Bounded continuous data are encountered in many applications of item response theory, including the measurement of mood, personality, and response times and in the analyses of summed item scores. Although different item response theory models exist to analyze such bounded continuous data, most models assume the data to be in an open interval and…

The uncertainty arising from item parameter estimation is often not negligible and must be accounted for when calculating latent variable (LV) scores in item response theory (IRT). It is particularly so when the calibration sample size is limited and/or the calibration IRT model is complex. In the current work, we treat two-stage IRT scoring as a…

Paired-samples designs are used frequently in educational and behavioral research. In applications where the response variable is quantitative, researchers are encouraged to supplement the results of a paired-samples t-test with a confidence interval (CI) for a mean difference or a standardized mean difference. Six CIs for standardized mean…

It is often assumed that a vertical scale is necessary when value-added models depend upon the gain scores of students across two or more points in time. This article examines the conditions under which the scale transformations associated with the vertical scaling process would be expected to have a significant impact on normative interpretations…

In this article, the authors outline methods for using fixed and random effects power analysis in the context of meta-analysis. Like statistical power analysis for primary studies, power analysis for meta-analysis can be done either prospectively or retrospectively and requires assumptions about parameters that are unknown. The authors provide…

Tryon presented a graphic inferential confidence interval (ICI) approach to analyzing two independent and dependent means for statistical difference, equivalence, replication, indeterminacy, and trivial difference. Tryon and Lewis corrected the reduction factor used to adjust descriptive confidence intervals (DCIs) to create ICIs and introduced…

In this article, a heterogeneous latent growth curve model for modeling heterogeneity of growth rates is proposed. The suggested model is an extension of a conventional growth curve model and a complementary tool to mixed growth modeling. It allows the modeling of heterogeneity of growth rates as a continuous function of latent initial status and…