This study presents the results of a partial credit Rasch analysis of in-depth interview data exploring statistical understanding of 73 school students in 6 contextual settings. The use of Rasch analysis allowed the exploration of a single underlying variable across contexts, which included probability sampling, representation of temperature…

It is a common practice in item response theory (IRT) to treat estimates of item parameters, say "B" circumflex, as if they were the known, true quantities, "B." However, ignoring the uncertainty associated with item parameters can lead to biases and over-confidence in subsequent inferences such as ability estimation,…

Describes and compares eight methods of estimating the parameters of the Zipf distribution. (CLB)

This paper asserts that causality is an intriguing but controversial topic in philosophy, statistics, and educational and psychological research. By supporting the Causal Markov Condition and the faithfulness condition, Clark Glymour attempted to draw causal inferences from structural equation modeling. According to Glymour, in order to make…

Regression artifacts are a source of mistaken causal inference in inferences based on time-series data and from longitudinal studies. These artifacts are illustrated, and it is noted that their magnitude is computable (and distinguishable from genuine effects) if the autocorrelation patterns for various lags is known. (SLD)

Differential item functioning (DIF) assessment procedures for items with more than two ordered score categories, referred to as polytomous items, were evaluated. Three descriptive statistics (standardized mean difference and two procedures based on the SIBTEST computer program) and five inferential procedures were used. Conditions under which the…

Derived a confidence interval for a ratio of correlated mean absolute deviations. Simulation results show that it performs well in small sample sizes across realistically nonnormal distributions and that it is almost as powerful as the most powerful test examined by R. Wilcox (1990). (SLD)

Explores posterior analysis in estimating factor score in a confirmatory factor analysis model with polytomous, censored or truncated data, and studies the accuracy of Bayesian estimates through simulation. Results support these Bayesian estimates for statistical inference. (SLD)

Theoretical nonparametric conditions under which evidence from salary studies using observed merit measures can provide a basis for inferences of fairness are discussed. Latent variable models as parametric special cases of the general conditions presented are illustrated with real salary data. Implications for empirical studies of salary equity…

Presents a hierarchical Bayes approach to modeling parameter heterogeneity in generalized linear models. The approach combines the flexibility of semiparametric latent class models that assume common parameters for each subpopulation and the parsimony of random effects models that assume normal distributions for the regression parameters.…

Many evaluation students are still being taught the use of tests of statistical significance without being warned about their limitations. This paper discusses other estimates of treatment effects necessary to interpret between-group differences correctly. Sources to improve evaluation practice are also suggested. (SLD)

Offering perspectives in the teaching of statistics assists students, immersed in the study of detail, to see the leading principles of the subject more clearly. Especially helpful can be a perspective on the logic of statistical inductive reasoning. Such a perspective can bring to prominence a broad principle on which both interval estimation and…

Locating pairwise differences among treatment groups is a common practice of applied researchers. Articles published in this journal have addressed the issue of statistical inference within the context of an analysis of variance (ANOVA) framework, describing procedures for comparing means, among other issues. In particular, 1 article (Jaccard &…

Languages are transmitted from person to person and generation to generation via a process of iterated learning: people learn a language from other people who once learned that language themselves. We analyze the consequences of iterated learning for learning algorithms based on the principles of Bayesian inference, assuming that learners compute…

This study examined the relationship between STAR Math gains and TCAP composite scores. The purpose of this study was to determine if there was a significant relationship between STAR Math pretest and posttest gains over the course of the 2005-2006 academic year through the use of the STAR Math software program and TCAP math composite scores at…