Checking the normality assumption is necessary to decide whether a parametric or non-parametric test needs to be used. Different ways are suggested in literature to use for checking normality. Skewness and kurtosis values are one of them. However, there is no consensus which values indicated a normal distribution. Therefore, the effects of…

The purpose of this study is to illustrate the use of functional data analysis (FDA) as a general methodology for analyzing person response functions (PRFs). Applications of FDA to psychometrics have included the estimation of item response functions and latent distributions, as well as differential item functioning. Although FDA has been…

A systematic review and meta-analysis is an important step in evidence synthesis. The current paradigm for meta-analyses requires a presentation of the means under a random-effects model; however, a mean with a confidence interval provides an incomplete summary of the underlying heterogeneity in meta-analysis. Prediction intervals show the range…

Often, when testing for shift in location, researchers will utilize nonparametric statistical tests in place of their parametric counterparts when there is evidence or belief that the assumptions of the parametric test are not met (i.e., normally distributed dependent variables). An underlying and often unattended to assumption of nonparametric…

This study analysed polytomous items' psychometric properties according to nonparametric item response theory (NIRT) models. Thus, simulated datasets--three different test lengths (10, 20 and 30 items), three sample distributions (normal, right and left skewed) and three samples sizes (100, 250 and 500)--were generated by conducting 20…

It is common to assume that worker productivity is normally distributed, but this assumption is rarely if ever tested. We estimate the distribution of worker productivity where individual productivity is measured with error, using the productivity of elementary school teachers as an example. Proposals to improve teacher productivity often focus on…

Standard approaches for estimating item response theory (IRT) model parameters generally work under the assumption that the latent trait being measured by a set of items follows the normal distribution. Estimation of IRT parameters in the presence of nonnormal latent traits has been shown to generate biased person and item parameter estimates. A…