An Improved Rank Correlation Effect Size Statistic for Single-Case Designs: Baseline Corrected Tau

Abstract

Measuring treatment effects when an individual's pretreatment performance is improving poses a challenge for single-case experimental designs. It may be difficult to determine whether improvement is due to the treatment or due to the preexisting baseline trend. Tau- U is a popular single-case effect size statistic that purports to control for baseline trend. However, despite its strengths, Tau- U has substantial limitations: Its values are inflated and not bound between -1 and +1, it cannot be visually graphed, and its relatively weak method of trend control leads to unacceptable levels of Type I error wherein ineffective treatments appear effective. An improved effect size statistic based on rank correlation and robust regression, Baseline Corrected Tau, is proposed and field-tested with both published and simulated single-case time series. A web-based calculator for Baseline Corrected Tau is also introduced for use by single-case investigators.