Computational Provenance & Reproducibility Record

RAISINS · Kruskal-Wallis Test Module

This Computational Provenance Record documents the statistical computing environment, software dependencies, computational provenance, and bibliographic references associated with the RAISINS Kruskal-Wallis 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	Kruskal-Wallis Test
Module Version	`2.0.0`
DOI	10.5281/zenodo.21988280
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
agricolae	`1.3-7`	CRAN	`kruskal()`
FSA	`0.10.1`	CRAN	`dunnTest()`
multcompView	`0.1-12`	CRAN	`multcompLetters()`
moments	`0.14.1`	CRAN	`kurtosis()`
stats	`4.5.2`	Base R	`kruskal.test()`

3 Statistical Function Registry

Analytical Role	Primary Function(s)
Kruskal-Wallis H-test (chi-squared statistic, p-value, df)	`stats::kruskal.test()`
Mean rank per group (LSD method) & compact letter grouping (LSD method)	`agricolae::kruskal(group = TRUE)`
Mean rank per group only (Dunn’s test method)	`agricolae::kruskal(group = FALSE)`
Post-hoc pairwise comparison (Dunn’s test method)	`FSA::dunnTest()`
Compact letter grouping from pairwise p-values (Dunn’s test method)	`multcompView::multcompLetters()`
Descriptive statistics (mean, SD) per group per response variable	`base::mean()`, `stats::sd()`

4 Default Methods & Parameters

Analysis	Step / Parameter	Default Method / Value
Kruskal-Wallis H-test	Test	Rank-based, distribution-free k-sample test via `stats::kruskal.test()`; tests whether the response variable's distribution differs across the levels of the selected grouping (Treatment) column. Applied independently, per selected response variable
	Significance level	User-selectable via a "Level of significance (α)" control; α = 0.05 (default) or 0.01
	Significance stars	p ≤ 0.01 → `*`; p ≤ 0.05 → ``; otherwise `NS` (not significant)
Multiple Comparison Test	Dunn's test (default)	Pairwise rank-sum comparisons via `FSA::dunnTest()`, using the pooled rank variance across all groups; p-value adjustment method user-selectable (default `none`; also offers `bonferroni`, `sidak`, `holm`, `hs`, `hochberg`, `bh`, `by`). Only performed when the overall Kruskal-Wallis test is significant at the chosen α
Multiple Comparison Test	LSD (least significant rank difference)	Pairwise comparison of mean ranks via `agricolae::kruskal(group = TRUE)`; p-value adjustment method user-selectable (default `none`; also offers `holm`, `hommel`, `hochberg`, `bonferroni`, `BH`, `BY`, `fdr`). Only performed when the overall Kruskal-Wallis test is significant at the chosen α
Compact Letter Grouping	Construction	For Dunn's test, the pairwise adjusted p-values are assembled into a symmetric comparison matrix (rows/columns ordered by descending mean rank, so "a" marks the highest-ranked group) and passed to `multcompView::multcompLetters(threshold = α)`. For LSD, the letters are taken directly from `agricolae::kruskal()`'s own grouping output. Groups sharing at least one letter are not significantly different
Descriptive Statistics	Per group, per response variable	Mean and standard deviation, computed via `base::mean()`/`stats::sd()` on the raw (unranked) values within each group
Descriptive Statistics	Mean rank display	Optional - a "Show mean ranks" toggle appends each group's mean rank (from `agricolae::kruskal()`) alongside the mean ± SD in the results table
Results Table Display	Cell format	Toggleable between "mean ± std" and mean-only display; results rounded to the user-selected number of decimal places (default 2)
Results Table Display	Letter grouping display	Optional - a "Show Letter Grouping" toggle controls whether the compact letter grouping superscripts (and the corresponding footnote) are shown in the on-screen results table and in the downloadable report (HTML/PDF/Word), independently of whether the letters were computed
Plots	Box, Violin, Mean Value, Connected Line, Bar, Summary, Raincloud, Advanced Raincloud, Circular, QQ, Distribution, Pair, Correlation	13 plot types built from the same per-group summary statistics and compact letter groupings as the results table, so a letter or value shown in a plot is always 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, using the module’s own bundled worked example (dataset1.csv: 4 varieties V1-V4, 5 sensory response variables - Appearance, Color, Texture, Taste, Flavour - rated 1-5 by judges).

5.1 Kruskal-Wallis H-test

df <- read.csv("dataset1.csv")
response  <- df$Appearance
treatment <- factor(df$Groups)

kw <- kruskal.test(response ~ treatment)
kw$statistic   # H (chi-squared) statistic
kw$parameter   # degrees of freedom
kw$p.value

alpha <- 0.05  # user-selectable in the app: 0.05 (default) or 0.01

5.2 Post-hoc: Dunn’s Test (default) with Compact Letter Grouping

library(FSA)
library(multcompView)

dunn <- FSA::dunnTest(response ~ treatment, method = "none")  # method is user-selectable
pvals <- dunn$res

groups <- levels(treatment)
comparison_matrix <- matrix(1, nrow = length(groups), ncol = length(groups),
                            dimnames = list(groups, groups))
for (i in seq_len(nrow(pvals))) {
  # matched against the known group names rather than split on " - ", so a group
  # whose own name contains " - " cannot corrupt the matrix
  comp <- strsplit(pvals$Comparison[i], " - ", fixed = TRUE)[[1]]
  if (!(length(comp) == 2 && all(comp %in% groups))) {
    comp <- unlist(lapply(groups, function(a) {
      b <- sub(paste0("^", a, " - "), "", pvals$Comparison[i])
      if (b != pvals$Comparison[i] && b %in% groups) c(a, b)
    }))
  }
  comparison_matrix[comp[1], comp[2]] <- pvals$P.adj[i]
  comparison_matrix[comp[2], comp[1]] <- pvals$P.adj[i]
}

# Reordered by descending mean rank before grouping, so "a" marks the
# highest-ranked group (matching the convention agricolae::kruskal() uses)
letters <- multcompView::multcompLetters(comparison_matrix, threshold = alpha)
letters$Letters

5.3 Post-hoc: LSD (Least Significant Rank Difference)

library(agricolae)

lsd <- agricolae::kruskal(response, treatment,
                          alpha = alpha,
                          p.adj = "none",      # user-selectable
                          group = TRUE,
                          console = FALSE)
lsd$groups       # mean rank + compact letter grouping, one row per group
lsd$statistics   # Chi-squared and its p-value

5.4 Mean Rank (for the optional “Show mean ranks” display)

mean_rank <- agricolae::kruskal(response, treatment,
                                alpha = alpha, p.adj = "none",
                                group = FALSE, console = FALSE)
mean_rank$means  # mean rank per group, used regardless of Dunn's/LSD selection

Explore the entire Kruskal-Wallis 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/

Mendiburu, F. de. (2023). agricolae: Statistical Procedures for Agricultural Research (R package version 1.3-7). https://CRAN.R-project.org/package=agricolae

Ogle, D. H., Doll, J. C., Wheeler, A. P., & Dinno, A. (2025). FSA: Simple Fisheries Stock Assessment Methods (R package version 0.10.1). https://CRAN.R-project.org/package=FSA

Graves, S., Piepho, H.-P., Selzer, L., & Dorai-Raj, S. (2019). multcompView: Visualizations of Paired Comparisons (R package version 0.1-12). https://CRAN.R-project.org/package=multcompView

Kruskal, W. H., & Wallis, W. A. (1952). Use of Ranks in One-Criterion Variance Analysis. Journal of the American Statistical Association, 47(260), 583-621. https://doi.org/10.1080/01621459.1952.10483441

Dunn, O. J. (1964). Multiple Comparisons Using Rank Sums. Technometrics, 6(3), 241-252. https://doi.org/10.1080/00401706.1964.10490181

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