Repeated Measures Outcome — Trajectory 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 same continuous outcome is measured repeatedly on the same units over a small number of waves.
• A paired-test / RM-ANOVA / mixed-ANOVA baseline is needed before mixed-model extensions.

Do not use this skill when:

• The data are a long univariate calendar-time series; use vera-data-timeseries-reviewing.
• The primary need is a richer mixed-model, GEE, or growth-curve analysis from the start.

Workflow

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

Step	Responsibility	Executor	Document	Input	Output
Collect	Collect Inputs	Main Agent	workflow/step01-collect-inputs.md	User input	Structured input summary
Diagnose	Check Distribution	Main Agent	workflow/step02-check-distribution.md	Prior step output	PART 1 code block
Test	Run Primary Test	Main Agent	workflow/step03-run-primary-test.md	Prior step output	PART 2-3 code blocks

Decision Tree

1. DATA FORMAT CHECK
   ├── Wide → reshape to long before proceeding
   └── Long → continue

2. TIME POINTS
   ├── Exactly 2 → paired comparisons path
   └── 3+ → repeated measures ANOVA / mixed ANOVA path

3. GROUP STRUCTURE
   ├── No between-subjects factor → one-way RM-ANOVA (within-subjects only)
   └── Between-subjects factor → mixed ANOVA (time × group)

4. SPHERICITY (if 3+ time points)
   ├── Mauchly p ≥ .05 → uncorrected F
   └── Mauchly p < .05 → Greenhouse-Geisser / Huynh-Feldt correction

Required Inputs

Role	What to collect
Outcome (Y)	Variable name, units, what it measures (continuous)
Time variable	Measurement occasions, how many, equally spaced?
Subject/ID variable	What identifies the same individual across time
Group variable	Between-subjects factor (treatment, condition, etc.)
Covariates	Time-varying? Time-invariant?
Data format	Long (one row per obs) or wide (one row per subject)

Code Structure

PART 0: Setup & Data Loading (+ reshape if wide)
PART 1: Trajectory Diagnostics → plot_01_trajectories.png
PART 2: Primary Hypothesis Test → plot_02_interaction.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 (paired t-test), partial eta-squared (RM-ANOVA/mixed ANOVA)
3. 95% CIs: always for mean differences
4. Degrees of freedom: always with t and F statistics
5. Sphericity: Mauchly's W, p; if violated, GG epsilon and corrected p
6. ICC: always name the specific form, not just "ICC". Use Shrout & Fleiss (1979) notation: ICC(1,1) one-way random, single measure; ICC(2,1) two-way random, single measure, absolute agreement; ICC(3,1) two-way mixed, single measure, consistency; and the corresponding (*,k) forms for averaged measures. For repeated-measures designs with the same rater/instrument across time on the same subjects, default to ICC(3,1) consistency (or ICC(3,k) if reporting the averaged score). For multiple independent raters of the same targets, use ICC(2,1) agreement. Report value + 95% CI + form + interpretation (Koo & Li 2016 bands: < 0.50 poor, 0.50–0.75 moderate, 0.75–0.90 good, > 0.90 excellent).
7. Sample size: final analytic N (subjects) and total observations
8. Decimal places: 2 for M/SD, 3 for p and effect sizes
9. Non-significance: "not statistically significant at alpha = .05" — never "no effect"

Hypothesis Tests

Scenario	Normal	Non-Normal
2 time points (paired)	Paired t-test	Wilcoxon signed-rank
3+ time points, 1 group	One-way RM-ANOVA + sphericity	Friedman test
3+ time points, 2+ groups	Mixed ANOVA (time x group)	—

Cross-sectional group comparisons → vera-data-continuous-reviewing.

Example Dataset

R built-in ChickWeight: outcome = weight, time = Time (0, 2, 4, ..., 21 days), subject = Chick, group = Diet (1, 2, 3, 4). Python: sm.datasets.get_rdataset("ChickWeight").data (with offline fallback to bundled examples/chickweight.csv).

Method Status

Status	Methods
Implemented in this skill	ICC reporting, paired tests, RM-ANOVA / mixed-ANOVA branching, sphericity corrections, trajectory diagnostics
Implemented downstream in vera-data-repeated-generating	Linear mixed models, GEE, growth-curve extensions, subgroup interactions, exploratory trees
Out of scope in this open-source baseline	Binary/count repeated-outcome families and high-frequency time-series forecasting workflows

Minimal Smoke Test

• Smoke-test prompt: "Run vera-data-repeated-reviewing on ChickWeight, using weight as the outcome, Time as the repeated factor, Chick as the subject ID, and Diet as the grouping variable. Produce the standard baseline artifacts."

Cross-Skill Interface

Output:
├── code_r      → .R script
├── code_python → .py script
├── figures/    → 2 PNGs (trajectories + interaction)
└── recommendations → text block (additional analyses available)

Next step: Invoke vera-data-repeated-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.