This function calculates indices of the Tau-U family as proposed by Parker et al. (2011a).
tau_u(
data,
dvar,
pvar,
tau_method = "b",
method = "complete",
phases = c(1, 2),
meta_analyses = TRUE,
ci = 0.95,
ci_method = "z",
meta_weight_method = "z",
continuity_correction = FALSE,
meta_method = NULL
)A data frame containing statistics from the Tau-U family, including: Pairs, positive and negative comparisons, S, and Tau
The matrix of comparisons used for calculating the statistics.
Tau-U value.
A single-case data frame. See scdf to learn about
this format.
Character string with the name of the dependent variable. Defaults to the attributes in the scdf file.
Character string with the name of the phase variable. Defaults to the attributes in the scdf file.
Character with values "a" or "b" (default) indicating whether Kendall Tau A or Kendall Tau B is applied.
"complete" (default) or "parker". The latter
calculates the number of possible pairs as described in Parker et al.
(2011) which might lead to tau-U values greater than 1.
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).
If TRUE, a meta analysis is conducted.
Confidence intervals
String to specify the method for calculating the standard error of tau. Either "tau", "z", or "s" (not recommended).
String to specify the method for calculating the weights of the studies. Either "tau" or "z".
If TRUE, a continuity correction is applied for calculating p-values of correlations (here: S will be reduced by one before calculating Z)
(not implemented) All meta analyses are based on a fixed model.
Juergen Wilbert
Tau-U is an inconsistently operationalized construct. Parker et al. (2011b) describe a method which may result in Tau-U lager than 1. A different implementation of the method (provided at http://www.singlecaseresearch.org/calculators/tau-u) uses tau-b (instead of tau-a as in the original formulation by Parker). Bossart et. al (2018) describe inconsistencies in the results from this implementation as well. Another problems lies in the calculation in overall Tau-U values from several single cases. The function presented here applies a metaanalyzes to gain the overall values. Each tau value is weighted by the inverse of the variance (ie. the tau standard error). The confidence intervals for single cases are calculated by Fisher-Z transforming tau, calculating the confidence intervals, and inverse transform them back to tau (see Long & Cliff, 1997).
Brossart, D. F., Laird, V. C., & Armstrong, T. W. (2018). Interpreting Kendall’s Tau and Tau-U for single-case experimental designs. Cogent Psychology, 5(1), 1–26. https://doi.org/10.1080/23311908.2018.1518687.
Long, J. D., & Cliff, N. (1997). Confidence intervals for Kendall’s tau. British Journal of Mathematical and Statistical Psychology, 50(1), 31–41. https://doi.org/10.1111/j.2044-8317.1997.tb01100.x
Parker, R. I., Vannest, K. J., & Davis, J. L. (2011a). Effect Size in Single-Case Research: A Review of Nine Nonoverlap Techniques. Behavior Modification, 35(4), 303–322. https://doi.org/10/dsdfs4 Parker, R. I., Vannest, K. J., Davis, J. L., & Sauber, S. B. (2011b). Combining Nonoverlap and Trend for Single-Case Research: Tau-U. Behavior Therapy, 42, 284-299.
Other overlap functions:
corrected_tau(),
nap(),
overlap(),
pand(),
pem(),
pet(),
pnd()
tau_u(Grosche2011$Eva)
## Replicate tau-U calculation from Parker et al. (2011)
bob <- scdf(c(A = 2, 3, 5, 3, B = 4, 5, 5, 7, 6), name = "Bob")
res <- tau_u(bob, method = "parker", tau_method = "a")
print(res, complete = TRUE)
## Request tau-U for all single-cases from the Grosche2011 data set
tau_u(Grosche2011)
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