Kruskal–Wallis alpha diversity by study group and fibre restriction

alpha-diversity
pre-specified
Non-parametric comparison of Shannon, richness, and other alpha metrics across study group and fibre-restriction levels.
Author

IBD Capstone team

Published

May 19, 2026

1 Research question

  1. Do alpha diversity metrics differ across study group?
  2. Do they differ across fibre restriction level (None, Low, Mid, High)?

Null (each metric): Distributions are equal across groups.

2 Data

  • Response: Value (alpha diversity metric).
  • Predictors: Study_group_new, Fiber_restriction.
  • Unit: Sample (one row per sample × metric in long format).
  • Input: data/intermediate/alpha_long.rds (from make wrangle).
  • Pre-specified script: src/mycobiome/03b_diversity_stats.R.

3 Methods

Item Choice
Test Kruskal–Wallis (rstatix::kruskal_test)
Stratification One test per Diversity_metric (group_by(Diversity_metric))
Formulae Value ~ Study_group_new; Value ~ Fiber_restriction
Post-hoc Not run in pipeline (Dunn + BH commented in stool_eda.Rmd)
Significance α = 0.05 (uncorrected across metrics)
Show code 
kw_diversity_group <- alpha_long |>
  group_by(Diversity_metric) |>
  kruskal_test(Value ~ Study_group_new)

kw_diversity_fibre <- alpha_long |>
  group_by(Diversity_metric) |>
  kruskal_test(Value ~ Fiber_restriction)

4 Assumptions and diagnostics

  • Kruskal–Wallis compares distributions (rank-based); does not assume normality.
  • Independence: assumed for samples; repeated measures per participant not modelled here.
  • Multiple metrics: several diversity indices tested; consider FDR if reporting many metrics together.

5 Results

5.1 By study group

Diversity_metric .y. n statistic df p method
Chao1 Value 16 1.4941 2 0.474 Kruskal-Wallis
Shannon Value 16 3.5103 2 0.173 Kruskal-Wallis
Simpson Value 16 1.4412 2 0.486 Kruskal-Wallis

5.2 By fibre restriction

Diversity_metric .y. n statistic df p method
Chao1 Value 16 2.1346 3 0.545 Kruskal-Wallis
Shannon Value 16 1.4463 3 0.695 Kruskal-Wallis
Simpson Value 16 1.1926 3 0.755 Kruskal-Wallis

Significant by study group (p < 0.05): none

Significant by fibre restriction (p < 0.05): none

6 Figure

Boxplots of alpha diversity by study group (one panel per metric).

Show code 
p_group <- ggplot(
  alpha_long,
  aes(x = Study_group_new, y = Value, fill = Study_group_new)
) +
  geom_boxplot(outlier.shape = NA, alpha = 0.85) +
  geom_jitter(width = 0.15, alpha = 0.5, size = 1) +
  facet_wrap(~ Diversity_metric, scales = "free_y") +
  labs(
    x = NULL,
    y = "Alpha diversity value",
    fill = "Study group"
  ) +
  theme_minimal() +
  theme(
    legend.position = "none",
    axis.text.x = element_text(angle = 25, hjust = 1)
  )
p_group
Figure 1: Alpha diversity by study group. Kruskal–Wallis p-values are in the results tables above.
Show code 
p_fibre <- ggplot(
  alpha_long,
  aes(x = Fiber_restriction, y = Value, fill = Fiber_restriction)
) +
  geom_boxplot(outlier.shape = NA, alpha = 0.85) +
  geom_jitter(width = 0.15, alpha = 0.5, size = 1) +
  facet_wrap(~ Diversity_metric, scales = "free_y") +
  labs(
    x = NULL,
    y = "Alpha diversity value",
    fill = "Fibre Restriction",
    title = "Alpha diversity by fibre restricted diets"
  ) +
  theme_minimal() +
  theme(
    legend.position = "none",
    axis.text.x = element_text(angle = 25, hjust = 1)
  )
p_fibre
Figure 2: Alpha diversity by fibre restrictive diet. Kruskal–Wallis p-values are in the results tables above.

7 Interpretation

Significant Kruskal–Wallis results indicate at least one group differs in distribution for that metric; they do not identify which pairs differ. Use Dunn tests (with multiplicity adjustment) in a follow-up post if needed.

8 Reproducibility

  • Notebook: notebooks/stool_eda.Rmd (§ Inference)
  • Makefile target: make diversity-stats