Repeated Measures

When the same subject is measured at multiple time points, standard ANOVA violates the independence assumption. Licklider detects repeated structure, selects between RM-ANOVA and Linear Mixed Models (LMM), applies Greenhouse-Geisser correction if needed, and produces time-series figures with within-subject variability disclosed.

STEP 1 — The Scenario

Researcher Profile

A behavioral neuroscientist measuring anxiety behavior (open-field center time, seconds) in mice treated with an anxiolytic compound. Measurements are taken at baseline (Day 0) and weekly for 4 weeks (Days 7, 14, 21, 28). Two groups: Vehicle (n=12) and Drug (n=12).

Research Question

"Does anxiolytic treatment progressively increase center time over 4 weeks, and does the trajectory differ from vehicle?"

Dataset

• 2 groups × 5 time points: 24 animals, 120 total observations (each animal measured 5 times)
• Outcome: Center time (seconds), continuous
• Design: Mixed design — between-subjects factor (Group) × within-subjects factor (Time)
• Subject ID column: required for repeated-measures handling

STEP 2 — Licklider Analysis Path

1. Data Upload & ID Mapping

Licklider detects the subject ID column and identifies the repeated structure: 24 unique subjects × 5 measurements each. The Variable & ID Mapping (2.1.2) step prompts the researcher to confirm: "Which column identifies the same subject across time points?"

2. Data Contract Declaration

Observation unit: one animal. Within-subject factor: Time (5 levels). Between-subject factor: Group (2 levels). Outcome type: continuous. Analysis purpose: confirmatory.

3. Sphericity Test

Mauchly's test for sphericity is applied to the within-subject factor (Time). If violated (p<0.05), Licklider automatically applies the Greenhouse-Geisser correction and discloses the ε value.

4. Test Selection: RM-ANOVA vs. LMM

If no missing data exist and sphericity holds (or is corrected), Repeated-Measures ANOVA is used. If missing data are present (e.g., some animals have only 3 of 5 measurements), Licklider upgrades to Linear Mixed Model (LMM) with a random intercept per subject, which handles unbalanced repeated data without listwise deletion.

5. Results & Post-Hoc

The mixed model (or RM-ANOVA) produces: main effect of Group, main effect of Time, and Group × Time interaction. If the interaction is significant, simple effects at each time point are tested with Holm correction.

6. Figure Generation

A line chart with two lines (Vehicle, Drug), mean ± SEM at each time point, and individual animal trajectories overlaid (spaghetti lines). Time-point-level n is annotated for each group if any dropouts occur.

STEP 3 — Guards & Disclosures Activated

Repeated Measures Model Suggestion (4.5.4)

Licklider detects the repeated structure from the subject ID column and confirms the analysis accounts for within-subject correlation. If the researcher submits data without a subject ID, the guard warns: "Repeated measures detected but no subject ID provided — independence assumption may be violated."

Sphericity Correction Disclosure

If Mauchly's test fails, the Greenhouse-Geisser ε and corrected df are both disclosed in the statistical report and Methods text. The correction cannot be silently applied — it is always surfaced to the researcher.

Missing Data Disclosure (4.1.7)

If any animals are missing one or more time points, the N Disclosure guard reports: input N, analyzed N, and number of observations dropped — per time point, per group.

Analysis Family Ledger (1.2.2)

Time-point-specific post-hoc comparisons (up to 5 per group pair) are tracked in the analysis family. The total number of comparisons and the correction method are locked into the report.

Effect Size Reporting (4.1.2)

Partial η² for the Group × Time interaction is reported alongside the F-statistic. For LMM, marginal R² and conditional R² are provided instead.

STEP 4 — Export Package

• Figure: Line chart — 2 lines with mean ± SEM and individual trajectories — 300 dpi TIFF/PDF
• Statistical Report: RM-ANOVA or LMM output table (main effects + interaction); Mauchly's test result (if RM-ANOVA); Greenhouse-Geisser ε (if corrected); post-hoc table; effect sizes; n per group per time point
• Methods Text: "Data were analyzed using a two-way mixed-design repeated-measures ANOVA (between-subjects: Group; within-subjects: Time). Mauchly's test for sphericity was applied; Greenhouse-Geisser correction was used where sphericity was violated. Post-hoc comparisons were Holm-corrected. Effect size is reported as partial η² (95% CI). n=12 per group."
• Figure Legend: Line color coding, error bar type, time-point n, significance annotations, correction method
• Preprocessing Audit Log: Subject ID mapping; time points per animal; missing observations count