corrected_tau: Baseline corrected tau

Description

Kendall's tau correlation for the dependent variable and the phase variable is calculated after correcting for a baseline trend.

Usage

corrected_tau(
  data,
  dvar,
  pvar,
  mvar,
  phases = c(1, 2),
  alpha = 0.05,
  continuity = FALSE,
  repeated = FALSE,
  tau_method = c("b", "a")
)

Arguments

data: A single-case data frame. See scdf() to learn about this format.
dvar: Character string with the name of the dependent variable. Defaults to the attributes in the scdf file.
pvar: Character string with the name of the phase variable. Defaults to the attributes in the scdf file.
mvar: Character string with the name of the measurement time variable. Defaults to the attributes in the scdf file.
phases: A vector of two characters or numbers indicating the two phases that should be compared. E.g., phases = c("A","C") or phases = c(2,4) for comparing the second to the fourth phase. Phases could be combined by providing a list with two elements. E.g., phases = list(A = c(1,3), B = c(2,4)) will compare phases 1 and 3 (as A) against 2 and 4 (as B). Default is phases = c(1,2).
alpha: Sets the p-value at and below which a baseline correction is applied.
continuity: If TRUE applies a continuity correction for calculating p
repeated: If TRUE applies the repeated median method for calculating slope and intercept.
tau_method: Character with values "a" or "b" (default) indicating whether Kendall Tau A or Kendall Tau B is applied.

Details

This method has been proposed by Tarlow (2016). The baseline data are checked for a significant autocorrelation (based on Kendall's Tau). If so, a non-parametric Theil-Sen regression is applied for the baseline data where the dependent values are regressed on the measurement time. The resulting slope information is then used to predict data of the B-phase. The dependent variable is now corrected for this baseline trend and the residuals of the Theil-Sen regression are taken for further calculations. Finally, Kendall's tau is calculated for the dependent variable and the dichotomous phase variable. The function here provides two extensions to this procedure: The more accurate Siegel repeated median regression is applied when repeated = TRUE and a continuity correction is applied when continuity = TRUE.

References

Tarlow, K. R. (2016). An Improved Rank Correlation Effect Size Statistic for Single-Case Designs: Baseline Corrected Tau. Behavior Modification, 41(4), 427–467. https://doi.org/10.1177/0145445516676750

Examples

Run this code

dat <- scdf(c(A = 33,25,17,25,14,13,15, B = 15,16,16,5,7,9,6,5,3,3,8,11,7))
corrected_tau(dat)