The residuals obtained from fitting a structural equation model are crucial ingredients in obtaining chi-square goodness-of-fit statistics for the model. The authors present a didactic discussion of the residuals, obtaining a geometrical interpretation by recognizing the residuals as the result of oblique projections. This sheds light on the…

When the results of a series of independent studies are combined, it is useful to quantitatively estimate the magnitude of the effects. Several methods for estimating effect size are compared in this paper. Glass' estimator and the uniformly minimum variance unbiased estimator are based on the ratio of the sample mean difference and the pooled…

In the process of fitting a quantitative synthesis model, the assumption of homogeneous effect size variation is assessed via omnibus test statistics. Graphical representations of data on techniques for teaching composition skills are used to help determine the extent to which sample estimates deviate from modeled population estimates. (TJH)

The mean and variance of the statistic psi-star, which is useful for measuring agreement between two raters and allows for tests of significance in the case of large samples, are considered. Results may also be applied for the "G" index of J. W. Holley and J. P. Guilford (1964). (SLD)

Three separate papers are included in this report. The first describes a two-stage procedure for choosing from among several instructional programs the one which maximizes the probability of passing the test. The second gives the exact sample sizes required to determine whether a squared multiple correlation coefficient is above or below a known…

A new approach to assessing unexpected differential item performance (item bias or item fairness) is introduced and applied to the item responses of different subpopulations of Scholastic Aptitude Test (SAT) takers. The essential features of the standardization approach are described. The primary goal of the standardization approach is to control…

Five comparisons were made relative to the quality of estimates of ability parameters and item calibrations obtained from the one-parameter and three-parameter logistic models. The results indicate: (1) The three-parameter model fit the test data better in all cases than did the one-parameter model. For simulation data sets, multi-factor data were…

The statistical properties of two methods of estimating gain scores for groups in quasi-experiments are compared: (1) gains in scores standardized separately for each group; and (2) analysis of covariance with estimated true pretest scores. The fan spread hypothesis is assumed for groups but not necessarily assumed for members of the groups.…

The stability of Rasch test item difficulty parameters was investigated under varying conditions. Data were taken from a mathematics achievement test administered to over 2,000 Australian students. The experiments included: (1) relative stability of the Rasch, traditional, and z-item difficulty parameters using different sample sizes and designs;…

Goodness of fit of raw test score data were compared, using two latent trait models: the Rasch model and the Birnbaum three-parameter logistic model. Data were taken from various achievement tests and the Scholastic Aptitude Test (Verbal). A minimum sample size of 1,000 was required, and the minimum test length was 40 items. Results indicated that…