Researchers continue to choose PCA in scale development and adaptation studies because it is the default setting and overestimates measurement quality. When PCA is utilized in investigations, the explained variance and factor loadings can be exaggerated. PCA, in contrast to the models given in the literature, should be investigated in…

In practice, some test items may display misfit at the upper-asymptote of item characteristic curve due to distraction, anxiety, or carelessness by the test takers (i.e., the slipping effect). The conventional item response theory (IRT) models do not take the slipping effect into consideration, which may violate the model fit assumption in IRT.…

In random-effects meta-analysis the between-study variance ([tau][superscript 2]) has a key role in assessing heterogeneity of study-level estimates and combining them to estimate an overall effect. For odds ratios the most common methods suffer from bias in estimating [tau][superscript 2] and the overall effect and produce confidence intervals…

The standard deviation (SD) of a random sample is defined as the square-root of the sample variance, which is the "mean" squared deviation of the sample observations from the sample mean. Here, we interpret the sample SD as the square-root of twice the mean square of all pairwise half deviations between any two sample observations. This…

A fundamental aspect of statistical inference is representation of real-world data using statistical models. This article analyzes students' articulations of statistical models and modeling during their first steps in making informal statistical inferences. An integrated modeling approach (IMA) was designed and implemented to help students…