TestsSymmetry (version 1.0.0)

mod.symm.test: 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"
)

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.

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.

Author

Jiaojiao Zhou, Xinyu Gao, Albert Vexler

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).

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

# \donttest{
  # 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. 
# }