Normality & Homoscedasticity Check

Selecting a parametric test for non-normal data, or an equal-variance test for heteroscedastic groups, is one of the most common assumption violations in published research. It rarely causes explicit errors —it simply produces results that do not mean what the author believes they mean.

STEP 1 —The Pitfall

Most researchers select t-tests or ANOVA by habit, not by checking whether their data meet parametric assumptions. Normality is often assumed by default. Heteroscedasticity is often ignored. When violations exist, the test's Type I error rate is no longer controlled at the declared alpha, and confidence intervals become unreliable.

The problem is compounded by selective reporting: researchers may run normality tests but not report them, or report only the tests that passed. Without a systematic record, reviewers have no way to evaluate whether the test selection was appropriate.

[Image placeholder: Side-by-side histograms showing normal vs. skewed distributions with the same t-test applied. The skewed case should have a visible assumption violation annotation.]

Applying a parametric test to non-normal data without disclosure: the p-value is reported, but the assumption check is absent.

STEP 2 —Journal Requirement

Nature, Science, NEJM, and most major journals require that assumption checks be reported in the Methods section when parametric tests are used. The standard language is: "Data were tested for normality using [test] and for equal variance using [test]. [Parametric / non-parametric] tests were applied accordingly."

Failure to report this creates a reviewer comment in most rigorous journals and triggers rejection in statistics-intensive fields such as pharmacology and clinical research.

STEP 3 —Licklider Solution

Input

Raw data columns with group structure declared via Variable & ID Mapping
Observation unit (e.g., mouse, patient, cell) declared via Observation Unit Declaration
Analysis intent (inferential / confirmatory) declared via Outcome Type Lock

Output

Shapiro-Wilk (n 竕､ 50), D'Agostino窶撤earson (n > 50), or Kolmogorov-Smirnov —selected automatically based on sample size
Levene's test for equal variance across groups
Normality check result displayed per group alongside the figure
Validity Score dimension updated: Pass (normal + equal variance), Warning (borderline), Fail (non-normal + parametric test selected)
If violation detected: advisory messaging and links — a verified automatic switch into rank-based tests is not guaranteed (see Non-Parametric Alternatives)

Guard

If a parametric test is applied to data that fail normality (p < 0.05 on the normality test), the Validity Score for this dimension is set to Warning. If the analysis is marked as confirmatory or publication-ready and the violation is flagged, the dimension is set to Fail —blocking publication-ready export until the user either switches to a non-parametric test or provides an explicit justification that the test is robust to the observed deviation.

[Image placeholder: Licklider UI showing the normality check results panel —Shapiro-Wilk p-value per group, Levene p-value, and the Validity Score dimension indicator (Pass/Warning/Fail) with the suggested alternative test.]

Licklider's normality check panel: per-group results, equal-variance test, and Validity Score dimension updated in real time.

STEP 4 —Draft Output (Draft / Needs review)

The following text is auto-generated for the Methods section when normality checks are run:

Data were tested for normality using the Shapiro-Wilk test (n 竕､ 50)
or D'Agostino窶撤earson test (n > 50), and for equal variance using Levene's
test. [Parametric tests were applied to normally distributed data with equal
variance / Non-parametric tests were applied where normality or equal variance
assumptions were violated]. Statistical tests and results are reported per
figure in the figure legends.