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Dissertation
Impact of ability distribution on IRT observed score equating and IRT chained equipercentile equating
University of Iowa
Doctor of Philosophy (PhD), University of Iowa
Autumn 2024
DOI: 10.25820/etd.007592
Abstract
Equating is an important statistical process used to adjust for differences in difficulty across different test forms. Based on Item Response Theory (IRT), observed score equating (OSE) method is widely used in practice. When implementing IRT OSE, item parameters and ability distributions are necessary to construct fitted score distributions for both new and old forms. Traditional equipercentile equating is then used to equate the two forms.
The main purpose of this dissertation was to explore how ability distribution conditions influence fitted score distributions and equating results under both random groups design and the common item non-equivalent groups (CINEG) design. Additionally, under the CINEG design, IRT chained equipercentile equating was proposed and investigated through comparisons with IRT OSE under different ability distribution conditions and other factors.
There are two studies using different data types under the random design: (1) pseudo forms and pseudo groups analysis; and (2) simulated data. The analysis results indicated that, among the three main ability distribution conditions under the random groups design, separate posterior distributions could decrease the bias of equating results, while the standard normal distribution exhibited the smallest standard error of equating.
Under the CINEG design, there are three studies: (1) real data analysis; (2) pseudo forms and pseudo groups analysis; and (3) simulated data. The results indicated that IRT OSE had smaller bias than IRT chained equipercentile equating, while the latter had smaller standard error of equating (SEE). For ability distribution, the standard normal distribution condition resulted in smaller SEE, bias, and RMSE than the posterior distribution when IRT OSE was applied. For IRT chained equipercentile equating, the posterior distribution was preferable in terms of bias and root mean square error (RMSE), while the standard normal condition was more favorable for SEE.
Details
- Title: Subtitle
- Impact of ability distribution on IRT observed score equating and IRT chained equipercentile equating
- Creators
- Min Liang
- Contributors
- Won-Chan Lee (Advisor)Jonathan Templin (Committee Member)Ariel M. Aloe (Committee Member)Stella Yun Kim (Committee Member)
- Resource Type
- Dissertation
- Degree Awarded
- Doctor of Philosophy (PhD), University of Iowa
- Degree in
- Psychological and Quantitative Foundations (Educational Measurement and Statistics)
- Date degree season
- Autumn 2024
- DOI
- 10.25820/etd.007592
- Publisher
- University of Iowa
- Number of pages
- xvii, 205 pages
- Copyright
- Copyright 2024 Min Liang
- Language
- English
- Date submitted
- 11/14/2024
- Description illustrations
- tables, graphs
- Description bibliographic
- Includes bibliographical references (pages 196-205).
- Public Abstract (ETD)
- Equating is a statistical process used to enhance fairness in testing by adjusting for differences in difficulty between various parallel forms of a test. Equating methods can be categorized into traditional methods and those based on Item Response Theory (IRT). Among IRT based methods, the observed score equating (OSE) method is widely utilized in practice. In this dissertation, the author compares two principal IRT equating methods: OSE and chained equipercentile equating. Both methods consider the ability distribution, which is a critical factor in the equating process. Consequently, the primary objective of this dissertation is to investigate how different ability distribution conditions affect the equating results. The study employs two data collection designs: the random groups design and the common item non-equivalent groups (CINEG) design. Under the random groups design, the focus is on contributing to the literature by examining how ability distribution conditions influence fitted score distributions and equating results. Additionally, under the CINEG design, IRT chained equipercentile equating is proposed and evaluated through comparisons with IRT OSE across various ability distribution conditions and other factors. The analysis results reveal that, among the three main ability distribution conditions under the random groups design, separate posterior distributions can reduce the bias of equating results, while the standard normal distribution tends to exhibit the smallest standard error of equating (SEE). The results also indicate that IRT OSE generally has smaller bias compared to IRT chained equipercentile equating, although the latter method tends to have a smaller SEE. For the ability distribution, the standard normal distribution condition resulted in smaller equating errors compared to the posterior distribution when IRT OSE was applied. Conversely, for IRT chained equipercentile equating, the posterior distribution has smaller bias and root mean square error (RMSE), while the standard normal condition has smaller SEE.
- Academic Unit
- Psychological and Quantitative Foundations
- Record Identifier
- 9984774457402771
Metrics
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