Confidence-based assessment in the 1st year medical end-of-year exam

Tony Gardner-MedwinPhysiology, UCL a useful study tool - but why in exams?it reflects the proper meaning of knowledgeconventional marking disadvantages able studentshow did the students do in the exam?conf-asst was a more reliable measure of student abilityit saves on the number of questions required

a useful study tool - but why in exams?it reflects the proper meaning of knowledgeconventional marking disadvantages able studentshow did the students do in the exam?conf-asst was a more reliable measure of student abilityit saves on the number of questions required

Knowledge depends on degree of belief, or confidence:knowledge uncertainty ignorance misconception delusionWhat is Knowledge?Knowledge depends on degree of belief, or confidence:knowledgeuncertaintyignorancemisconceptiondelusion=0-log2(confidence*) for truth of a=1true proposition

>>1

Measurement of knowledge requires the eliciting of confidence (or *subjective probability) for the truth of correct statements.

This requires a proper scheme of incentives

LAPT confidence-based scoring scheme

Confidence Level 1 2 3Score if Correct 1 2 3Score if incorrect 0 -2 -6P(correct) < 67% >67% >80%Odds < 2:1 >2:1 >4:1

conventional marking disadvantages able studentsSuppose 4 students go for the same answer options in an exam: 75 , 25 Ai is confident of all his answers Bo is very hesitant about all her answersCyis realistic (expects 75%), but cant distinguish reliable & uncertain answersDi is confident of 50 answers (90% ) and uncertain of the others (60% )Clearly: Di > Cy > Bo, AiDi has extra insight - about her knowledge, or maybe about subtleties in questions How can she use this insight?Conventional scoring: Her only option is to omit uncertain answers: % correct: Ai = Bo = Cy = 75%, Di = 45% negative marking score (1): Ai = Bo = Cy = 50%, Di = 40% Confidence-based scoring: She can moderate her confidence:Ai enters all at C=3, Bo at C=1:Ai = Bo = 25%Cy enters all at C=2:Cy = 33%Di splits answers C=3, C=1:Di = 48%[adjust] 33%

Summary aimsreward the ability to distinguish reliable and uncertain answers (whatever the reason for uncertainty)penalise confident errors more than errors from uncertaintyWhat people sometimes think is the aim!to penalise a general over-confidence or under-confidence - probably helped by practice & feedback, but not an exam issue

How well did students discriminate? exam: 500 T/F Qs, in 2 sessions, each 2hrs331 students: 190 F, 141 M

0%20%40%60%80%100%0%20%40%60%80%100%conventional scaled score (simple score) confidence-based scoreA. (50% correct)dacb

Simple scores (scaled conventional scores)- 65% of the variance came from answers at C=1, but only 18% of the credit.

Breakdown of credit and variance due to uncertaintyConfidence-based scores: these give less weight to uncertain answers; uncertainty variance is then more in proportion to credit, and was reduced by 46% (relative to the variation of student marks)

Exam marks are determined by:1. the students knowledge and skills in the subject area2. the level of difficulty of the questions3. chance factors in the way questions relate to details of the students knowledge 4. chance factors in the way uncertainties are resolved (luck)The most convincing test of this is to compare marks on one set of questions with marks for the same student on a different set . A good correlation means we are measuring something about the student, not just noise(1) = signal (its measurement is the object of the exam) (3,4) = noise (random factors obscuring the signal)Confidence-based marks improve the signal-to-noise ratio

The correlation, across students, between scores on one set of questions and another is higher for confidence than for simple scores.But perhaps they are just measuring ability to handle confidence ?

How should one handle students with poor calibration?Significantly overconfident: 2 students (1%)e.g. 50% correct @C=1, 59%@C=2, 73%@C=3Significantly underconfident: 41 students (14%)e.g. 83% correct @C=1, 89%@C=2, 99%@C=3Maybe one shouldnt penalise such students Adjusted confidence-based score:Mark the set of answers at each C level as if they were entered at the C level that gives the highest score. mean benefit = 1.5% 2.1% (median 0.6%)

0%20%40%60%80%100%0%20%40%60%80%100%simple scaled score confidence-based scoreA. (50% correct)(100% correct)

simple conf conf (adj)Signal / noise variance ratio: 2.8 5.3 4.3Savings in no. of Qs required: - 48% 35%

SUMMARY CONCLUSIONSAdjusted confidence scores seem the best scores to use (they dont discriminate on the basis of the calibration of a persons confidence judgements, and are also the best predictors of performance on a separate set of questions).Reliable discrimination of student knowledge can be achieved with one third fewer questions, compared with conventional scoring.Confidence scoring is not only fundamentally more fair (rewarding students who can correctly identify which answers are uncertain) but it is more efficient at measuring performance.

www.ucl.ac.uk/~cusplap

confident errors are far worse than acknowledged ignorance and are a wake-up call (-6!) to pay attention to explanationsexpressing uncertainty when you are uncertain is a good thingthinking about the basis and reliability of answers can help tie bits of knowledge together (to form understanding)checking an answer and rereading the question are worthwhilesound confidence judgement is a valued intellectual skill in every context, and one they can improve

Principles that students seem readily to understand :-both under- and over- confidence are impediments to learning

biba talk feb 2002