Calculates the Tau (non-overlap) index (Parker, Vannest, Davis, & Sauber 2011).

Tau(
A_data,
B_data,
condition,
outcome,
baseline_phase = NULL,
intervention_phase = NULL,
improvement = "increase",
SE = "unbiased",
confidence = 0.95,
trunc_const = FALSE
)

## Arguments

A_data

vector of numeric data for A phase. Missing values are dropped.

B_data

vector of numeric data for B phase. Missing values are dropped.

condition

vector identifying the treatment condition for each observation in the series.

outcome

vector of outcome data for the entire series.

baseline_phase

character string specifying which value of condition corresponds to the baseline phase. Defaults to first observed value of condition.

intervention_phase

character string specifying which value of condition corresponds to the intervention phase. Defaults to second unique value of condition.

improvement

character string indicating direction of improvement. Default is "increase".

SE

character value indicating which formula to use for calculating the standard error of NAP, with possible values "unbiased" for the exactly unbiased estimator, "Hanley" for the Hanley-McNeil estimator, "null" for the (known) variance under the null hypothesis of no effect, or "none" to not calculate a standard error. Defaults to "unbiased".

confidence

confidence level for the reported interval estimate. Set to NULL to omit confidence interval calculations.

trunc_const

logical value indicating whether to return the truncation constant used to calculate the standard error.

## Value

A list containing the estimate, standard error, and/or confidence interval.

## Details

Tau (non-overlap) a linear re-scaling of NAP to the range [-1,1], with a null value of 0.

Standard errors and confidence intervals for Tau are based on transformations of the corresponding SEs and CIs for NAP.

## References

Parker, R. I., Vannest, K. J., Davis, J. L., & Sauber, S. B. (2011). Combining nonoverlap and trend for single-case research: Tau-U. Behavior Therapy, 42(2), 284--299. doi:doi:10.1016/j.beth.2010.08.006

## Examples

A <- c(20, 20, 26, 25, 22, 23)
B <- c(28, 25, 24, 27, 30, 30, 29)
Tau(A_data = A, B_data = B)
#>    ES       Est        SE  CI_lower  CI_upper
#> 1 Tau 0.8333333 0.1380131 0.1946812 0.9720352