granova: an R package for graphical analysis of variance

The granova package for R consists of four functions (granova.1w, granova.2w, granova.contr and granova.ds) that create what we term elemental graphics.  That is, these functions have been developed to provide information and graphics that pertain directly to the fundamental questions that drive each of the particular methods for analysis: one-way anova, two-way anova, contrast-driven anova and dependent sample comparisons using anova. Assuming you have a working R platform, you can download the package using


An article that documents these functions has been submitted for publication. Any comments you have would be appreciated.

Download ElementalGraphicsForANOVA.finalJune11.pdf


PSAgraphics: An R package to Support Propensity Score Analysis

Propensity score analysis is a technique for adjusting for selection bias in observational data. Estimated propensity scores (probability of treatment given observed covariates) are used for stratification of observations. Within strata covariates should be more balanced between the two treatments than without the stratification. PSAgraphics is an R package that provides flexible graphical tools to assess within strata balance between treatment groups, as well as how covariate distributions differ across strata. Additional graphical tools facilitate estimation of treatment effects having adjusted for covariate differences. Several new and conventional numerical measures of balance are also provided.

Helmreich, J & Pruzek, R.M. (2009) PSAgraphics: An R package to Support Propensity Score AnalysisJour. of Stat. Software, 29, 06. [ ]


Enhancing dependent sample analyses with graphics

A standard topic in many Introductory Statistics courses is the analysis of dependent samples. A simple graphical approach that is particularly relevant to dependent sample comparisons is presented, illustrated and discussed in the context of analyzing five real data sets. Each data set to be presented has been published in a textbook, usually introductory. Illustrations show that comprehensive graphical analyses often yield more nuanced, and sometimes quite different interpretations of data than are derived from standard numerical summaries. Indeed, several of our findings would not readily have been revealed without the aid of graphic or visual assessment. Several arguments made by John Tukey about data analysis are seen to have special force and relevance.

Pruzek, R.M. & Helmreich, J. (2009) Enhancing dependent sample analyses with graphicsJour. of Statisical Education, 17, 1.    [ ]

A New Graphic for One-Way ANOVA

This document describes and illustrates a new ‘elemental’ graphic for one-way analysis of variance, i.e., ANOVA. The primary motivation for developing the central function was to facilitate a deeper understanding of the key features of analysis of variance by focusing on the central question of the method in the context of using modern graphics that can facilitate sound data analyses. It is also hoped that use of this function will facilitate development of modern data-analytic thinking and skills in ANOVA applications. The function that produces this graphic can be found in my R package (coauthored with Prof. James Helmreich): granova.

Download  aNewGraphic4one-wayANOVA.BP11


Some new regression methods for predictive and construct validation

Both predictive and construct validation are essential to instrument development in all social and behavioral sciences. Ideally, both types of validation entail theoretical as well as empirical studies; moreover, the term validation implies a process that takes place over time, often in a sequentially articulated fashion. The choice of methods and methodology for empirical data analyses is of course central to the viability of validation studies. This article describes and reports on the empirical functionality of some modern methods for linear prediction, methods that appear to hold special promise for improving both the theoretical and empirical usefulness of validation studies in the social and behavioral sciences. Because ordinary least squares (OLS) methods are, far and away, the most popular forms of multiple regression, particular attention will be given to comparing the new methods with OLS regression.

Rabinowitz, S.N., Rule, D., & Pruzek, R.M. (1998). Some new regression methods for predictive and construct validation. Social Indicators Research, 45, 201-231

Download RabRulePrzSIR98c.pdf


Weighted structural regression: A broad class of adaptive methods for improving linear prediction

Given a criterion variable and two or more predictors, applied linear prediction usually   entails some form of OLS regression. But when there are several predictors, and especially when these are subject to non-ignorable errors of measurement, applications of OLS methods are often fraught with problems. Weighted structural regression (WSR) methods can mitigate many difficulties through the incorporation of prior structural models into analyses. WSR methods are sufficiently general to include OLS, ridge, reduced rank regression, as well as most covariance structural regression models, as special cases; many other regression methods, heretofore not available, are also included. In this article adaptive forms of WSR are developed and discussed. According to our bootstrapping studies the new methods have potential to recover known population regression weights and predict criterion score values routinely better than OLS with which they are compared. These new methods are scale free as well as simple to compute; they seem well suited to many prediction applications in behavioral research.

Pruzek, R.M., & Lepak, G. (1992). Weighted structural regression: A broad class of adaptive methods to improving linear prediction. Multivariate Behavioral Research, 27, 95-129.

Download Pruzek.Lepak.WeightedStructRegressMBR92