Computational Provenance & Reproducibility Record

RAISINS · Mann-Whitney U and Wilcoxon Signed-Rank Test Module

This Computational Provenance Record documents the statistical computing environment, software dependencies, computational provenance, and bibliographic references associated with the RAISINS Mann-Whitney U and Wilcoxon Signed-Rank Test module. It is intended to support computational reproducibility and software transparency. Detailed statistical methodology, mathematical derivations, and user guidance are provided separately in the official module documentation.

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1 Module Metadata

Parameter	Specification
Module	Mann-Whitney U and Wilcoxon Signed-Rank Test
Module Version	`2.0.0`
DOI	10.5281/zenodo.22023869
Document Type	Computational workflow
Statistical Engine	R
R Version	`4.5.2`
Reproducibility	Execution Environment: Posit Connect · GCR · renv-locked

2 Statistical Dependency Manifest

Package	Version	Repository	Core Statistical Functions
stats	`4.5.2`	Base R	`wilcox.test()`, `median()`, `IQR()`, `sd()`
ggplot2	`4.0.3`	CRAN	plot construction for all six figure types
ggbeeswarm	`0.7.3`	CRAN	`geom_beeswarm()`
gghalves	`0.1.4`	CRAN	half-violin geoms (raincloud)
ggdist	`3.3.3`	CRAN	`stat_halfeye()` (distribution plot)
patchwork	`1.3.2`	CRAN	side-by-side Q-Q panel assembly
ggpubr	`0.6.3`	CRAN	publication-ready plot theming

3 Statistical Function Registry

Analytical Role	Primary Function(s)
Mann-Whitney U test (W statistic, p-value) - two independent groups	`stats::wilcox.test(paired = FALSE)`
Wilcoxon Signed-Rank test (V statistic, p-value) - paired observations	`stats::wilcox.test(paired = TRUE)`
Hodges-Lehmann location-shift estimate and its confidence interval	`stats::wilcox.test(conf.int = TRUE)`
Descriptive statistics (mean, median, IQR) per group per response variable	`base::mean()`, `stats::median()`, `stats::IQR()`
Q-Q assessment of each group’s distributional shape	`ggplot2::stat_qq()`, `ggplot2::stat_qq_line()`

4 Default Methods & Parameters

Analysis	Step / Parameter	Default Method / Value
Rank-based two-sample test	Test type	User-selectable via a "Select Test type" control. Mann-Whitney U Test (default) for two independent groups, or Wilcoxon Signed-Rank Test when the same experimental units are measured twice. Both are computed by `stats::wilcox.test()`, which is called with `paired = FALSE` or `paired = TRUE` accordingly. Applied independently, per selected response variable
	Test statistic	`W` (rank-sum) for the unpaired test; `V` (signed-rank sum) for the paired test. The results table labels the column accordingly and records the test actually used in a "Test Used" column
	Exact vs normal approximation	`exact = FALSE` - the normal approximation is used at all sample sizes, so that a confidence interval is always returned and results remain well defined in the presence of tied ranks
	Grouping requirement	The selected Group column must contain exactly two levels; the module stops with a message if it does not
Hypotheses	Alternative hypothesis	User-selectable: "Medians are not equal" (`two.sided`, default), "Median 1 is less than Median 2" (`less`), or "Median 1 is greater than Median 2" (`greater`)
Hypotheses	Significance level	User-selectable via a "Level of significance (α)" control; α = 0.05 by default
Confidence Interval	Construction	`conf.int = TRUE` with `conf.level = 1 - α`, giving the Hodges-Lehmann estimate of the location shift between the two groups together with its distribution-free confidence interval. Reported as a "(lower, upper)" pair at the chosen α
Significance stars	Thresholds	p < 0.01 → `*`; p < 0.05 → ``; p < 0.10 → `*`; otherwise `NS` (not significant)
Descriptive Statistics	Per group, per response variable	Mean, median and interquartile range, computed on the raw (unranked) values within each group via `base::mean()`, `stats::median()` and `stats::IQR()`
Descriptive Statistics	Rounding	All reported values are formatted to the user-selected number of decimal places (default 2) via `formatC()`
Plots	Box & Violin, Raincloud, Beeswarm, Stripchart, Distribution (Half-Eye), Q-Q	Six plot types chosen from an icon panel, all built from the same two-group data and the same statistic and p-value as the results table, so any value annotated on a plot is traceable to the same underlying computation as the table

5 R Code for Key Analytical Steps

The code blocks below demonstrate the exact computation behind each reported result. They use datasets that ship with base R (the datasets package), so anyone can run them as they stand, with no file to download and nothing to install:

Dataset	Design	Used to demonstrate
`ToothGrowth`	60 guinea pigs, tooth length by supplement type (`OJ` vs `VC`), 30 per group - independent	Mann-Whitney U test
`sleep`	10 subjects, extra hours of sleep under two drugs, each subject measured twice - paired	Wilcoxon Signed-Rank test

The values shown in the comments were produced under R 4.5.2 with alpha = 0.05, and are what you should obtain if the computation is reproduced correctly.

5.1 Mann-Whitney U test (two independent groups)

# ToothGrowth: tooth length under two supplements, 30 guinea pigs each
x <- ToothGrowth$len[ToothGrowth$supp == "OJ"]
y <- ToothGrowth$len[ToothGrowth$supp == "VC"]

alpha <- 0.05

test <- wilcox.test(x, y,
                    alternative = "two.sided",   # user-selectable
                    conf.int    = TRUE,
                    conf.level  = 1 - alpha,
                    paired      = FALSE,         # Mann-Whitney U
                    exact       = FALSE)

test$statistic   # W value      -> 575.5
test$p.value     #              -> 0.06449
test$conf.int    # Hodges-Lehmann CI for the location shift -> (-0.100, 8.500)

5.2 Wilcoxon Signed-Rank test (paired observations)

# sleep: the SAME 10 subjects measured under two drugs, so the rows pair up
a <- sleep$extra[sleep$group == 1]
b <- sleep$extra[sleep$group == 2]

# the paired test requires equal group sizes; pairs are matched by position
length(a) == length(b)   # -> TRUE (10 pairs)

# identical call, with paired = TRUE; the statistic is then reported as V
test_paired <- wilcox.test(a, b,
                           alternative = "two.sided",
                           conf.int    = TRUE,
                           conf.level  = 1 - alpha,
                           paired      = TRUE,   # Wilcoxon Signed-Rank
                           exact       = FALSE)

test_paired$statistic   # V value -> 0
test_paired$p.value     #         -> 0.009091
test_paired$conf.int    #         -> (-2.950, -1.050)

5.3 Descriptive statistics reported alongside the test

data.frame(
  Group  = c("OJ", "VC"),
  Mean   = c(mean(x),   mean(y)),     # -> 20.663, 16.963
  Median = c(median(x), median(y)),   # -> 22.700, 16.500
  IQR    = c(IQR(x),    IQR(y))       # -> 10.200, 11.900
)

5.4 Significance stars

pval <- test$p.value

star <- ifelse(pval < 0.01, "***",
        ifelse(pval < 0.05, "**",
        ifelse(pval < 0.10, "*", "NS")))

star   # ToothGrowth -> "*"   (0.06449 falls between 0.05 and 0.10)

Explore the entire Mann-Whitney U and Wilcoxon Signed-Rank Test module in preview mode using our demo datasets. To submit suggestions or report a workflow issue, please use the discussion section below, or visit the official RAISINS website.

6 RAISINS Native Statistical Framework

RAISINS uses R for all its statistical computations. Every package used to generate major results is listed and demonstrated with examples, so results can be reproduced independently. These results are then organized and formatted on the RAISINS website along with visualisation to make them easier to use and interpret. RAISINS also has its own custom-built statistical tools for managing workflows, validating results, and generating reports. Details of these are not fully covered here, they’re shared with outside researchers only on request, and are subject to licensing terms.

7 Package References

R Core Team. (2025). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/

Wickham, H. (2016). ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York. https://ggplot2.tidyverse.org

Clarke, E., & Sherrill-Mix, S. (2023). ggbeeswarm: Categorical Scatter (Violin Point) Plots (R package version 0.7.3). https://CRAN.R-project.org/package=ggbeeswarm

Tiedemann, F. (2022). gghalves: Compose Half-Half Plots Using Your Favourite Geoms (R package version 0.1.4). https://CRAN.R-project.org/package=gghalves

Kay, M. (2024). ggdist: Visualizations of Distributions and Uncertainty (R package version 3.3.3). https://CRAN.R-project.org/package=ggdist

Pedersen, T. L. (2024). patchwork: The Composer of Plots (R package version 1.3.2). https://CRAN.R-project.org/package=patchwork

Wilcoxon, F. (1945). Individual Comparisons by Ranking Methods. Biometrics Bulletin, 1(6), 80-83. https://doi.org/10.2307/3001968

Mann, H. B., & Whitney, D. R. (1947). On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other. The Annals of Mathematical Statistics, 18(1), 50-60. https://doi.org/10.1214/aoms/1177730491

Hodges, J. L., & Lehmann, E. L. (1963). Estimates of Location Based on Rank Tests. The Annals of Mathematical Statistics, 34(2), 598-611. https://doi.org/10.1214/aoms/1177704172

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