Interpreting Kendall's Tau and Tau-U for single-case experimental designs
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abstract
2018, 2018 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. Tau (), 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-Us 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-Us 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.
