Analysing Badly Skewed, Highly Variable Data

Many important psychological variables have uncorrectable skew and radically different amounts of variability across different subsections of the population. Conventional statistical methods are largely unable to handle such data. Michael Smithson and Jay Verkuilen at the University of Illinois at Urbana-Champaign have developed a multivariate regression technique using the beta distribution, which is very flexible and handles skew and heterogeneous variability quite well. Their technique, called "beta-regression," models both means (location) and variances (dispersion) with their own distinct sets of predictors (continuous and/or categorical), thereby modeling heteroscedasticity.

They have applied beta-regression to a number of real data-sets and shown that it can reveal important trends and relationships among variables that other techniques cannot. For instance, reading accuracy test-scores and IQ-scores were collected by Kristen Pammer and Alison Kevan on dyslexic and non-dyslexic readers. The reading accuracy scores display uncorrectable skew for the non-dyslexics (the Controls in the right-hand graph). Conventional statistical analyses were unable to isolate the effects of IQ from those of dyslexia on reading accuracy. However, beta-regression showed clearly that dyslexia has a separate impact from that of IQ, and moreover that IQ predicts reading accuracy for the Controls but not for Dyslexics.

Smithson and Verkuilen also have developed software resources for implementing their beta-regression in several popular statistical computing packages, and provide them free of charge via the web. They have recently submitted a paper describing this technique to Psychological Methods, a prominent outlet for this kind of work.