Vera Data Continuous Reviewing

Continuous 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 is a single continuous variable and the first need is a transparent baseline comparison across groups.
• A primary t-test / ANOVA-style analysis is appropriate before regression or nonlinear exploratory work.

Do not use this skill when:

• The design is repeated / paired, multivariate, or time-indexed.
• The outcome is binary, count, survival, ordinal, or SEM-based rather than continuous.

Workflow

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

Decision Tree

1. CHECK DISTRIBUTION
   ├── Normal (Shapiro-Wilk p ≥ .05, |skewness| < 1) → parametric primary
   └── Non-normal → nonparametric primary + recommend QR/trees

2. GROUP COMPARISON
   ├── 2 groups → Welch's t + Cohen's d + Mann-Whitney U
   └── 3+ groups → ANOVA + η² + Tukey HSD + Kruskal-Wallis

Required Inputs

Code Structure

PART 0: Setup & Data Loading
PART 1: Distribution Diagnostics → plot_01_distribution.png
PART 2: Primary Hypothesis Test  → plot_02_boxplot_[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: Cohen's d (t-test), η² (ANOVA) — always alongside p
3. 95% CIs: always for mean differences
4. Degrees of freedom: always with t and F statistics
5. Sample size: final analytic N
6. Decimal places: 2 for M/SD, 3 for p and effect sizes
7. Non-significance: "not statistically significant at α = .05" — never "no effect"
8. Normality check: Shapiro–Wilk W, p on residuals (not Y directly) for t-test and ANOVA; also report skewness and kurtosis. With large samples (N > 200), Shapiro–Wilk is over-sensitive — trivial deviations from normality reach significance. When N > 200, rely primarily on visual inspection (Q–Q plot) and skewness/kurtosis magnitudes; treat Shapiro–Wilk p as a supporting diagnostic, not a gatekeeper.
9. Variance homogeneity: Levene's test (F, p) before choosing Student's t vs Welch's t or pooled ANOVA vs Welch ANOVA. Default to Welch's t (robust to unequal variances) unless Levene p ≥ .05 and sample sizes are balanced.

Hypothesis Tests

When Levene's test indicates heterogeneous variances across 3+ groups, use Welch ANOVA for the omnibus test and Games-Howell for pairwise comparisons — Tukey HSD assumes equal variances and inflates Type I error when variances differ. Report which post-hoc was used and why.

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

Example Dataset

R built-in mtcars: outcome = mpg, 2-group = am, 3+ group = cyl. Python: sm.datasets.get_rdataset("mtcars").data (with offline fallback to bundled examples/mtcars.csv).

Method Status

Minimal Smoke Test

• Smoke-test prompt: "Run vera-data-continuous-reviewing on mtcars, using mpg as the outcome and am 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 (distribution + boxplot)
└── recommendations → text block (additional analyses available)

Next step: Invoke vera-data-continuous-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.