In many educational assessment programs, the use of multiple test forms developed from the same test specification is very common because requiring different examinees to take different test forms of the same test makes it possible to maintain the security of the test. When multiple test forms are used, it is necessary to make the assessment fair to all examinees by using a statistical procedure called "equating" to adjust for differences in the test forms. If equating is successfully carried out, equated scores are comparable as if they were from the same test form. Two commonly used observed score equating methods that use the Non-Equivalent groups with Anchor Test (NEAT) design to collect equating data include the chain equating (CE) method and the post-stratification equating (PSE) method. It has been documented that the CE method produced smaller equating biases than the PSE method, when two groups of examinees differ greatly in abilities. Therefore, the CE method has been used more widely in practice, even though the PSE method is more theoretically sound than the CE method. Larger equating biases are due to the fact that the anchor test score fails to remove unintended differences between groups of examinees. Aiming to reduce equating biases of the PSE method, this study used collateral information about examinees as a new way to construct synthetic population functions, rather than a single variable such as the anchor test score or the anchor test true score. Collateral information used in this study included the anchor test score, sub-scores, and examinees' demographic variables. This study investigated two different methods of using such collateral information about examinees to improve equating results of the PSE method. These two methods included the propensity score method (Rosenbaum & Rubin, 1983) and the multiple imputation method (Rubin, 1987). Both simulation data and empirical data were used to develop the equating function to explore if it was feasible to use collateral information to reduce equating biases under different conditions including test length, group differences, and missing data treatment. The results from simulation data show that sub-scores or sub-scores combined with other collateral information in a form of propensity scores had a potential to reduce equating biases for long tests, when there were group differences in abilities. However, demographic variables had a potential to reduce equating biases for the multiple imputation method. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]