A Numerical Approach for Computing Standard Errors of Linear Equating

Abstract

A numerical approach for computing standard errors (SES) of a linear equating is described. In the proposed approach, the first partial derivatives of the equating function needed to compute the SES are derived numerically. Thus, the difficulty of deriving the analytical formulas of the partial derivatives for a complicated equating method is avoided. The numerical and analytical approaches were compared using the Tucker equating method. The SES derived numerically were found to be indistinguishable from the SES derived analytically. In a computer simulation of the numerical approach using the Levine equating method, the SES based on the normality assumption were found to be less accurate than those derived without the normality assumption when the score distributions were skewed.