Beta observed score and true score equating methods

Equating is a statistical process that is used to adjust scores on test forms so that scores on the forms can be used interchangeably. This dissertation offered intensive investigation of beta true and observed score methods by comparing them to existing traditional and IRT equating methods under multiple designs and various conditions using real data, pseudo-test data and simulated data. Weighted and conditional bias, standard error of equating and root mean squared error were used to evaluate the accuracy of equating results obtained from the pseudo data and simulated data analyses. The single group equipercentile equating based on large sample sizes was used as the criterion equating. Overall, results showed that of the methods examined, the IRT methods performed best, followed by the chained equipercentile methods. Results from beta methods presented different trends from traditional and IRT methods. Relatively, they were closer to those from traditional methods for both the random groups and common item nonequivalent groups designs. Beta true scores methods were less sensitive to group difference compared to traditional methods. The length of common items played an important role in the stability of results of beta true score methods.