tau_u: Tau-U for single-case data

In scan: Single-Case Data Analyses for Single and Multiple Baseline Designs

Tau-U for single-case data

Description

This function calculates indices of the Tau-U family as proposed by Parker et al. (2011a).

Usage

tau_u(
  data,
  dvar,
  pvar,
  tau_method = c("b", "a"),
  method = c("complete", "parker"),
  phases = c(1, 2),
  meta_analyses = TRUE,
  ci = 0.95,
  ci_method = c("z", "tau", "s"),
  meta_weight_method = c("z", "tau"),
  continuity_correction = FALSE,
  meta_method = NULL
)

## S3 method for class 'sc_tauu'
print(
  x,
  complete = FALSE,
  digits = "auto",
  select = c("Tau", "CI lower", "CI upper", "SD_S", "Z", "p"),
  nice_p = TRUE,
  ...
)

## S3 method for class 'sc_tauu'
export(
  object,
  caption = NA,
  footnote = NA,
  filename = NA,
  select = "auto",
  kable_styling_options = list(),
  kable_options = list(),
  meta = TRUE,
  ...
)

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.
tau_method	Character with values "a" or "b" (default) indicating whether Kendall Tau A or Kendall Tau B is applied.
method	"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.
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).
meta_analyses	If TRUE, a meta analysis is conducted.
ci	Confidence intervals
ci_method	String to specify the method for calculating the standard error of tau. Either "tau", "z", or "s" (not recommended).
meta_weight_method	String to specify the method for calculating the weights of the studies. Either "tau" or "z".
continuity_correction	If TRUE, a continuity correction is applied for calculating p-values of correlations (here: S will be reduced by one before calculating Z)
meta_method	(not implemented) All meta analyses are based on a fixed model.
x	Object returned from tau_u().
complete	Print all parameters.
digits	The minimum number of significant digits to be use. If set to "auto" (default), values are predefined.
select	Character vector with name of variables to be included. When the vector is named, variables are renamed appropriately.
nice_p	If TRUE, p-values are printed in publication friendly form.
...	Further arguments passed to the function.
object	An scdf or an object exported from a scan function.
caption	Character string with table caption. If left NA (default) a caption will be created based on the exported object.
footnote	Character string with table footnote. If left NA (default) a footnote will be created based on the exported object.
filename	String containing the file name. If a filename is given the output will be written to that file.
kable_styling_options	list with arguments passed to the kable_styling function.
kable_options	list with arguments passed to the kable function.
meta	If TRUE, the results of the meta analysis will be exported. If FALSE, each single-case is exported.

Details

Tau-U is an inconsistently operationalized construct. Parker et al. (2011b) describe a method which may result in Tau-U outside the [-1;1] interval. 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 meta-analysis 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).

Value

table	A data frame containing statistics from the Tau-U family, including: Pairs, positive and negative comparisons, S, and Tau
matrix	The matrix of comparisons used for calculating the statistics.
tau_u	Tau-U value.

Functions

• print(sc_tauu): Print results

• export(sc_tauu): Export results as html table

Author(s)

Juergen Wilbert

References

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.

See Also

Other overlap functions: cdc(), nap(), overlap(), pand(), pem(), pet(), pnd()

Examples

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)

scan documentation built on Aug. 8, 2023, 5:07 p.m.