Normality Testing Workflow

Normality testing is often misused: passing Shapiro-Wilk does not prove normality, and failing it with large n does not mean parametric tests are invalid. Licklider combines formal tests with visual inspection and provides a defensible, documented decision about parametric vs. non-parametric test selection.

STEP 1 — The Scenario

Researcher Profile

A postdoctoral researcher who has just collected data from a three-group experiment (n=15 per group). Before choosing between ANOVA and Kruskal-Wallis, they need to assess whether the data distribution is consistent with parametric test assumptions.

Research Question

"Are the data in each group approximately normally distributed? Should I use one-way ANOVA or Kruskal-Wallis for the primary comparison?"

Dataset

• 3 groups: Control, Dose A, Dose B (n=15 per group)
• Outcome: Protein expression (arbitrary units, AU), continuous
• Group sizes: n=15 — small-to-moderate sample where normality matters for test validity

STEP 2 — Licklider Analysis Path

1. Data Upload & Group Detection

Licklider detects three groups and one continuous outcome. Normality assessment is triggered automatically before test selection.

2. Visual Inspection

Licklider generates, for each group:

• Histogram with a normal curve overlay
• Q-Q plot (quantile-quantile plot against theoretical normal distribution) with 95% confidence envelope
• Box plot showing median, IQR, whiskers, and individual outlier points

These visual tools are shown to the researcher with the instruction: "Visual inspection should always accompany formal normality tests, especially with small n where formal tests have low power."

3. Formal Normality Tests

Licklider runs, for each group:

• Shapiro-Wilk test (recommended for n < 50)
• D'Agostino-Pearson test (tests skewness and kurtosis separately)

Results are presented as a table: W-statistic or D-statistic, p-value, and interpretation per group.

4. Decision Support

Based on the combined visual + formal assessment, Licklider suggests one of three paths:

• Parametric (ANOVA): If normality passes in all groups and no extreme outliers are visible
• Non-parametric (Kruskal-Wallis): If normality clearly fails in one or more groups
• Transformation then re-check: If a right-skewed distribution is detected, log10 transformation is offered, followed by re-assessment

5. Decision Locking

The researcher confirms the decision. If they choose to override Licklider's recommendation (e.g., using ANOVA despite failed Shapiro-Wilk), the override is recorded with the researcher's justification in the Preprocessing Audit Log.

STEP 3 — Guards & Disclosures Activated

Normality & Homoscedasticity Check (4.1.1)

The Normality & Homoscedasticity Check guard requires that both normality (per group) and variance homogeneity (Levene's or Bartlett's test across groups) are assessed and disclosed before parametric test selection is confirmed. The guard runs Levene's test automatically alongside Shapiro-Wilk.

Low-Power Warning for Small n

With n=15 per group, Shapiro-Wilk has limited power to detect moderate deviations from normality. Licklider displays: "At n=15, Shapiro-Wilk may not detect deviations from normality reliably. Visual inspection via Q-Q plot is strongly recommended and should be reported alongside the formal test result."

Preprocessing Audit Log (1.1.1)

The normality test decision — including which tests were run, their results, and the final test selection — is logged automatically. If log-transformation was applied, this is also recorded as a preprocessing step and disclosed in the Methods text.

Transformation Disclosure

If log10 transformation is applied to achieve normality, this transformation must appear in the figure axis label, the Methods text, and the figure legend. Licklider enforces this and updates all downstream labels automatically.

STEP 4 — Export Package

• Figures: Q-Q plots and histograms for all groups (diagnostic panel) — 300 dpi TIFF/PDF
• Normality Test Report: Shapiro-Wilk and D'Agostino-Pearson results (W/D, p) per group; Levene's test result; visual interpretation summary; decision rationale
• Methods Text: "Normality was assessed for each group using the Shapiro-Wilk test and visual inspection of Q-Q plots and histograms. Variance homogeneity was assessed using Levene's test. Based on these assessments, [one-way ANOVA / Kruskal-Wallis] was selected for the primary comparison. [If applicable: Data were log10-transformed prior to analysis.]"
• Preprocessing Audit Log: Test selection decision with formal test results; any transformations applied; any researcher overrides with recorded justification