Package 'wmwm'

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. If observed samples contain tied samples, ties defaults to TRUE. If observed samples do not contain tied samples, ties defaults to FALSE.
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)

---