A general delta method is described for computing the standard error (SE) of a chain of linear equations. The general delta method derives the SEs directly from the moments of the score distributions obtained in the equating chain. Computer simulations demonstrate the method. (SLD)

The reliability coefficient is predicted from the test information function (TIF) or two modified TIF formulas and a specific trait distribution. Examples illustrate the variability of the reliability coefficient across different trait distributions, and results are compared with empirical reliability coefficients. (SLD)

The delta method was used to derive standard errors (SES) of the Levine observed score and Levine true score linear test equating methods using data from two test forms. SES derived without the normality assumption and bootstrap SES were very close. The situation with skewed score distributions is also discussed. (SLD)

Evaluated the distribution of person fit within the computerized-adaptive testing (CAT) environment through simulation. Found that, within the CAT environment, these indexes tend not to follow a standard normal distribution. Person fit indexes had means and standard deviations that were quite different from the expected. (SLD)