Interpreting Kendall's Tau and Tau-U for single-case experimental designs

• Published in: Cogent psychology Vol. 5; no. 1; p. 1518687
• Main Authors: Brossart, Daniel F., Laird, Vanessa C., Armstrong, Trey W.
• Format: Journal Article
• Language: English
• Published: Abingdon Cogent 31.12.2018; Taylor & Francis Ltd; Taylor & Francis Group
• Subjects: Data analysis; Datasets; Educational psychology; effect size; Medical research; Research methodology; single-case; single-subject; Statistical analysis; Statistical methods; Statistics; Tau; time series; Variables
• ISSN: 2331-1908; 2331-1908
• DOI: 10.1080/23311908.2018.1518687

Tau (τ), a nonparametric rank order correlation statistic, has been applied to single-case experimental designs with promising results. Tau-U, a family of related coefficients, partitions variance associated with changes in trend and level. By examining within-phase trend and across-phase differences separately with Tau-U, single-case investigators may gain useful descriptive and inferential insights about their data. Heuristic data sets were used to explore Tau-U's conceptual foundation, and 115 published single-case data sets were analyzed to demonstrate that Tau-U coefficients perform predictably when they are well understood. An understanding of Tau-U's theoretical basis and unique limitations will help investigators select the appropriate statistical method to test their hypotheses and interpret their results appropriately. Limitations of Tau-U include as follows: vague or inconsistent Tau-U terminology in published single-case research; arithmetic problems that lead to unexpected and difficult-to-interpret results, especially when controlling for baseline trend; Tau-U methods are difficult to graph visually, and a comparison with visual raters found that several Tau-U effect size statistics are weakly correlated with visual analysis.