An Edgeworth approximation for accurate significance probabilities for the Wilcoxon two-sample test is substantially simplified. A method is developed that allows quick calculations of very accurate probabilities. Exact formulas are given for most of the remaining cases, and tables are presented comparing the new simplification to likely…

The most familiar models of item response theory are defined at the level of individual subjects. It is possible, however, to define such models for groups of subjects. This paper discusses group-level item response models, their uses, and their relationships to subject-level models. (Author/JKS)

Use of linear combinations of Fisher's "z" transformations as a combined test for the common correlation parameter based on "k" independent sample correlations has been previously studied. This article considers additional "z" additive properties and methods of combining independent studies when planning the number of…

A distribution theory is derived for a G. V. Glass-type (1976) estimator of effect size from studies involving paired comparisons. The possibility of combining effect sizes from studies involving a mixture of related and unrelated samples is also explored. Resulting estimates are illustrated using data from previous psychiatric research. (SLD)

Recently, C. E. McCulloch (1987) suggested a modification of the Morgan-Pitman test for comparing the variances of two dependent groups. This paper demonstrates that there are situations where the procedure is not robust. A subsample approach, similar to the Box-Scheffe test, and the Sandvik-Olsson procedure are also assessed. (TJH)

An empirical sampling approach was used to assess the accuracy of a Taylor approximation for the estimation of sampling errors. The sampling errors were in the statistics involved in estimating a path model based on medium-sized samples gathered using five sample designs commonly used in educational research. (TJH)

A method is proposed for calculating the sample size needed to achieve acceptable statistical power with a given test. The minimally important difference significant (MIDS) criterion for sample size is explained and supported with recommendations for determining sample size. The MIDS criterion is computationally simple and easy to explain. (SLD)

The use of sampling weights in deriving population estimates for the National Assessment of Educational Progress (NAEP) and the effects of nonresponse and undercoverage on those estimates are described. The estimation of sampling variability from complex sample surveys is also reviewed, concentrating on the jackknife repeated replication…

The effects of certain characteristics (e.g., sample design) of National Assessment of Educational Progress (NAEP) data on statistical analysis techniques are considered. Ignoring special features of NAEP data and proceeding with a standard analysis can produce inferences that underestimate the true variability and overestimate the true degrees of…

Surveys in which one can observe--after sample selection--that each sample member belongs to one or more aggregations are considered. A formula for the probability that a given aggregation contains at least one sample member is applied to eighth grade data from the National Educational Longitudinal Study of 1988 (NELS:88). (TJH)

Estimating item parameters from a two-parameter normal ogive model is considered using Gibbs sampling to simulate draws from the joint posterior distribution of ability and item parameters. The method gives marginal posterior density estimates for any parameter of interest, as illustrated using data from a 33-item mathematics placement…

Procedures for obtaining student samples for the National Assessment of Educational Progress (NAEP) and deriving survey weights for analysis of survey data are described. Sample designs are economically and operationally feasible, and weighting procedures result in increased precision of estimates as they account for the probabilities of student…

In studies involving matrix sampling on items, it is often the case that there are too few responses per individual to use latent trait item response models. A model is formulated wherein individual level variability appears as independent error within the cells of a cross classification of demographic variables. (JKS)

A three-level multivariate statistical modeling strategy is presented that resolves the question of whether the unit of analysis should be the teacher or the student. A reanalysis of U.S. high school data (51 Catholic and 59 public schools from the High School and Beyond survey) illustrates the model. (SLD)