| wmwm.test {wmwm} | R Documentation |
Wilcoxon-Mann-Whitney Test in the Presence of Arbitrarily Missing Data
Description
Performs the two-sample Wilcoxon-Mann-Whitney test in the presence of missing data, which controls the Type I error regardless of the values of missing data.
Usage
wmwm.test(X, Y, alternative = c("two.sided", "less", "greater"),
ties = NULL, lower.boundary = -Inf, upper.boundary = Inf,
exact = NULL, correct = TRUE)
Arguments
X, Y |
numeric vectors of data values with potential missing data. Inf and -Inf values will be omitted. |
alternative |
a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter. |
ties |
a logical indicating whether samples could be tied.
|
lower.boundary |
(when ties is TRUE) a number specifying the lower bound of the data set, must be smaller or equal than the minimum of all observed data. |
upper.boundary |
(when ties is TRUE) a number specifying the upper bound of the data set, must be larger or equal than the maximum of all observed data. |
exact |
a logical indicating whether the bounds should be of an exact p-value. |
correct |
a logical indicating whether the bounds should be of a p-value applying continuity correction in the normal approximation. |
Details
wmwm.test() performs the two-sample hypothesis test method
proposed in (Zeng et al., 2024) for univariate data
when not all data are observed.
Bounds of the Wilcoxon-Mann-Whitney test statistic and its p-value
will be computed in the presence of missing data.
The p-value of the test method proposed in (Zeng et al., 2024) is then
returned as the maximum possible p-value of the Wilcoxon-Mann-Whitney test.
By default (if exact is not specified), this function returns
bounds of an exact p-value if the length of X and Y are both
smaller than 50, and there are no tied observations.
Otherwise, bounds of a p-value calculated using normal approximation
with continuity correction will be returned.
Value
p.value |
the p-value for the test. |
bounds.statistic |
bounds of the value of the Wilcoxon-Mann-Whitney test statistic. |
bounds.pvalue |
bounds of the p-value of the Wilcoxon-Mann-Whitney test. |
alternative |
a character string describing the alternative hypothesis. |
ties.method |
a character string describing whether samples are considered tied. |
description.bounds |
a character string describing the bounds of the p-value. |
data.name |
a character string giving the names of the data. |
References
Zeng Y, Adams NM, Bodenham DA. On two-sample testing for data with arbitrarily missing values. arXiv preprint arXiv:2403.15327. 2024 Mar 22.
Mann, Henry B., and Donald R. Whitney. "On a test of whether one of two random variables is stochastically larger than the other." The Annals of Mathematical Statistics (1947): 50-60.
Lehmann, Erich Leo, and Howard J. D'Abrera. Nonparametrics: statistical methods based on ranks. Holden-day, 1975.
See Also
stats::wilcox.test() when data are fully observed.
Examples
#### Assume all samples are distinct.
X <- c(6.2, 3.5, NA, 7.6, 9.2)
Y <- c(0.2, 1.3, -0.5, -1.7)
## By default, when the sample sizes of both X and Y are smaller than 50,
## exact distribution will be used.
wmwm.test(X, Y, ties = FALSE, alternative = 'two.sided')
## using normality approximation with continuity correction:
wmwm.test(X, Y, ties = FALSE, alternative = 'two.sided', exact = FALSE, correct = TRUE)
#### Assume samples can be tied.
X <- c(6, 9, NA, 7, 9)
Y <- c(0, 1, 0, -1)
## When the samples can be tied, normality approximation will be used.
## By default, lower.boundary = -Inf, upper.boundary = Inf.
wmwm.test(X, Y, ties = TRUE, alternative = 'two.sided')
## specifying lower.boundary and upper.boundary:
wmwm.test(X, Y, ties = TRUE, alternative = 'two.sided', lower.boundary = -1, upper.boundary = 9)