The Integrated Violin-Box-Scatter (VBS) Plot to Visualize the Distribution of a Continuous Variable

The histogram remains a widely used tool for visualization of the distribution of a continuous variable, despite the disruption of binning the underlying continuity into somewhat arbitrarily sized discrete intervals imposed by the simplicity of its pre-computer origins. Alternatives include three visualizations, namely a smoothed density distribution such as a violin plot, a box plot, and the direct visualization of the individual data values as a one-dimensional scatter plot. To promote ease of use, the plotting function discussed in this work, Plot(x), automatically integrates these three visualizations of a continuous variable x into what is called a VBS plot here, tuning the resulting plot to the sample size and discreteness of the data. This integration complements the information derived from the histogram well and more easily generalizes to a multi-panel presentation at each level of a second categorical variable

Enhancement of the Command-Line Environment for Use in the Introductory Statistics Course and Beyond

R and Python are commonly used software languages for data analytics. Using these languages as the course software for the introductory course gives students practical skills for applying statistical concepts to data analysis. However, the reliance upon the command line is perceived by the typical nontechnical introductory student as sufficiently esoteric that its use detracts from the teaching of statistical concepts and data analysis. An R package was developed based on the successive feedback of hundreds of introductory statistics students over multiple years to provide a set of functions that apply basic statistical principles with command-line R. The package offers gentler error checking and many visualizations and analytics, successfully serving as the course software for teaching and homework. This software includes pedagogical functions, data analytic functions for a variety of analyses, and the foundation for access to the entire R ecosystem and, by extension, any command-line environment

Improper solutions in the analysis of covariance structures: Their interpretability and a comparison of alternate respecifications

improper solutions, analyses of covariance structures, confirmatory factor analysis, maximum likelihood,