# Vera Stat Ordinal Testing

> 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.

- Skill: `aibot88/vera-stat-ordinal-testing` (Agent Skill, multi-file: 2 files)
- Install (CLI): `npx skillmds@latest add aibot88/vera-stat-ordinal-testing`
- Raw SKILL.md: https://api.skillmd.com/api/skills/aibot88/vera-stat-ordinal-testing/raw
- Safety review: pending (external: skill-scanner PASS, skillspector PASS)
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: aibot88 (https://skillmd.com/u/aibot88)
- Updated: 2026-09-09
- Page: https://skillmd.com/skills/aibot88/vera-stat-ordinal-testing

---


# 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

1. p-values: "< .001" not "0.000"; exact to 3 decimals otherwise
2. Effect sizes: rank-biserial r (Mann-Whitney), Cliff's delta (2 groups), epsilon-squared (Kruskal-Wallis)
3. Always report medians and IQRs for ordinal data, not means/SDs
4. Mann-Whitney U: U = X, p = .XXX, rank-biserial r = .XXX
5. Kruskal-Wallis: H(df) = X.XX, p = .XXX
6. Proportions per level: report as percentages with 1 decimal
7. 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)
```