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 Construction  Operational  Proportion by Number of Items/Strand  G Theory  ICCs  Construct 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

Variance Calculation – ICC Use the median P(θ) as the average in calculating within strand variability P(θ) θ

Equating Item Selection 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 Distributions

Discussion Equating 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

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