| mod.symm.test {TestsSymmetry} | R Documentation |
Wilcoxon and Sign tests for symmetry about an unknown center
Description
R built-in function 'wilcox.test()' is designed to perform both the one- and two-sample Wilcoxon test when the center of symmetry is specified. The procedure 'mod.symm.test()' extends the capabilities of 'wilcox.test()' for situations where the center of symmetry is unknown. Such cases can be found in, e.g., regression residuals evaluations, as well as in the book 'Nonparametric statistical methods using R' by Kloke and McKean, and in the scholarly work of Gastwirth.
Usage
mod.symm.test(
x,
y = NULL,
alternative = c("two.sided", "left.skewed", "right.skewed"),
method = "wilcox"
)
Arguments
x |
numeric vector of data values. Non-finite (e.g., infinite or missing) values will be omitted. |
y |
an optional numeric vector of data values: as with x non-finite values will be omitted. |
alternative |
a character string specifying the alternative hypothesis, must be one of "two sided" (default), "right.skewed", or "left.skewed". You can specify just the initial letter. "right.skewed": test whether positively skewed, "left.skewed" : test whether negatively skewed. |
method |
a character string specifying which symmetry test to be used, "wilcox" refers to Wilcoxon signed-rank test, and "sign" is sign test. |
Details
When "wilcox", the default method, is used, the test statistic 'W' has the form of the Wilcoxon test statistic with the unknown center of symmetry replaced by its sample mean estimator. For more details, see Vexler et al. (2023)
When method="sign" is used, the test statistic 'S' is the total number of the observations that smaller than sample mean. For more details, see Gastwitrh (1971).
Value
A list of class "htest" containing the following components:
statistic - the value of the test statistic.
var - the asymptotic variance.
alternative - a character string describing the alternative hypothesis.
p.value - the p-value for the test.
method - the type of test applied.
Author(s)
Jiaojiao Zhou, Xinyu Gao, Albert Vexler
References
Vexler, A., Gao, X., & Zhou, J. (2023). How to implement signed-rank 'wilcox.test()' type procedures when a center of symmetry is unknown. Computational Statistics & Data Analysis, 107746.
Gastwirth, J. L. (1971). On the Sign Test for Symmetry. Journal of the American Statistical Association, 66(336), 821-823.
Examples
# A study measures the plasma silicon levels before and after silicone implants surgery in 30
# women to evaluate the effect of the surgery. Informally speaking, we can be interested
# in that there is an unknown constant shift such that the the plasma silicon level of
# post-surgery can be explained completely based on that of pre-surgery. This can be stated
# as the null hypothesis `H_0` The difference of plasma silicon level between post-surgery and
# pre-surgery has a symmetric distribution around a shift that is unknown.
data("plasma.silicon")
post <- plasma.silicon$postoperative
pre <- plasma.silicon$preoperative
# post <- c(0.21,0.24,0.1,0.12,0.28,0.25,0.22,0.21,0.22,0.23,0.22,0.24,0.45,0.38,
# 0.23,0.22,0.18,0.15,0.04,0.14,0.24,0.2,0.24,0.18,0.19,0.15,0.26,0.3,0.22,0.24)
# pre <- c(0.15,0.13,0.39,0.2,0.39,0.42,0.24,0.18,0.26,0.12,0.1,0.11,0.19, 0.15,0.27,
# 0.28,0.11,0.11,0.18,0.18,0.24,0.48,0.27,0.22,0.18,0.19,0.32,0.31,0.19,0.21)
mod.symm.test(x=post, y=pre, alternative ="two.sided", method = "wilcox")
# Result:
# Modified Wilcoxon signed-rank test
# data: post and pre
# W = 238, p-value = 0.767
# alternative hypothesis: two.sided
# Interpretation:
# Test statistic `W` is the number of walsh average higher than sample mean, see more details
# in paper authored by Vexler, etc.
# p-value is 0.767, which implies there is no clue to reject the null hypothesis that
# the distribution of the difference of plasma silicon levels before and after
# silicone implants surgery is symmetric.