Statistics & Reproducibility (pnas-statistics)

When to trigger

• Results report P values but not effect sizes or n.
• "Three independent experiments" is claimed but replication is unclear.
• Multiple comparisons are run with no correction.
• A reviewer is likely to ask "were analyses pre-specified?" and there's no answer.
• The analysis is not reproducible from the deposited code (pnas-data).

The reporting backbone (every quantitative claim)

Each claim needs: effect size + uncertainty + n + test + what n means.

• n stated, with the unit of replication (biological vs technical replicates; cells vs animals vs subjects vs experiments).
• Effect size with 95% CI (preferred) or SD/SEM clearly labeled — not P alone.
• Exact P values (e.g., P = 0.013), not "P < 0.05", unless extremely small.
• Test named and justified (assumptions checked: normality, variance homogeneity, independence).
• Multiple comparisons corrected (Bonferroni/Holm/FDR) when many tests are run.

Replication and design

• Distinguish biological replication (independent samples) from technical replication (re-measurement). The former is what counts.
• State how the sample size was chosen (power analysis or explicit rationale), not post-hoc.
• Report randomization of subjects/treatments and blinding of measurement/analysis where applicable, or state why not.
• Report inclusion/exclusion criteria and any excluded data, with reasons, decided in advance.

Discipline-specific notes across PNAS divisions

PNAS spans Biological, Physical, and Social Sciences, so match the rigor conventions of your division:

• Biological: replication unit, ARRIVE-style animal reporting, antibody/reagent validation.
• Social/behavioral: pre-registration is increasingly expected; report power, sampling frame, and deviations from the plan.
• Physical/computational: report uncertainties, error propagation, and numerical reproducibility (seeds, solver settings).

Avoid the classic reviewer kills

• Pseudoreplication: treating technical replicates / cells from one animal as independent n.
• HARKing / p-hacking: presenting exploratory findings as confirmatory. Label exploratory work as such.
• "Representative" images with no quantification across replicates.
• Bar chart + SEM masking a tiny, variable n.
• Comparing two effects by their significance ("significant here, not there") instead of testing the difference.

Reproducibility package

• Analysis code in a repository (see pnas-data), with a README and environment/versions.
• A reproducibility/reporting summary if requested; list software, versions, seeds.
• Deterministic where possible; report random seeds for simulations/ML.

Pre-registration & transparency (where relevant)

• For confirmatory studies (especially human-subjects / behavioral work in the Social Sciences division), note pre-registration (OSF/AsPredicted) if done.
• Separate pre-specified analyses from post-hoc exploration explicitly in the text.

Before / after: a reporting sentence in PNAS register

PNAS reviewers span divisions, so a statistics sentence has to survive a reader who does not share your field's shorthand. Tighten a vague claim into the reporting backbone.

• Before: "Treatment significantly increased expression (P < 0.05, n = 3), confirming our hypothesis."
• After: "Treatment raised expression 2.4-fold (95% CI 1.7–3.3; two-sided Welch's t test, P = 0.008; n = 6 biological replicates, each the mean of 3 technical replicates), consistent with the predicted mechanism."

The revision names the effect and its uncertainty, states the unit of replication, gives an exact P, and separates biological from technical n — the four things a PNAS editor flags when a general-audience claim rests on thin evidence.

PNAS editor / referee expectation checklist

What a PNAS handling editor and cross-division referees actively look for:

• Broad significance is earned, not asserted — the statistical advance supports the general claim in the Significance Statement, not a narrower one.
• Reporting standards met — every panel's n, test, and error definition appears in its legend, not buried in Methods.
• Reproducibility — a referee could re-run the analysis from deposited code, versions, and seeds (pnas-data).
• Data availability — primary data underlying each quantitative figure is deposited, not "available on request."
• No selective reporting — exploratory and confirmatory analyses are labeled; excluded data and its rationale are disclosed.

Output format

【Per-claim backbone】 effect+CI / n / unit-of-n / test / assumptions → list gaps
【Replication】 biological vs technical clear? yes/no
【Sample-size rationale】 power/justification present? yes/no
【Randomization & blinding】 reported / N/A-justified / missing
【Multiplicity】 corrected? method
【Division-specific rigor】 (Bio / Physical / Social) conventions met? yes/no
【Reproducibility】 code + versions + seeds present? yes/no
【Next】 pnas-data

Anti-patterns

• Do not report P without effect size and n.
• Do not count technical replicates as independent observations.
• Do not infer "no effect" from a non-significant test on an underpowered sample.
• Do not present post-hoc subgroup findings as if pre-specified.