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Tau-U for single-case data

Source: R/tau_u.R, R/print.sc_tauu.R, R/export.sc_tauu.R
tau_u.Rd

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

Usage

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

# S3 method for 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 sc_tauu
export(
  object,
  caption = NA,
  footnote = NA,
  filename = NA,
  select = "auto",
  kable_styling_options = list(),
  kable_options = list(),
  meta = FALSE,
  round = 3,
  decimals = 3,
  ...
)

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.

method

"complete" (default), "parker" or "tarlow". The "parker" calculates the number of possible pairs as described in Parker et al. (2011) which might lead to tau-U values greater than 1. "tarlow" follows an online calculator and R code developed by Tarlow (2017).

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".

tau_method

Character with values "a" or "b" (default) indicating whether Kendall Tau A or Kendall Tau B is applied. Ignored for methods 'tarlow' and 'parker'.

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). Ignored for methods 'tarlow' and 'parker'.

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.

round

Integer passed to the digits argument internally used to round values.

decimals

Decimal places that are reported.

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.

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).

Functions

  • print(sc_tauu): Print results

  • export(sc_tauu): Export results as html table

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(2), 284–299. https://doi.org/10.1016/j.beth.2010.08.006

Tarlow, K. R. (2017, March). Tau-U for single-case research (R code). Retrieved from http://ktarlow.com/stats/

See also

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

Author

Juergen Wilbert

Examples


tau_u(Grosche2011$Eva)
#> Tau-U
#> Method: complete 
#> Applied Kendall's Tau-b
#> 95% CIs for tau are reported.
#> CI method: z
#> 
#> Case: Eva 
#>                              Tau CI lower CI upper  SD_S    Z     p
#> A vs. B                     0.38    -0.08     0.71 22.80 1.32   .19
#> A vs. B - Trend A           0.26    -0.22     0.64 23.42 1.41   .16
#> A vs. B + Trend B           0.49     0.05     0.77 28.08 2.85 <.001
#> A vs. B + Trend B - Trend A 0.49     0.04     0.77 28.58 2.90 <.001
#> 

## 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")
print(res, complete = TRUE)
#> Tau-U
#> Method: parker 
#> Applied Kendall's Tau-a
#> 95% CIs for tau are reported.
#> CI method: z
#> 
#> Case: Bob 
#>                             pairs pos neg ties  S  D  Tau CI lower CI upper
#> A vs. B                        20  17   1    2 16 20 0.80     0.29     0.96
#> Trend A                         6   4   1    1  3  6 0.50    -0.89     0.99
#> Trend B                        10   8   1    1  7 10 0.70    -0.48     0.98
#> A vs. B - Trend A              20  18   5    3 13 20 0.65    -0.02     0.92
#> A vs. B + Trend B              30  25   2    3 23 30 0.77     0.21     0.95
#> A vs. B + Trend B - Trend A    36  26   6    4 20 36 0.56    -0.17     0.89
#>                             SD_S VAR_S SE_Tau    Z    p n
#> A vs. B                     8.16 66.67   0.40 2.00  .05 9
#> Trend A                     2.94  8.67   0.46 1.08  .28 4
#> Trend B                     4.08 16.67   0.40 1.77  .08 5
#> A vs. B - Trend A           8.48 71.86   0.42 1.53  .13 9
#> A vs. B + Trend B           8.91 79.37   0.30 2.58 <.05 9
#> A vs. B + Trend B - Trend A 9.35 87.33   0.26 2.14 <.05 9
#> 

## Request tau-U for all single-cases from the Grosche2011 data set
tau_u(Grosche2011)
#> Tau-U
#> Method: complete 
#> Applied Kendall's Tau-b
#> 95% CIs for tau are reported.
#> CI method: z
#> 
#> Tau-U meta analyses:
#> Weight method: z
#> 95% CIs are reported.
#> 
#>                        Model Tau_U   se CI lower CI upper    z    p
#>                      A vs. B 0.071 0.14   -0.193     0.33 0.52 0.60
#>            A vs. B - Trend A 0.083 0.14   -0.181     0.34 0.61 0.54
#>            A vs. B + Trend B 0.183 0.14   -0.082     0.42 1.36 0.17
#>  A vs. B + Trend B - Trend A 0.207 0.14   -0.057     0.44 1.54 0.12
#> 
#> Case: Eva 
#>                              Tau CI lower CI upper  SD_S    Z     p
#> A vs. B                     0.38    -0.08     0.71 22.80 1.32   .19
#> A vs. B - Trend A           0.26    -0.22     0.64 23.42 1.41   .16
#> A vs. B + Trend B           0.49     0.05     0.77 28.08 2.85 <.001
#> A vs. B + Trend B - Trend A 0.49     0.04     0.77 28.58 2.90 <.001
#> 
#> Case: Georg 
#>                               Tau CI lower CI upper  SD_S     Z   p
#> A vs. B                     -0.04    -0.44     0.37 31.49 -0.16 .87
#> A vs. B - Trend A            0.06    -0.36     0.45 32.18  0.34 .73
#> A vs. B + Trend B            0.14    -0.28     0.51 39.75  0.93 .35
#> A vs. B + Trend B - Trend A  0.19    -0.23     0.55 40.30  1.32 .19
#> 
#> Case: Olaf 
#>                               Tau CI lower CI upper  SD_S     Z   p
#> A vs. B                     -0.10    -0.52     0.35 25.92 -0.39 .70
#> A vs. B - Trend A           -0.06    -0.49     0.40 29.74 -0.34 .74
#> A vs. B + Trend B           -0.09    -0.51     0.37 27.15 -0.52 .61
#> A vs. B + Trend B - Trend A -0.07    -0.50     0.38 30.82 -0.45 .65
#>