Tau-U with baseline-trend correction

Parker, Vannest, Davis & Sauber's (2011) Tau-U combines the A-vs-B non-overlap with a correction for baseline (phase A) trend. Two reference conventions differ on the denominator and this function exposes both:

Usage

scedTauU(
  A_data,
  B_data = NULL,
  improvement = c("increase", "decrease"),
  method = c("parker", "scan"),
  confidence = 0.95
)

Arguments

A_data, B_data: Numeric baseline (A) and intervention (B) observations, or pass a data.frame to the phase orchestrator scedABAB().
improvement: "increase" (default) if higher scores are better, or "decrease" if lower scores are the therapeutic goal.
method: Denominator convention, "parker" (default) or "scan".
confidence: Confidence level for the interval (default 0.95).

Value

An AnalysisResult (type = "sced_tau_u") whose estimate is Tau-U, with result$S, result$se_S, result$z, result$p_value and the component S values.

Details

method = "parker" (default): matches SingleCaseES::Tau_U: $(S_{AB} - S_{trend A}) / (m n)$, where $S_{AB}$ is the A-vs-B Kendall S and $S_{trend A}$ the within-baseline Kendall S. Can exceed 1 when a baseline trend runs counter to improvement.
method = "scan": matches scan::tau_u()'s "A vs. B - Trend A" row: the same S numerator over a tie-corrected pair count $D$, giving a Kendall tau-b in [-1, 1].

The Z statistic and p-value come from the tie-corrected variance of the Kendall S numerator and are identical under both methods (they depend on S, not the denominator), matching scan's Z and p.

References

Parker RI, Vannest KJ, Davis JL, Sauber SB (2011). Combining nonoverlap and trend for single-case research: Tau-U. Behavior Therapy, 42(2), 284-299.

Examples

scedTauU(c(20, 20, 26, 25, 22, 23), c(28, 25, 24, 27, 30, 30, 29, 28))
#> <AnalysisResult> sced_tau_u 
#>   estimate: 0.7708333 
#>   method: Tau-U (parker) 
#>   fields: estimate, ci_lower, ci_upper, S, S_AB, S_trendA, D, z, p_value, method, n_A, n_B, improvement 
#>   provenance: 1 entr(ies)