| name | vera-stat-ordinal-testing |
| description | Runs distribution diagnostics and primary hypothesis tests for ordinal outcome variables. Produces frequency tables, cumulative proportions, ordinal bar chart, and one fully interpreted nonparametric group comparison (Mann-Whitney U for 2 groups or Kruskal-Wallis for 3+ groups) with effect sizes (rank-biserial r or Cliff's delta) and Jonckheere-Terpstra trend test. Ends with a recommendation block listing additional analyses available. Outputs .R and .py scripts with 2 publication-quality plots. Triggered when user has an ordinal outcome and says "ordinal outcome," "Likert scale," "ordered categories," "rating scale," "severity levels," "none/mild/moderate/ severe," "low/medium/high," "improvement levels," "ranked outcome," "ordered factor," or names an ordinal variable like satisfaction, severity, agreement, stage, grade, rating. Does not handle continuous, binary, count, survival, repeated measures, or SEM outcomes. |
| user-invocable | true |
| allowed-tools | Read, Bash, Write, Edit |
Ordinal Outcome — Distribution Diagnostics & Hypothesis Testing
Open-source skill.
Workflow
Read each step file in workflow/ before executing that step.
| Step | File | Executor | Output |
|---|
| Collect | workflow/01-collect-inputs.md | Main Agent | Structured input summary |
| Diagnose | workflow/02-check-distribution.md | Main Agent | PART 1 code block |
| Test | workflow/03-run-primary-test.md | Main Agent | PART 2-3 code blocks |
Decision Tree
1. CHECK DISTRIBUTION
├── Balanced levels (no cell < 5) → standard nonparametric tests
└── Sparse levels (any cell < 5) → warn, consider collapsing levels
2. GROUP COMPARISON
├── 2 groups → Mann-Whitney U + rank-biserial r
└── 3+ groups → Kruskal-Wallis + pairwise Dunn's + Cliff's delta
3. TREND TEST (if predictor is ordered)
└── Jonckheere-Terpstra trend test
Required Inputs
| Role | What to collect |
|---|
| Outcome (Y) | Variable name, ordered levels (confirm ordering with user) |
| Group variable | What defines groups, how many levels |
| Predictors | For recommendation block (not executed) |
| Covariates | For recommendation block (not executed) |
Code Structure
PART 0: Setup & Data Loading
PART 1: Distribution Diagnostics → plot_01_ordinal_distribution.png
PART 2: Primary Hypothesis Test → plot_02_stacked_bar_[var].png
PART 3: Recommendation Block → text listing additional analyses available
Reporting Standards
- p-values: "< .001" not "0.000"; exact to 3 decimals otherwise
- Effect sizes: rank-biserial r (Mann-Whitney), Cliff's delta (2 groups), epsilon-squared (Kruskal-Wallis)
- Always report medians and IQRs for ordinal data, not means/SDs
- Mann-Whitney U: U = X, p = .XXX, rank-biserial r = .XXX
- Kruskal-Wallis: H(df) = X.XX, p = .XXX
- Proportions per level: report as percentages with 1 decimal
- Non-significance: "not statistically significant at α = .05" — never "no effect"
Hypothesis Tests
| Scenario | Test | Effect Size |
|---|
| 2 independent groups | Mann-Whitney U | Rank-biserial r |
| 3+ independent groups | Kruskal-Wallis + Dunn's | Cliff's delta (pairwise) |
| Ordered groups (trend) | Jonckheere-Terpstra | — |
Paired/repeated designs → vera-stat-repeated-testing.
Example Dataset
R: vcd::Arthritis — Outcome = Improvement (None/Some/Marked), Predictors: Treatment, Sex, Age.
Python: reconstruct via statsmodels.datasets or manual construction from R dataset.
Cross-Skill Interface
Output:
├── code_r → .R script
├── code_python → .py script
├── figures/ → 2 PNGs (ordinal distribution + stacked bar)
└── recommendations → text block (additional analyses available)
