Comparing Decision Rules

Decision accuracy of different decision rules combining multiple measures in a higher educational contextIris Yocarini, Samantha Bouwmeester, Guus Smeets, and Lidia ArendsCEMO conference standard setting 23rd september 2015

The decision to be made

End of first bachelor year

Start of first bachelor year

Student to second bachelor year

Student leaves bachelor program

BSA decision

Decision accuracy

• Given high stakes an accurate decision is required

• Comparison decision based on true score vs. observed score

True Score

Observed scoreError

Decision accuracy

• Given high stakes an accurate decision is required

• Comparison decision based on true score vs. observed score

Decision based on true score

Fail Pass

Decision based on observed score

Fail Correct classification

MisclassificationFalse negative

Pass Misclassification False positive

Correct classification

Decision accuracy

• Total proportion of misclassifications • (C + B / total sample)

Decision based on true score

Fail Pass

Decision based on observed score

Fail Correct classification

A MisclassificationFalse negative

B

Pass Misclassification False positive

C Correct classification

D

Decision accuracy

• Total proportion of misclassifications • (C + B / total sample)

• False negative rate• from all truly competent students those who are identified as fails

(B/B+D)

Decision based on true score

Fail Pass

Decision based on observed score

Fail Correct classification

A MisclassificationFalse negative

B

Pass Misclassification False positive

C Correct classification

D

Decision accuracyDecision based on true score

Fail Pass

Decision based on observed score

Fail Correct classification

A MisclassificationFalse negative

B

Pass Misclassification False positive

C Correct classification

D

• Total proportion of misclassifications • (C + B / total sample)

• False negative rate• from all truly competent students those who are identified as fails

(B/B+D)• False positive rate• from all truly failing students those who are identified as passes

(C/A+C)

Decision accuracyDecision based on true score

Fail Pass

Decision based on observed score

Fail Correct classification

A MisclassificationFalse negative

B

Pass Misclassification False positive

C Correct classification

D

• Total proportion of misclassifications • (C + B / total sample)

• False negative rate• from all truly competent students those who are identified as fails

(B/B+D)• False positive rate• from all truly failing students those who are identified as passes

(A/A+C)• Positive predictive value• from all students who passed those who are correctly classified

(D/C+D)

Testing system

• Compensatory testing system at Erasmus University Rotterdam• Vs. standard conjunctive testing system in Dutch

higher education

• Debate

Reasons behind implementation

• Educational views

• Psychometric argument• Classical Test Theory (CTT): average more

reliable

Assumption of parallel tests• Equal true ability levels• Similar test reliabilities

Factors influencing decision accuracy

• Reliability

• Decision accuracy

True Score

Observed score

ErrorDecision based on true score

Fail Pass

Decision based on observed score

Fail Correct classification

MisclassificationFalse negative

Pass Misclassification False positive

Correct classification

Error

Decision rules in practice

• Educational setting: combinatory decision rules• Compensatory aspect: required GPA• Conjunctive aspect: required minimum grade

• Clusters

• First year psychology at Erasmus University • Grading scale: 1.0 – 10.0• GPA: 6.0• Minimum grade: 4.0• Two clusters with each 8 courses

Our study

• Aim of study• Comparing decision accuracy different decision

rules that combine multiple tests• Evaluating psychometric argument for

implementation compensatory testing system• CTT: average grade is more reliable than using

individual test scores

• Context of first year Psychology students at Erasmus University Rotterdam

Decision rules

• Varying• Conjunctive aspect: minimum required grade• Compensatory aspect: required GPA

• Also included • Fully conjunctive rule• Fully compensatory rule

Decision rule Minimum grade GPA

Fully Conjunctive 5.5 5.5

Fully Compensatory

1.0 5.5 / 6.0 / 6.5

Complex rules 3.0 / 4.0 / 5.0 5.5 / 6.0 / 6.5

*Grading from 1.0 to 10.0

Simulation

• Simulation study

• Manipulation of factors

Decision based on true score

Fail Pass

Decision based on observed score

Fail Correct classification

MisclassificationFalse negative

Pass Misclassification False positive

Correct classification

Results – minimum grade & GPA

• Minimum grade • 1.0/ 3.0/ 4.0/ 5.0• GPA• 5.5/ 6.0/ 6.5

Results – minimum grade & GPA

Results – minimum grade & GPA

Results – minimum grade & GPA

Results – average test reliability

Proportion of Misclassifications

Results – average test reliability

Positive Predictive Value

Results – number of retakes

Proportion of Misclassifications

Results – number of retakes

False Negative Rate

Results – number of retakes

False Positive Rate

Results – number of retakes

Positive Predictive Value

Comparison conjunctive & compensatory• In compensatory decision rule:• Fewer classification errors• Fewer false negatives, more false positives• Positive predictive value higher

Conclusion

• Increasing the degree of compensation results in less classification errors

• Within compensatory decision rule relatively fewer false negatives and more false positives

• Depends on specific setting & tests used• Most important: test reliability and number of

retakes

• Psychometric argument• Standard setting

Take home message

• Decision accuracy important consideration• Focus on both specific decision rule as well as tests

Thank you for your attention!

Questions?

yocarini@fsw.eur.nl

Results – proportion of misclassifications

Decision Rule

GPA

Minimum

MeanProportion

Errors

Average TestCorrelation

Average TestReliability

Number ofTests

Number ofRetakes

.1 .3 .5 .7 .4 .6 .8 8 12 0 2

1 5.5 5.5 .18 .16 .18 .19 .19 .24 .18 .12 .19 .17 .20 .16

2 5.5 1 .05 .03 .04 .05 .06 .06 .04 .03 .05 .04 .06 .03

3 5.5 3 .08 .09 .09 .08 .07 .14 .07 .04 .08 .09 .13 .04

4 5.5 4 .17 .20 .18 .16 .13 .27 .16 .08 .15 .19 .26 .08

5 5.5 5 .22 .23 .23 .22 .21 .31 .22 .14 .22 .23 .28 .16

6 6 1 .09 .09 .10 .09 .09 .13 .09 .06 .10 .09 .10 .08

7 6 3 .11 .13 .11 .10 .09 .16 .10 .06 .11 .11 .14 .08

8 6 4 .16 .20 .17 .14 .12 .24 .15 .08 .15 .17 .22 .10

9 6 5 .21 .23 .22 .21 .19 .29 .21 .13 .20 .22 .27 .15

10 6.5 1 .13 .17 .13 .12 .10 .18 .13 .08 .14 .12 .13 .13

11 6.5 3 .13 .17 .14 .12 .10 .19 .13 .08 .14 .13 .13 .13

12 6.5 4 .15 .19 .15 .13 .11 .21 .14 .09 .15 .14 .16 .13

13 6.5 5 .17 .20 .18 .16 .14 .24 .17 .11 .17 .17 .20 .14

Results - sensitivity

Decision Rule

GPA

Minimum

MeanSensitivity

Average TestCorrelation

Average Test Reliability

Number ofTests

Number of Retakes

.1 .3 .5 .7 .4 .6 .8 8 12 0 2

1 5.5 5.5 .60 .52 .59 .64 .67 .45 .60 .76 .65 .56 .44 .77

2 5.5 1 .97 .98 .97 .97 .97 .96 .98 .99 .97 .98 .96 .99

3 5.5 3 .93 .91 .92 .93 .95 .87 .94 .98 .94 .92 .88 .98

4 5.5 4 .83 .79 .81 .84 .87 .71 .84 .93 .85 .80 .71 .94

5 5.5 5 .67 .61 .66 .69 .72 .52 .68 .82 .71 .63 .51 .83

6 6 1 .95 .94 .95 .95 .95 .93 .95 .97 .94 .95 .92 .98

7 6 3 .92 .90 .91 .93 .94 .87 .93 .96 .92 .92 .87 .97

8 6 4 .85 .80 .83 .87 .90 .74 .86 .93 .87 .83 .75 .95

9 6 5 .68 .61 .67 .71 .75 .53 .69 .83 .73 .64 .52 .84

10 6.5 1 .92 .89 .91 .93 .94 .89 .92 .94 .91 .92 .88 .96

11 6.5 3 .90 .86 .90 .92 .93 .86 .91 .94 .90 .90 .85 .95

12 6.5 4 .86 .80 .85 .88 .91 .78 .87 .93 .87 .85 .78 .94

13 6.5 5 .73 .64 .71 .76 .81 .59 .74 .86 .77 .69 .58 .88

Results - specificity

Decision Rule

GPA

Minimum

MeanSpecificity

Average TestCorrelation

Average TestReliability

Number ofTests

Number ofRetakes

.1 .3 .5 .7 .4 .6 .8 8 12 0 2

1 5.5 5.5 .93 .92 .92 .93 .94 .93 .92 .93 .91 .94 .96 .89

2 5.5 1 .67 .57 .66 .71 .74 .58 .67 .77 .66 .69 .76 .58

3 5.5 3 .72 .66 .72 .75 .77 .69 .71 .77 .70 .75 .82 .63

4 5.5 4 .80 .75 .79 .83 .85 .82 .79 .81 .78 .83 .87 .74

5 5.5 5 .89 .86 .88 .90 .92 .90 .88 .89 .87 .91 .93 .85

6 6 1 .73 .65 .73 .77 .79 .64 .73 .82 .72 .75 .81 .65

7 6 3 .75 .68 .75 .78 .80 .69 .74 .83 .73 .77 .84 .66

8 6 4 .80 .75 .80 .82 .83 .78 .78 .84 .78 .82 .88 .72

9 6 5 .89 .86 .88 .90 .91 .90 .88 .89 .87 .91 .93 .84

10 6.5 1 .80 .74 .80 .83 .84 .72 .80 .88 .79 .82 .87 .74

11 6.5 3 .81 .75 .80 .83 .84 .73 .81 .88 .79 .82 .87 .74

12 6.5 4 .83 .78 .82 .85 .86 .78 .82 .89 .81 .85 .90 .76

13 6.5 5 .88 .87 .88 .89 .90 .88 .87 .90 .86 .91 .94 .83

Results – positive predictive value

Decision Rule

GPA

Minimum

MeanPositive

PredictiveValue

Average TestCorrelation

Average TestReliability

Number ofTests

Number ofRetakes

.1 .3 .5 .7 .4 .6 .8 8 12 0 2

1 5.5 5.5 .82 .68 .80 .88 .93 .79 .82 .86 .83 .81 .79 .86

2 5.5 1 .98 .99 .98 .97 .96 .97 .98 .98 .97 .98 .98 .97

3 5.5 3 .98 .99 .98 .97 .97 .97 .98 .98 .98 .98 .98 .97

4 5.5 4 .97 .96 .97 .97 .98 .97 .97 .97 .97 .97 .97 .97

5 5.5 5 .90 .82 .88 .93 .96 .88 .89 .91 .91 .89 .87 .92

6 6 1 .93 .95 .93 .93 .93 .91 .93 .96 .93 .94 .94 .93

7 6 3 .94 .95 .94 .93 .93 .92 .94 .96 .93 .94 .95 .93

8 6 4 .94 .94 .94 .94 .94 .93 .93 .95 .93 .94 .94 .93

9 6 5 .89 .81 .88 .92 .95 .88 .89 .91 .90 .89 .87 .91

10 6.5 1 .85 .82 .85 .87 .88 .80 .85 .91 .85 .86 .87 .84

11 6.5 3 .86 .82 .85 .87 .88 .81 .85 .91 .85 .86 .87 .84

12 6.5 4 .86 .82 .86 .87 .88 .82 .86 .91 .85 .87 .88 .85

13 6.5 5 .85 .77 .85 .89 .91 .83 .84 .89 .85 .86 .85 .85

Results – average test reliability

False Negative Rate

Results – average test reliability

False Positive Rate

Previous studies

• Douglas & Mislevy (2010)• Van Rijn, Béguin, & Verstralen (2012)• McBee, Peters, & Waterman (2014)