rank.two.samples {rankFD}

A function for analyzing two-sample problems

Description

The rank.two.samples() function calculates purely nonparametric rank-based methods for the analysis of two independent samples. Specifically, it implements the Brunner-Munzel test and its generalizations for the Nonparametric Behrens-Fisher Problem, that is, testing whether the relative effect p=P(X<Y)+1/2*P(X=Y) of the two independent samples X and Y is equal to 1/2. Range preserving confidence intervals (and corresponding test statistics) are available using Logit or Probit transformations. The function also implements studentized permutation tests and permutation based confidence intervals for p using any of the method above (see the details below). Furthermore, the Wilcoxon-Mann-Whitney test (exact and asymptotic) can be used to test the equality of the two distribution functions of the two samples. The user can specify whether confidence intervals for shift effects shall be computed. The rank.two.samples() function implements one-sided and two-sided tests and confidence intervals. You can plot the confidence intervals (for the relative effects) with the plot() function.

Usage

rank.two.samples(
  formula,
  data,
  conf.level = 0.95,
  alternative = c("two.sided", "less", "greater"),
  rounds = 4,
  method = c("t.app", "logit", "probit", "normal"),
  permu = TRUE,
  info = TRUE,
  wilcoxon = c("asymptotic", "exact"),
  shift.int = TRUE,
  nperm = 10000
)

Arguments

formula

A model formula object. The left hand side contains the response variable and the right hand side contains the factor variables of interest.

data

A data.frame, list or environment containing the variables in formula. The default option is NULL.

conf.level

A number specifying the confidence level; the default is 0.95.

alternative

A character string specifying the alternative hypothesis. One of "two.sided", "less", "greater". You can specify just the initial letter.

rounds

Value specifying the number of digits the results are rounded to. Default is 4 decimals.

method

specifying the method used for calculation of the confidence intervals. One of "t.app", "logit", "probit" or "normal".

permu

A logical variable indicating whether you want to compute a studentized permutation test.

info

A logical variable. Here, info = FALSE suppresses the output of additional information concerning e.g. the interpretation of the test results.

wilcoxon

asymptotic or exact calculation of Wilcoxon test.

shift.int

Logical, indicating whether or not shift effects should be considered.

nperm

Number of permutations used, default is 10000.

Details

The rank.two.samples() function calculates both transformed (logit or probit) and untransformed statistics (normal or t.app) for testing the null hypothesis p=1/2. If a studentized permutation test is performed, then the permutation distribution of the respective statistics are computed, see Pauly et al.(2016) for details. In any case, the function reports the point estimator and its estimated standard error, value of the test statistic, confidence interval and p-value. In case of separated samples, point estimator and standard error would be 0 and thus, test statistics would not be defined. In such a case, point estimator and its standard error are replaced by the numbers one would obtain if samples overlapped in a single point. A plot of the confidence interval can be obtained with the plot function.

Author(s)

Frank Konietschke Brunner, E., Bathke, A. C., Konietschke, F. (2018). Rank and Pseudo-Rank Procedures for Independent Observations in Factorial Designs. Springer International Publishing.

References

Brunner, E. and Munzel, U. (2000). The nonparametric Behrens-Fisher problem: Asymptotic theory and a small-sample approximation. Biometrical Journal 1, 17 - 21.

Kaufmann, J., Werner, C., and Brunner, E. (2005). Nonparametric methods for analysing the accuracy of diagnostic tests with multiple readers. Statistical Methods in Medical Research 14, 129 - 146

Pauly, M., Asendorf, T., Konietschke, F. (2016). Permutation-based inference for the AUC: a unified approach for continuous and discontinuous data.##' Biometrical Journal, 58(6), 1319 – 1337.

See Also

rankFD

Examples

data(Muco)  
Muco2 <- subset(Muco, Disease != "OAD")
Muco2$Disease <- droplevels(Muco2$Disease)

twosample <- rank.two.samples(HalfTime ~ Disease, data = Muco2, 
wilcoxon = "exact", permu = TRUE, shift.int = TRUE, nperm = 1000)
twosample <- rank.two.samples(HalfTime ~ Disease, data = Muco2, 
   alternative = "greater", method = "probit", wilcoxon = "exact", permu = TRUE,
   shift.int = FALSE, nperm = 1000)
plot(twosample)