One-Way ANOVA

Four dose groups, one outcome, multiple comparisons. Licklider runs a one-way ANOVA, enforces multiple comparison correction, selects the appropriate post-hoc test, and produces CLD (compact letter display) annotations — fully disclosed, publication-ready.

STEP 1 — The Scenario

Researcher Profile

A pharmacologist testing a new anti-inflammatory compound at four doses (Vehicle, 1 mg/kg, 10 mg/kg, 100 mg/kg) in a rodent model of arthritis. The outcome is paw edema volume (mL) at 24 hours post-treatment.

Research Question

"Does the compound reduce paw edema in a dose-dependent manner, and which doses differ significantly from vehicle?"

Dataset

• 4 groups: Vehicle (n=10), 1 mg/kg (n=10), 10 mg/kg (n=10), 100 mg/kg (n=10)
• Outcome: Paw edema volume (mL), continuous
• Design: Independent groups, one-way factorial

STEP 2 — Licklider Analysis Path

1. Data Upload & Profiling

Licklider detects 4 groups, continuous outcome, n=10 per group. No missing values. Balanced design confirmed.

2. Data Contract Declaration

Observation unit: one animal. Outcome type: continuous. Analysis purpose: confirmatory (comparing against vehicle). Design: independent groups, one-way.

3. Assumption Checks

Licklider runs Shapiro-Wilk per group and Levene's test for homogeneity of variance. Both pass. One-way ANOVA is confirmed as appropriate.

4. ANOVA & Post-Hoc

One-way ANOVA: F(3,36) is calculated. Significant omnibus result triggers post-hoc analysis. Licklider selects Holm-Šidák correction for pairwise comparisons against vehicle (Dunnett's can also be selected if the comparison is exclusively vs. control). η² and 95% CI are calculated.

5. Figure Generation

Bar chart (mean ± SEM) with individual data points and CLD annotation. CLD letters (a, ab, b, c) are placed above each group. Significance brackets are available as an alternative.

STEP 3 — Guards & Disclosures Activated

Multiple Comparison Compliance (4.1.5)

Licklider detects that 4 groups require multiple comparison correction. The post-hoc method and the family-wise error rate correction are mandatory disclosures. The number of comparisons tested is locked into the statistical report.

Effect Size + CI + N Mandatory (3.1.2)

η² (partial eta-squared) and its 95% CI are reported alongside the F-statistic. CLD annotations are exported only with the full statistical table.

Error Bar Type Enforcement (3.1.1)

Bar chart error bars are set to ± SEM with explicit declaration. The guard notes: "SEM reflects precision of the mean estimate, not the spread of individual data. For individual variability, use ± SD or show raw data points."

Analysis Family Ledger (1.2.2)

The four groups constitute one analysis family. The ledger records the number of comparisons (6 pairwise, or 3 vs. vehicle). Any additional exploratory subgroup analyses outside this family require separate labeling.

STEP 4 — Export Package

• Figure: Bar chart (mean ± SEM) with individual data points, CLD annotation — 300 dpi TIFF/PDF
• Statistical Report: One-way ANOVA F-statistic, df, p-value; Holm-corrected post-hoc table (all pairwise); η² (95% CI); n per group
• Methods Text: "Paw edema volumes were compared across dose groups using one-way ANOVA followed by Holm-corrected pairwise post-hoc tests. Effect size is reported as η² (95% CI). Data are presented as mean ± SEM with individual data points. n=10 per group."
• Figure Legend: CLD letters, test name, correction method, n, effect size
• Preprocessing Audit Log: No transformations; no exclusions