Calculates the baseline-corrected Tau index (Tarlow 2017).
Tau_BC( A_data, B_data, condition, outcome, baseline_phase = NULL, intervention_phase = NULL, improvement = "increase", SE = "unbiased", confidence = 0.95, trunc_const = FALSE, Kendall = FALSE, pretest_trend = FALSE, report_correction = FALSE, warn = TRUE )
vector of numeric data for A phase. Missing values are dropped.
vector of numeric data for B phase. Missing values are dropped.
vector identifying the treatment condition for each observation in the series.
vector of outcome data for the entire series.
character string specifying which value of
condition corresponds to the baseline phase. Defaults to first
observed value of
character string specifying which value of
condition corresponds to the intervention phase. Defaults to second
unique value of
character string indicating direction of improvement. Default is "increase".
character value indicating which formula to use for calculating the
standard error of Tau-BC, with possible values
"unbiased" for the
exactly unbiased estimator,
"Hanley" for the Hanley-McNeil
"null" for the (known) variance under the null hypothesis
of no effect, or
"none" to not calculate a standard error. Defaults
to "unbiased". Note that the "unbiased" standard error is unbiased for
Tau, but not necessarily unbiased for
None of the standard error formulas account for the additional uncertainty
due to use of the baseline trend correction.
confidence level for the reported interval estimate. Set to
NULL to omit confidence interval calculations.
logical value indicating whether to return the truncation constant used to calculate the standard error.
logical value indicating whether to use Kendall's rank
correlation to calculate the Tau effect size measure. If
Kendall's rank correlation (with adjustment for ties) is calculated between
the data and a dummy coded phase variable, which is consistent with the
method used in Tarlow (2017). Default is
FALSE, which calculates
Tau (non-overlap) index (without adjustment for ties).
significance level for the initial baseline trend test.
The raw data are corrected and
Tau_BC is calculated only if
the baseline trend is statistically significant. Otherwise,
Tau_BC is equal to
Tau. Default is
FALSE, which always adjusts for the baseline trend.
logical value indicating whether to report the
baseline corrected slope and intercept values. Default is
logical value indicating whether to print a message regarding the
outcome of the baseline trend test. Default is
A list containing the estimate, standard error, and/or confidence interval.
Tau-BC is an elaboration of the
Tau that includes a
correction for baseline trend. The calculation of Tau-BC involves two or
three steps, depending on the
pretest_trend = FALSE (the default), the first step involves
adjusting the outcomes for baseline trend estimated using Theil-Sen
regression. In the second step, the residuals from Theil-Sen regression are
used to calculate the
Tau (using either Kendall's rank correlation,
with adjustment for ties, or computing Tau directly, without adjustment for
pretest_trend can be set equal to a significance level
between 0 and 1 (e.g.
pretest_trend = .05, as suggested by Tarlow
(2017). In this case, the first step involves a significance test for the
slope of the baseline trend based on Kendall's rank correlation. If the
slope is not significantly different from zero, then no baseline trend
adjustment is made and Tau-BC is set equal to
Tau index. If the
slope is significantly different from zero, then in the second step, the
outcomes are adjusted for baseline trend using Theil-Sen regression. Then,
in the third step, the residuals from Theil-Sen regression are used to
Tau index. If
Kendall = FALSE (the default),
Tau (non-overlap) index is calculated. If
= TRUE, then Kendall's rank correlation is calculated, including
adjustment for ties, as in Tarlow (2017).
Note that the standard error formulas are based on the standard errors for
Tau (non-overlap) and they do not account for the additional
uncertainty due to use of the baseline trend correction (nor to the
pre-test for statistical significance of baseline trend, if used).
Tarlow, K. R. (2017). An improved rank correlation effect size statistic for single-case designs: Baseline corrected Tau. Behavior modification, 41(4), 427-467. doi:doi:10.1177/0145445516676750