rand_test: Randomization Tests for single-case data

Description

The rand_test function computes a randomization test for single or multiple baseline single-case data. The function is based on an algorithm from the SCRT package (Bulte & Onghena, 2009, 2012), but rewritten and extended for the use in AB designs.

Usage

rand_test(
  data,
  dvar,
  pvar,
  statistic = c("Mean B-A", "Mean A-B", "Median B-A", "Median A-B", "Mean |A-B|",
    "Median |A-B|", "SMD hedges", "SMD glass", "W-test", "T-test", "NAP",
    "NAP decreasing", "Slope B-A", "Slope A-B"),
  statistic_function = NULL,
  number = 500,
  complete = FALSE,
  limit = 5,
  startpoints = NA,
  exclude.equal = FALSE,
  phases = c(1, 2),
  graph = FALSE,
  output = NULL,
  seed = NULL
)

Value

statistic: Character string from function call (see Arguments above).
N: Number of single-cases.
n1: Number of data points in phase A.
n2: Number of data points in phase B.
limit: Numeric from function call (see Arguments above).
startpoints: A vector defining the start points passed from the function call (see Arguments above).
p.value: P-value of the randomization test for the given data.
number: Sample size of randomization distribution from function call (see Arguments above).
complete: Logical argument from function call (see Arguments above).
observed.statistic: Test statistic observed for the given single-case data. (see statistic in the Arguments above.)
Z: Z-value of observed test statistic.
p.z.single: Probability of z-value.
distribution: Test statistic distribution from randomized data sets.
possible.combinations: Number of possible combinations under the given restrictions.
auto.corrected.number: TRUE indicates that a corrected number of combinations was used. This happens, if the number of possible combinations (under the given restrictions) undercuts the requested number of combinations.
ecxlude.equal: see argument above

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.
statistic: Defines the statistic on which the comparison of phases A and B is based on. Default setting is statistic = "Mean B-A". See details.
statistic_function: A list with a user defined function to calculate the statistic. When set, overwrites the statistic argument. See details.
number: Sample size of the randomization distribution. The exactness of the p-value can not exceed \(1/number\) (i.e., number = 100 results in p-values with an exactness of one percent). Default is number = 500. For faster processing use number = 100. For more precise p-values set number = 1000).
complete: If TRUE, the distribution is based on a complete permutation of all possible starting combinations. This setting overwrites the number Argument. The default setting is FALSE.
limit: Minimal number of data points per phase in the sample. The first number refers to the A-phase and the second to the B-phase (e.g., limit = c(5,3)). If only one number is given, this number is applied to both phases. Default is limit = 5.
startpoints: Alternative to the limit-parameter startpoints exactly defines the possible start points of phase B (e.g., startpoints = 4:9 restricts the phase B start points to measurements 4 to 9. startpoints overruns the limit-parameter.
exclude.equal: If set to exclude.equal = FALSE, which is the default, random distribution values equal to the observed distribution are counted as null-hypothesis conform. That is, they decrease the probability of rejecting the null-hypothesis (increase the p-value). exclude.equal should be set to TRUE if you analyse one single-case design (not a multiple baseline data set) to reach a sufficient power. But be aware, that it increases the chance of an alpha-error.
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).
graph: If graph = TRUE, a histogram of the resulting distribution is plotted. It is FALSE by default. Note: use the more versatile plot_rand() function instead.
output: (deprecated and not implemented)
seed: A seed number for the random generator.

Author

Juergen Wilbert

Details

Predefinded statisic

Use the statistic argument to choose a predefnied statistic. The following comparisons are possible:

Mean A-B: Uses the difference between the mean of phase A and the mean of phase B. This is appropriate if a decrease of scores was expected for phase B.
Mean B-A: Uses the difference between the mean of phase B and the mean of phase A. This is appropriate if an increase of scores was expected for phase B.
Mean |A-B|: Uses the absolute value of the difference between the means of phases A and B.
Median A-B: The same as Mean A-B, but based on the median.
Median B-A: The same as Mean B-A, but based on the median.
SMD hedges / SMD glass: Standardizes mean difference of B-A as Hedges's g or Glass' delta.
NAP: Non-overlap of all pairs.
W-test: Wilcoxon-test statistic W.
T-test: T-test statistic t.

Create own statistic function

Use the statistic_function argument to proved your own function in a list. This list must have an element named statistic with a function that takes two arguments a and b and returns a single numeric value. E.g. list(statistic = function(a, b) mean(a) - mean(b). A second element of the list is named aggregate which takes a function with one numeric argument that returns a numeric argument. This function is used to aggregate the values of a multiple case design. If you do not provide this element, it uses the default function(x) sum(x)/length(x). The third optional argument is name which provides a name for your user function.

References

Bulte, I., & Onghena, P. (2009). Randomization tests for multiple-baseline designs: An extension of the SCRT-R package. Behavior Research Methods, 41, 477-485.

Bulte, I., & Onghena, P. (2012). SCRT: Single-Case Randomization Tests. Available from: https://CRAN.R-project.org/package=SCRT

Examples

Run this code


## Compute a randomization test on the first case of the byHeart2011 data and include a graph
rand_test(byHeart2011[1], statistic = "Median B-A", graph = TRUE, seed = 123)

## Compute a randomization test on the Grosche2011 data using complete permutation
rand_test(Grosche2011, statistic = "Median B-A", complete = TRUE, limit = 4, seed = 123)

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