Standard Error of Linear Equating for the Counterbalanced Design

Large-sample standard errors of linear equating for the counterbalanced design are derived using the general delta method. Computer simulations were conducted to compare the standard errors derived by Lord under the normality assumption with those derived in this article without such an assumption. The standard errors derived without the normality assumption were found to be more accurate than those derived with the normality assumption in an example using large sample size and moderately skewed score distributions. In an example using nearly symmetric distributions, the standard errors computed with the normality assumption were found to be at least as accurate as those derived without the normality assumption.