The equity properties can be used to assess the quality of an equating. The degree to which expected scores conditional on ability are similar between test forms is referred to as first-order equity. Second-order equity is the degree to which conditional standard errors of measurement are similar between test forms after equating. The purpose of this dissertation was to investigate the use of a multidimensional IRT framework for assessing first- and second-order equity of mixed format tests.
Both real and simulated data were used for assessing the equity properties for mixed-format tests. Using real data from three Advanced Placement (AP) exams, five different equating methods were compared in their preservation of first- and second-order equity. Frequency estimation, chained equipercentile, unidimensional IRT true score, unidimensional IRT observed score, and multidimensional IRT observed score equating methods were used. Both a unidimensional IRT framework and a multidimensional IRT framework were used to assess the equity properties. Two simulation studies were also conducted. The first investigated the accuracy of expected scores and conditional standard errors of measurement as tests became increasingly multidimensional using both a unidimensional IRT framework and multidimensional IRT framework. In the second simulation study, the five different equating methods were compared in their ability to preserve first- and second-order equity as tests became more multidimensional and as differences in group ability increased.
Results from the real data analyses indicated that the performance of the equating methods based on first- and second-order equity varied depending on which framework was used to assess equity and which test was used. Some tests showed similar preservation of equity for both frameworks while others differed greatly in their assessment of equity. Results from the first simulation study showed that estimates of expected scores had lower mean squared error values when the unidimensional framework was used compared to when the multidimensional framework was used when the correlation between abilities was high. The multidimensional IRT framework had lower mean squared error values for conditional standard errors of measurement when the correlation between abilities was less than .95. In the second simulation study, chained equating performed better than frequency estimation for first-order equity. Frequency estimation better preserved second-order equity compared to the chained method. As tests became more multidimensional or as group differences increased, the multidimensional IRT observed score equating method tended to perform better than the other methods.