Tau-U and baseline-corrected Tau

Both indices start from Kendall's tau and can take a trend in baseline into account. Tau-U (Parker et al. 2011) counts the pairs from A and B in which B is better, subtracts the worse ones and divides by the number of pairs; “minus trend A” also subtracts the direction over time within A. The value can therefore lie slightly outside −1 to +1. Baseline-corrected Tau (Tarlow 2017) first tests whether A has a significant trend (Kendall τ, p ≤ .05). If so, the trend line of A (Theil-Sen) is subtracted from all values; then τ is computed between the adjusted values and the phase. Otherwise no correction is made. Tarlow's index stays between −1 and +1 and is considered better protected against false positives. Classification according to Vannest and Ninci (2015): up to .20 small, up to .60 moderate, up to .80 large, above that very large.

Example: Tau-U = .93, p = .002; Tau-BC = .59, p = .002.

Caution: Removing the trend assumes that the baseline trend would have continued through B - with a long B phase this is a strong assumption. With fewer than 3 measurements in A no trend can be tested. The p values assume independent measurements.