Methods to generate random correlation matrices have been proposed in the literature, but very few instances exist where these correlation matrices are structured or where the statistical properties of the algorithms are known. By relying on the tetrad relation discovered by Spearman and the properties of the beta distribution, an algorithm is…

To further understand the properties of data-generation algorithms for multivariate, nonnormal data, two Monte Carlo simulation studies comparing the Vale and Maurelli method and the Headrick fifth-order polynomial method were implemented. Combinations of skewness and kurtosis found in four published articles were run and attention was…

Heterogeneity within English language learners (ELLs) groups has been documented. Previous research on differential item functioning (DIF) analyses suggests that accurate DIF detection rates are reduced greatly when groups are heterogeneous. In this simulation study, we investigated the effects of heterogeneity within linguistic (ELL) groups on…

Previous studies have rarely examined the impact of outliers on the decisions about the number of factors to extract in an exploratory factor analysis. The few studies that have investigated this issue have arrived at contradictory conclusions regarding whether outliers inflated or deflated the number of factors extracted. By systematically…

There is a lack of research on the effects of outliers on the decisions about the number of factors to retain in an exploratory factor analysis, especially for outliers arising from unintended and unknowingly included subpopulations. The purpose of the present research was to investigate how outliers from an unintended and unknowingly included…

The impact of outliers on Cronbach's coefficient [alpha] has not been documented in the psychometric or statistical literature. This is an important gap because coefficient [alpha] is the most widely used measurement statistic in all of the social, educational, and health sciences. The impact of outliers on coefficient [alpha] is investigated for…

One theoretical feature that makes item response theory (IRT) models those of choice for many psychometric data analysts is parameter invariance, the equality of item and examinee parameters from different examinee populations or measurement conditions. In this article, using the well-known fact that item and examinee parameters are identical only…

Many measures found in educational research are ordered categorical response variables that are empirical realizations of an underlying normally distributed variate. These ordered categorical variables are commonly referred to as Likert or rating scale data. Regression models are commonly fit using these ordered categorical variables as the…