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abwm

This package includes one function abwm.test(), which performs the Ansari-Bradley test (Ansari & Bradley, 1960) with missing data proposed in (Zeng et al., 2025). This method is a theoretical extension of the Ansari-Bradley test, with controlled Type I error regardless of values of missing data.

Bounds of the Ansari-Bradley 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., 2025) is then returned as the maximum possible p-value of the Ansari-Bradley test.

Installation

You can install the development version of abwm from GitHub with:

# install.packages("devtools")
devtools::install_github("Yijin-Zeng/Ansari-Bradley-Test-with-Missing-data")

Example

This is a basic example which shows you how to perform the test with missing data:

library(abwm)

#### Two-sided test
X <- c(6.2, 3.5, NA, 7.6, 9.2)
Y <- c(NA, 1.3, -0.5, -1.7)
abwm.test(X, Y, alternative = 'two.sided')
#> $p.value
#> [1] 1
#> 
#> $bounds.statistic
#> [1]  7 14
#> 
#> $bounds.pvalue
#> [1] 0.04795881 1.00000000
#> 
#> $alternative
#> [1] "two.sided"
#> 
#> $data.name
#> [1] "X and Y"

## One-sided test
X <- c(6.2, 3.5, NA, 7.6, 9.2)
Y <- c(NA, 1.3, -0.5, -1.7)
abwm.test(X, Y, alternative = 'less')
#> $p.value
#> [1] 0.9176989
#> 
#> $bounds.statistic
#> [1]  7 14
#> 
#> $bounds.pvalue
#> [1] 0.02397941 0.91769888
#> 
#> $alternative
#> [1] "less"
#> 
#> $data.name
#> [1] "X and Y"

See Also

The R function stats::ansari.test() performs the Ansari-Bradley test when data are completely observed.

References

Y. Zeng, N. M. Adams, D. A. Bodenham. Scale two-sample testing with arbitrarily missing data. arXiv preprint arXiv:2509.20332. 2025.

A. R. Ansari, R. A. Bradley. Rank-Sum Tests for Dispersions. The Annals of Mathematical Statistics, pages 1174–1189, 1960.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.