300 + 2000 + 1000 + 300 + 600 + 1000 + 50 + 0) / 200 = 56.25 % Similarly, the MPL for Judges B [MPLB], C [MPLc], D [MPLD] …..N [MPLN] are determined. The MPL for the exam (cut-off score) is: (MPLA+ MPLB+ MPLc+ MPLD + …..MPLN) / N

PROPOSED EBEL MODIFICATION. EASY. MEDIUM. HARD ESSENT. 6x 100% = 600 PROPOSED EBEL MODIFICATION EASY MEDIUM HARD ESSENT. 6x 100% = 600 12 x 80% = 960 7 x 50% = 350 IMPORT. 12 x 80% = 960 24 x 60% = 1440 19 x 40% = 760 ACCEPT. 5 x 60% = 300 12 x 50% = 600 3 x 10% = 30 MPL: =600 + 960 + 350 + 960 + 1440 + 760 + 300 + 600 + 30 =6000/100 = 60

HOFSTEE METHOD fmin fmax cmin cmax A B Failure Rate% Cut-off score(%) 10 15 20 35 40 45 50 fmin fmax cmin cmax A B

HOFSTEE METHOD Example A plot of cut-off scores for a given exam against resulting failure rates is given cmin = 40% cmax = 45% fmin = 10% fmax = 20% A = point representing cmin,fmax B = point representing cmax,fmin Line AB intersects the curve at a cut-off point of 42.5% Thus, operational cut-off score = 42.5%

CUT-OFF SCORE FOR 1 IN 5 MCQ [FRACS PART 1] Probability of guessing (=1 in 5) = 20% ‘Total ignorance’ score = 20% Maximum possible score =100% Effective range of scores = 20% to 100% Mid-point of this range = 60% Additional factor (as PG exam) = 5% Nominal cut-off score (60%+5%) = 65%

CUT-OFF SCORES: “MARKER QUESTIONS” 1. Comparison of exam scores Mean score in this exam: 56.7% Average exam mean score over last 4 years: 59.4% Thus mean score in this exam is: 2.7% lower Assuming this candidate group is of same standard as in last 4 yrs, this exam is: 2.7% harder

CUT-OFF SCORES: “MARKER QUESTIONS” - contd. 2. Comparison of “marker” scores Mean score in this exam on previously used questions (N=162): 62.5% Mean score on same questions when they were each last used: 60.5% Thus, when compared with previous candidates, this group of candidates, on these items, scored (62.5-60.5)% = 2.0% higher Thus this group of candidates is: 2.0% better than previous groups

CUT-OFF SCORES: “MARKER QUESTIONS” – contd. 3. Estimating examination difficulty Thus it is expected that their mean score in this exam would be: 2.0% higher But their mean score in this exam is: 2.7% lower Thus this exam is really: 4.7% harder

CUT-OFF SCORES: “MARKER QUESTIONS” –contd. 4. Determining cut-off score The cut-off level for an average exam is: 65.0% Thus the cut-off level for this exam should be (65 – 4.7)% = 60.3% Cut-off score = 60.3%

HOFSTEE CURVE Failure Rate% Cut-off score(%) 10 15 20 55 60 65 70