Vera Data Ordinal Reviewing

Ordinal Outcome — Distribution Diagnostics & Hypothesis Testing

Table of Contents

• Scope Boundary
• Workflow
• Decision Tree
• Required Inputs
• Code Structure
• Reporting Standards
• Hypothesis Tests
• Example Dataset
• Method Status
• Minimal Smoke Test
• Cross-Skill Interface

Open-source skill.

Scope Boundary

Use this skill when:

• The outcome has a meaningful order and the first need is a nonparametric baseline plus ordinal distribution reporting.
• The goal is to establish an ordered-response checkpoint before ordinal regression or richer modeling.

Do not use this skill when:

• The classes are unordered or collapse naturally to a binary endpoint.
• The design is paired / repeated, survival, or latent-variable rather than cross-sectional ordinal data.

Workflow

Read each step file in workflow/ before executing that step.

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

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

Paired/repeated designs → vera-data-repeated-reviewing.

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.

Method Status

Minimal Smoke Test

• Smoke-test prompt: "Run vera-data-ordinal-reviewing on the Arthritis example, treating Improvement as the ordinal outcome and Treatment as the primary grouping variable. Produce the standard baseline artifacts."

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)

Note: proportional-odds logistic regression and Brant/parallel-regression test for PO assumption are delivered by vera-data-ordinal-generating.

Next step: Invoke vera-data-ordinal-generating from this skillset to run the full pipeline (additional tests, subgroup analysis, modeling, manuscript generation). See ../../CROSS-SKILL-INTERFACE.md for the shared handoff contract.