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SETTING & MAINTAINING EXAM STANDARDS

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SETTING & MAINTAINING EXAM STANDARDS

Raja C. Bandaranayake

NORM-REFERENCED

Relative

Based on peer-performance

Varies with each group

Cut-off point not related to competence

CRITERION-REFERENCED

Absolute

Not related to peer performance

Standard set prior to exam

Referenced to a definedlevel of performance

- 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

- 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

- 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.
- EASYMEDIUMHARD
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

- EASYMEDIUMHARD

- 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 MODIFICATIONEASY MEDIUM HARDESSENT. 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

A

fmax

20

Failure

Rate%

15

B

fmin

10

35

40

45

50

Cut-off score(%)

cmin

cmax

HOFSTEE METHOD

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%

- 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% betterthan 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%