Two-Way ANOVA

Factorial designs require reporting interaction effects — not just main effects. Licklider enforces interaction term reporting, produces interaction plots, and ensures that simple main effects are not over-interpreted when the interaction is significant.

STEP 1 — The Scenario

Researcher Profile

A neuroscientist studying the effect of a stress-relieving intervention on corticosterone levels in male and female mice. The factorial design has two factors: Intervention (Control vs. Treatment) and Sex (Male vs. Female), with 10 animals per cell.

Research Question

"Does the intervention reduce corticosterone levels, and does this effect differ by sex? Is there an interaction between intervention and sex?"

Dataset

• 2×2 factorial: Intervention (2 levels) × Sex (2 levels) = 4 cells, n=10 per cell
• Outcome: Plasma corticosterone (ng/mL), continuous
• Design: Independent groups, balanced factorial

STEP 2 — Licklider Analysis Path

1. Data Upload & Profiling

Licklider detects two categorical predictors and one continuous outcome. It automatically identifies the 2×2 factorial structure (40 total observations, balanced).

2. Data Contract Declaration

Observation unit: one animal. Factors declared: Intervention (fixed), Sex (fixed). Outcome type: continuous. Analysis purpose: confirmatory.

3. Assumption Checks

Shapiro-Wilk per cell, Levene's test across all 4 groups. Both pass. Two-way ANOVA is confirmed as appropriate.

4. Two-Way ANOVA with Interaction

Licklider runs the two-way ANOVA and reports all three tests: main effect of Intervention, main effect of Sex, and the Intervention × Sex interaction. If the interaction is significant, Licklider warns: "Main effects should be interpreted with caution when an interaction is present. Simple main effect analyses are recommended."

5. Simple Main Effects (if interaction significant)

If interaction p < 0.05, Licklider runs simple main effects — the effect of Intervention within males and within females separately — with Bonferroni or Holm correction applied.

6. Figure Generation

An interaction plot is proposed: two lines (one per sex) showing mean ± SEM at both intervention levels. Individual data points are overlaid. Diverging or parallel lines visualize the presence or absence of interaction.

STEP 3 — Guards & Disclosures Activated

Multiple Comparison Compliance (4.1.5)

Post-hoc comparisons (4 cells, 6 pairwise) require correction. The number of comparisons and the correction method are locked into the report.

Interaction Effect Reporting Guard

Licklider requires explicit reporting of the interaction F-statistic, df, p-value, and partial η². Suppressing the interaction term from the results table is not permitted in the export.

Effect Size + CI + N Mandatory (3.1.2)

Partial η² and 95% CI are reported for each effect (main effects and interaction). Cell-level n is declared in the figure legend.

Causal Language Detection (3.1.5)

If the auto-generated Methods text or figure legend uses phrases like "treatment caused a sex-dependent reduction," the causal language guard flags this for replacement with correlation-safe phrasing: "the intervention was associated with a sex-dependent change."

STEP 4 — Export Package

• Figure: Interaction plot — two lines (Male, Female), mean ± SEM, individual data points — 300 dpi TIFF/PDF
• Statistical Report: Full two-way ANOVA table (main effects + interaction); simple main effects table (if applicable); partial η² (95% CI) for all effects; n per cell
• Methods Text: "Data were analyzed using two-way ANOVA with Intervention and Sex as fixed factors. The interaction term was included and tested. Simple main effects were evaluated where the interaction was significant. Effect sizes are reported as partial η² (95% CI). n=10 per cell."
• Figure Legend: Interaction plot description, line color coding, error bar type, all F-statistics and p-values, n
• Preprocessing Audit Log: No transformations; no exclusions