abcs of irt
DESCRIPTION
An introduction to Item Response Theory for test developers and program managers of certification programs. Please feel free to contact me for more information.TRANSCRIPT
November 18, 2010
Diane M. Talley, MA
Stephen B. Johnson, PhD
James A. Penny, PhD
Psychometrics as Science and Art
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� IRT and Classical
� Concepts of IRT
� A logit
� The abc’s
� Benefits
� Pre-equating
� immediate scoring
� Population invariance
� Assumptions
� Implications
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The right tools for the job
� Data
� Program
� Tool
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Versus
Classical versus IRT model
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Classical versus IRT
Classical Model IRT Model
� Traditional � Modern
� Requires less strict
adherence to assumptions
� Requires stricter
adherence to assumptions
� Sample dependent � Population invariant
� Statistics
(p – diff, p-biserial – disc)
� Probability-based statistics
(b-diff, a-disc, c-guessing)
� Simple scoring model (raw
score)� Scoring is more complex
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What’s a logit?
Ability
The
Performance
StandardProbability
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b (difficulty)
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0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00-3
-2.8
-2.5
-2.3 -2
-1.8
-1.5
-1.3 -1
-0.8
-0.5
-0.3 0
0.25 0.5
0.75 1
1.25 1.5
1.75 2
2.25 2.5
2.75
THETA
P(u
=1
| T
HE
TA
)
Paint by Numbers Leonardo
1
43
2
5
a (discrimination) and b
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0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00-3
-2.7
5
-2.5
-2.2
5 -2
-1.7
5
-1.5
-1.2
5 -1
-0.7
5
-0.5
-0.2
5 0
0.25 0.5
0.75 1
1.25 1.5
1.75 2
2.25 2.5
2.75
THETA
P(u
=1
| T
HE
TA
)
Paint by Numbers Leonardo
1
2
3
a, b, and c (guessing)
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0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
-3
-2.7
5
-2.5
-2.2
5 -2
-1.7
5
-1.5
-1.2
5 -1
-0.7
5
-0.5
-0.2
5 0
0.25 0.5
0.75 1
1.25 1.5
1.75 2
2.25 2.5
2.75
THETA
P(u
=1
| T
HE
TA
)
Paint by Numbers Leonardo
1
2
3
Fit statistics
Comparison of Infit and Outfit
0
1
2
3
4
5
6
Infit OutfitIt
em
Ord
er
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Outfit Mean Square Plot
0
0.2
0.4
0.6
0.8
1
1.2
0 5 10 15 20 25 30
Item Order
MS
Q
Infit Mean Square Plot
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 5 10 15 20 25 30
Item Order
MS
Q
Population Invariance
Item 3
Item 2
Item 1
.92.70
.80.60
.50.15
High
Performing
Low
Performing
Classical Difficulty Values IRT Difficulty Values
Item 3
Item 2
Item 1
-.75-.75
0.000.00
1.501.50
High
Performing
Low
Performing
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IRT Pre-Equating
� What does it mean?
� Why would you want to do it?
� What does it mean for building item banks
and forms?
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Test Information Function (TIF)
Comparison of Test Information Functions
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
-3 -2.75 -2.5 -2.25 -2 -1.75 -1.5 -1.25 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.775 1.025 1.275 1.525 1.775 2.025 2.275 2.525 2.775 3.025
Theta
Info
rmat
ion Form A
Form B
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Assumptions
� Unidimensionality
� Local Independence
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Implications
� Item writing� Leave those scored items alone!
� Focused item writing targeting the performance standard
� Assembly� Items selected for a form should be around the standard
� Testing and Reporting � Field test items for pre-equating/on-demand scoring
� Form assignment
� Scoring
� Recalibration
� Harder to explain to stakeholders
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Does IRT make sense for you?
� What is the size and maturity of your program and
item bank?� Do you like to tinker with items?
� Do your program requirements change frequently?
� How experienced/capable are your item writers?
� How do you score candidates?� IRT or number correct
� Do you hold scores or do immediate scoring?
� Can you afford a psychometrician?
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Questions?
Diane M. Talley [email protected] A. Penny [email protected] B. Johnson [email protected]
919.572.6880www.castleworldwide.com