Using cluster analysis to validate the angoff standard setting method in mixed-format assessments

Test validity is a property of the interpretation assigned to test scores. To provide an objective validating evidence for a standard-referenced assessment is especially important. In this study we utilize a statistical technique, cluster analysis, to explore the validity of one of the expert judgement technique-Yes/No Angoff standard setting method. We first segregated each examinee ability cluster using the hierarchical clustering (HC). Assume that each ability cluster is a Gaussian distribution and that the distribution of each test subject data can be modeled by mixture of Gaussians (MoG), where the mean, variance and the proportion of each cluster were initialized by the HC results. Finally, the ability clustering was implemented by the expectation maximization (EM) method. The results from the traditional standard-setting procedure and cluster analysis were compared. The study concludes that cluster analysis appears useful for helping to set standards on educational tests. In addition, it suggested that cluster analysis could be applied as a support tool to provide validating information in the process of standard setting for high-stakes achievement tests.