Standard Errors of Variance Components, Measurement Errors, and Generalizability Coefficients in Balanced and Unbalanced Nested Design

• In Event: Advances in Estimating Reliability: Innovative Approaches and Applications

Abstract

Single-facet nested design is a common design in testing such as adaptive testing and rating assessments, where each examinee/rater interact with different items/tasks. Number of items might be equal (balanced) or different (unbalanced) across examinees. Estimates of variance components, measurement error variances, generalizability coefficients are subject to sampling variability. Although this design is a simple design but there is yet no acceptable estimates of associated standard errors. The paper presents new standard errors for all variance components and generalizability coefficients for single-facet nested design (both balanced and unbalanced) using delta method. A monte carlo simulation are performed for normal data items with different test conditions. Results showed that the standard errors for all estimators are converging to the true scores.

Author

• Rashid S. Almehrizi, Sultan Qaboos University