statistical-analyzer

Stage 2c of the data-master pipeline. The router in ../../SKILL.md owns the end-to-end run; this skill owns one stage and one gate. Read the parent contract before changing anything here: the invariants in ../../SKILL.md (additive-only, types decided once, default-FAIL gates, three-part provenance) are not restated, they are inherited.

When to invoke

When the data has a comparison or association structure. If there is no natural grouping variable, run descriptive analysis only and say so -- inventing a grouping variable is worse than reporting none.

Inputs

• cleaned data with --group <column>
• analysis/descriptive.json for distributional context

Outputs

• analysis/inferential.json: group, group_levels, group_sizes, alpha, n_rows, unit_of_analysis, tests, analysis_question, multiple_comparisons, correlations, rule_source
• each test: outcome, estimable, method, statistic_name, statistic, dof, dof_denom, p_raw, p_adjusted, effect_sizes, rejected_alternatives, robustness_cross_check, post_hoc

Commands

python scripts/stats_inferential.py --clean outputs/cleaned/cleaned.csv --group <column> --unit-key <column> --outcomes <a,b> --out outputs/analysis/inferential.json

For confirmatory scope, also pass --unit-key <column> and --outcomes <a,b>. Omitting either declaration, or using an automatically selected group, marks the comparison exploratory. Preserve that scope in the report and the audit.

Gate (default FAIL)

• more than one test implies a declared multiplicity family with finite adjusted values (a single NaN poisons a whole BH family);
• analysis_question.confirmatory_ready is true only when unit, group, and outcomes were explicitly named by the user; automatic selections remain exploratory;
• every estimable test carries an effect size and a 95%% CI;
• a non-estimable outcome returns estimable: false with a reason and no p-value;
• Welch ANOVA records both numerator and denominator df.

Failure modes seen in real runs

• Compare nested mixed models with different fixed effects using ML (reml=False), with convergence and finite-result checks. Preserve optimizer diagnostics. If the model cannot be fitted, report AUTHOR_INPUT_NEEDED; ordinary tests on repeated cell means are not an independent-samples fallback.
• A failed or violated ANCOVA slopes check leaves the adjusted question unresolved. Do not silently substitute an unadjusted question. OLS coefficient intervals use the residual t distribution.

Method basis: lme4 model-comparison guidance.

• df = 0.0 beside a p of 1e-70. The Welch ANOVA denominator df was computed with a formula that collapsed to zero; the Satterthwaite form must be used and checked against statsmodels.stats.oneway.
• A synonym column enters the family. species_code restates species; including it double-counts one hypothesis and shrinks the corrected p-values for the others.
• A NaN p-value is corrected as if it were a number. One NaN propagates through the step-down correction and nulls the entire family.

Do not

• do not report a p-value for a degenerate or constant group;
• do not "fix" non-normality by switching tests when n >= 30 -- use Welch and cross-check with the rank test;
• do not correct a subset of the family and present it as the family.

Upstream / downstream

• previous: ../data-explorer/SKILL.md
• next: ../visualizer/SKILL.md
• checklist: ../../references/nature-statistics-checklist.md