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Research Article

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

ORCID Icon, & | (Reviewing editor)
Article: 1518687 | Received 21 Aug 2017, Accepted 06 Aug 2018, Published online: 21 Oct 2018

Figures & data

Figure 1. Heuristic examples for Tau and Tau-U analyses. Data series presented are hypothetical single-case AB designs with baseline phase followed by experimental phase.

Figure 1. Heuristic examples for Tau and Tau-U analyses. Data series presented are hypothetical single-case AB designs with baseline phase followed by experimental phase.

Figure 2. Dependent variable scores are arranged in chronological order along the horizontal edge of a matrix from left to right, and in chronological order along the vertical edge of the matrix from bottom to top. Pairwise comparisons are made in a time-forward fashion within the corresponding cells of the matrix, with a “+” representing a concordant pair, a “−” representing a discordant pair, and a “T” representing a tied pair. For Figure 2A, S = 3, npairs = 45, and τ = .7. For Figure 2B, S = 5, npairs = 45, and τ = 5/45 = .1. (A) Difference matrix for time series in Figure . (B) Difference matrix for time series in Figure 1E.

Figure 2. Dependent variable scores are arranged in chronological order along the horizontal edge of a matrix from left to right, and in chronological order along the vertical edge of the matrix from bottom to top. Pairwise comparisons are made in a time-forward fashion within the corresponding cells of the matrix, with a “+” representing a concordant pair, a “−” representing a discordant pair, and a “T” representing a tied pair. For Figure 2A, S = 3, npairs = 45, and τ = .7. For Figure 2B, S = 5, npairs = 45, and τ = 5/45 = .1. (A) Difference matrix for time series in Figure 1C. (B) Difference matrix for time series in Figure 1E.

Table 1. Tau-U effect sizes and p values for graphs in Figure

Table 2. Means and standard deviations for Tau-U effect sizes of 115 published single-case data sets

Table 3. Correlations of Tau-U and PND coefficients for 115 published single-case data sets

Figure 3. Boxplot for effect sizes of 115 published single-case data sets. Absolute values used to compare relative magnitude of measured effects.

Figure 3. Boxplot for effect sizes of 115 published single-case data sets. Absolute values used to compare relative magnitude of measured effects.

Figure 4. Illustrative real-world data sets.

Figure 4. Illustrative real-world data sets.

Table 4. Spearman correlations of Tau-U coefficients and average visual ratings for 30 single-case data sets

Table 5. Quartiles of 30 visually rated graphs and their corresponding Tau-U effect size ranges