Robust regression for single-case data analysis: how can it help?

This study examined the degree to which outliers were present in a convenience sample of published single-case research. Using a procedure for analyzing single-case data Allison & Gorman (Behaviour Research and Therapy, 31, 621-631, 1993), this study compared the effect of outliers using ordinary least squares (OLS) regression to a robust regression method and attempted to answer four questions: (1) To what degree does outlier detection vary from OLS to robust regression? (2) How much do effect sizes differ from OLS to robust regression? (3) Are the differences produced by robust regression in more or less agreement with visual judgments of treatment effectiveness? (4) What is a typical range of effect sizes for robust regression versus OLS regression for data from "effective interventions"? Results suggest that outliers are common in single-case data. The effects of outliers in single-case data are explored, and the implications for researchers and practitioners using single-case designs are discussed.