Generalized symmetric means are redefined in a way which allows them to be calculated for any matrix sampling design. It is proved that these sample generalized symmetric means are unbiased estimates of the analogous population generalized symmetric means. Illustrative examples are given. (Author)

A test for multisample sphericity based on the efficient scores criterion is obtained as an alternative to the likelihood ratio test developed by Mendoza. (Author)

A procedure for testing heterogeneity of variance is developed which generalizes readily to complex, multi-factor experimental designs. Monte Carlo studies indicate that the Z-variance test statistic presented here yields results equivalent to other familiar tests for heterogeneity of variance in simple one-way designs where comparisons are…

In applied and experimental research, it has been demonstrated that the extreme groups procedure is more powerful than the standard correlational approach for some values of the correlation and extreme group size. Methods are provided for using the covariance information that is usually discarded in the classical extreme groups approach.…

A generalized variance criterion is used for sequential sampling in the two-parameter item response theory model. Some principles are offered to enable the researcher to select the best sampling design for efficient estimation of item parameters. Topics include the choice of an optimality criterion, two-stage designs, and sequential designs. (SLD)

A method is suggested to estimate the relationship between a latent trait and one or more manifest predictors without estimating subject parameters. The method, developed for the Rasch model, can be generalized to two-parameter and three-parameter logistic latent trait models. The model is illustrated with simulated and empirical data. (SLD)