Effect of Sample Size on Common Item Equating Using the Dichotomous Rasch Model

This study addresses equating issues with varying sample sizes using the Rasch model by examining how sample size affects the stability of item calibrations and person ability estimates. A resampling design was used to create 9 sample size conditions (200, 100, 50, 45, 40, 35, 30, 25, and 20), each replicated 10 times. Items were recalibrated using each of these 90 samples. The deviation of these calibrations from the full sample (N = 9,678) calibrations were then computed. The ability estimates for all 9,678 examinees were then recomputed 90 times using the item calibrations from each of the 90 different samples. The deviation of 90 sets of ability estimates from the original set of ability estimates was computed. This study found that less precision and item calibration instability occur with smaller sample sizes; however, the decreasing sample size has minimal effect on the person ability estimates.