A Balancing Act:Common Items Nonequivalent Groups (CING) Equating Item Selection

Tia Sukin

Jennifer Dunn

Wonsuk Kim

Robert Keller

July 24, 2009

Background

Equating using a CING design requires the creation of an anchor set

Angoff (1968) developed guidelines for developing the anchor set Length: 20% of operational test (OT) or 20 items Content: Proportionate to OT by strand Statistical Properties: Same mean / S.D. Contextual Effects: Same locations, formats, key, etc.

Background

Majority of the research provides support for these guidelines (e.g., Vale et al., 1981; Klein & Jarjoura, 1985; Kingston & Dorans, 1984)

Research has included robustness studies (e.g., Wingersky & Lord, 1984; Beguin, 2002; Sinharay & Holland, 2007)

Background

Most research has used placement (e.g., AP), admissions (e.g., SAT), and military (e.g., ASVAB) exams for empirical and informed simulation studies

Research using statewide accountability exams is limited (e.g., Haertel, 2004; Michaelides & Haertel, 2004)

Background

General Science tests are administered in all states for all grade levels except: 19 states offer EOC Science exams in H.S. 10 offer more than one EOC Science exam 5 offer more than two

Research Questions

Do the long-established guidelines for maintaining content representation (i.e., proportion by number) hold in creating an anchor set across all major subject areas (i.e., Mathematics, Reading, Science)?

Are there significant changes between expected raw scores and proficiency classification when different methods for maintaining content representation are used?

Design

3 Subjects

(2 States, 3 Grades) Math Reading Science

5 Methods of Anchor Set ConstructionOperationalProportion by Number of

Items/StrandG Theory ICCsConstruct

Underrepresentation

Variance Calculation – G Theory

Multivariate Design p x i with content strand as a fixed facet

Multivariate Benefit Covariance components are calculated for every pair of

strands

Item Variance Component

'

'

' 1)( vv

p

ppvpv

p

pvv XX

n

XX

n

npS

pn

piMSiMSi

)()()(

2^

Variance Calculation – ICC

Use the median P(θ) as the average in calculating within strand variability

P(θ)

θ

22^

)(1

1)( XXn

i

Equating Item Selection

6980.515*301.

120.

nn

vv

vv

*

Example:

Equating Item Selection

Percentage of strands that differ by more than one item between selection methods (excluding the

construct underrepresentation method): Math: 13% Reading: 52% Science: 20%

Example Results – Scoring Category DistributionsAnchor Method Below Basic Basic Proficient Advanced

MATH Operational 0.15 0.24 0.34 0.27

Proportional 0.17 0.24 0.36 0.24

ICC 0.17 0.24 0.36 0.24

G-Theory 0.17 0.24 0.36 0.24

Strand 0.17 0.24 0.36 0.24

READING Operational 0.05 0.34 0.46 0.15

Proportional 0.06 0.38 0.41 0.15

ICC 0.06 0.38 0.45 0.11

G-Theory 0.06 0.38 0.45 0.11

Strand 0.05 0.34 0.46 0.15

SCIENCE Operational 0.24 0.34 0.24 0.18

Proportional 0.26 0.34 0.24 0.16

ICC 0.26 0.34 0.24 0.16

G-Theory 0.26 0.34 0.24 0.16

Strand 0.24 0.34 0.24 0.18

-4 -3 -2 -1 0 1 2 3 4

-2-1

01

2

Grade 04

DC_icc: 0.97DC_g-theory: 0.97DC_strand: 0.96

-4 -3 -2 -1 0 1 2 3 4

-2-1

01

2

Grade 08

DC_icc: 1DC_g-theory: 1DC_strand: 1

-4 -3 -2 -1 0 1 2 3 4

-2-1

01

2

Grade 10

DC_icc: 0.96DC_g-theory: 0.98DC_strand: 0.97

State_A MAT 2008-2009State_A MAT 2008-2009

E(R

aw S

core

) R

esid

ual

IccG-theoryStrand

-4 -3 -2 -1 0 1 2 3 4

-2-1

01

2

Grade 05

DC_icc: 0.99DC_g-theory: 0.99DC_strand: 0.99

-4 -3 -2 -1 0 1 2 3 4

-2-1

01

2

Grade 08

DC_icc: 1DC_g-theory: 1DC_strand: 0.95

-4 -3 -2 -1 0 1 2 3 4

-2-1

01

2

Grade 10

DC_icc: 1DC_g-theory: 1DC_strand: 1

State_B MAT 2008-2009State_B MAT 2008-2009

E(R

aw S

core

) R

esid

ual

IccG-theoryStrand

-4 -3 -2 -1 0 1 2 3 4

-2-1

01

2

Grade 04

DC_icc: 0.99DC_g-theory: 1DC_strand: 0.89

-4 -3 -2 -1 0 1 2 3 4

-2-1

01

2

Grade 08

DC_icc: 0.95DC_g-theory: 0.95DC_strand: 0.97

-4 -3 -2 -1 0 1 2 3 4

-2-1

01

2

Grade 10

DC_icc: 1DC_g-theory: 1DC_strand: 1

State_A REA 2008-2009State_A REA 2008-2009

E(R

aw S

core

) R

esid

ual

IccG-theoryStrand

-4 -3 -2 -1 0 1 2 3 4

-2-1

01

2

Grade 05

DC_icc: 0.96DC_g-theory: 0.96

DC_strand: 1

-4 -3 -2 -1 0 1 2 3 4

-2-1

01

2

Grade 08

DC_icc: 0.96DC_g-theory: 0.96DC_strand: 0.94

-4 -3 -2 -1 0 1 2 3 4

-2-1

01

2

Grade 10

DC_icc: 1DC_g-theory: 1DC_strand: 1

State_B REA 2008-2009State_B REA 2008-2009

E(R

aw S

core

) R

esid

ual

IccG-theoryStrand

-4 -3 -2 -1 0 1 2 3 4

-2-1

01

2

Grade 04

DC_icc: 0.99DC_g-theory: 0.99

DC_strand: 1

-4 -3 -2 -1 0 1 2 3 4

-2-1

01

2

Grade 08

DC_icc: 0.94DC_g-theory: 0.94DC_strand: 0.96

-4 -3 -2 -1 0 1 2 3 4

-2-1

01

2

Grade 10

DC_icc: 1DC_g-theory: 1DC_strand: 0.92

State_A SCI 2008-2009State_A SCI 2008-2009

E(R

aw S

core

) R

esid

ual

IccG-theoryStrand

-4 -3 -2 -1 0 1 2 3 4

-2-1

01

2

Grade 05

DC_icc: 1DC_g-theory: 1DC_strand: 1

-4 -3 -2 -1 0 1 2 3 4

-2-1

01

2

Grade 08

DC_icc: 1DC_g-theory: 1DC_strand: 1

-4 -3 -2 -1 0 1 2 3 4

-2-1

01

2

Grade 10

DC_icc: 0.94DC_g-theory: 0.94DC_strand: 0.94

State_B SCI 2008-2009State_B SCI 2008-2009

E(R

aw S

core

) R

esid

ual

IccG-theoryStrand

DiscussionEquating is highly robust to the selection process used

for creating anchor sets EXCEPT Choosing equating items from 1-2 strands is discouraged More caution may be needed with Science Item selection mattered for 22% of the conditions

2/18 for Math: Both were the under rep. condition 3/18 for Reading: All were the under rep. condition 7/18 for Science: 2 under rep. / 5 ICC and G

Content balance is important and can be conceptualized in different ways without impacting the equating

Future Study

A simulation study is needed so that raw score and proficiency categorizations using the different item selection methods can be compared to truth

Meta-analysis detailing published & unpublished studies that provide evidence for or against the robustness of CING equating designs

Thank you