Statistical Review

Common errors:

• Using independent t-test on paired/matched data
• Using parametric tests on heavily skewed data without justification
• Using chi-square when expected cell counts are below 5 (should use Fisher's exact)
• Using Pearson correlation on non-linear relationships
• Using repeated t-tests instead of ANOVA (inflates Type I error)
• Treating ordinal data as continuous without justification

2. Assumption Verification

For each statistical test, verify that assumptions are checked:

Parametric Tests (t-test, ANOVA, linear regression)

• Normality assessed (Shapiro-Wilk, Q-Q plot, or central limit theorem invoked for large n)
• Method of normality assessment stated
• Homogeneity of variance tested (Levene's test) and reported
• Action taken when assumptions violated (non-parametric alternative, transformation, or robust method)

Regression Models

• Linear regression: linearity, normality of residuals, homoscedasticity, independence, VIF for multicollinearity
• Logistic regression: linearity of continuous predictors with log-odds, adequate events per variable (EPV >= 10)
• Cox regression: proportional hazards assumption tested (Schoenfeld residuals, log-log plot)

Non-parametric Tests

• Justified by violation of parametric assumptions (not just by default)
• Appropriate non-parametric test selected

3. Multiple Testing Correction

Red flags:

• Multiple comparisons without any correction mentioned
• Selective reporting of only "significant" comparisons from a larger set
• Subgroup analyses presented as confirmatory without pre-specification
• P-values reported for dozens of comparisons without correction

4. Effect Size Reporting

Every comparison or association should report an effect size alongside the p-value.

Red flags:

• Only p-values reported, no effect sizes
• Statistically significant p-value with trivially small effect size (especially in large samples)
• Effect sizes reported without confidence intervals
• No discussion of clinical or practical significance

5. Confidence Intervals

• 95% CIs reported for primary outcome measures
• CIs reported for effect sizes (not just point estimates)
• CIs interpreted correctly (the interval, not the point estimate, conveys precision)
• CIs consistent with reported p-values (CI crossing null should correspond to non-significant p)

6. Sample Size Justification

• A priori power analysis performed and reported
• Effect size used in power analysis justified (pilot data, literature, or MCID)
• Alpha, power, and calculated N stated
• Actual sample size meets or exceeds calculated requirement
• If sample is smaller than calculated, acknowledged as a limitation
• Software used for power calculation stated

Red flags:

• No power analysis mentioned anywhere in the manuscript
• Post-hoc power analysis presented as if it were a priori
• Power analysis based on observed effect size (circular reasoning)
• Impossibly small sample for the claimed power level

7. Missing Data Handling

• Amount of missing data reported per variable
• Pattern of missingness assessed (MCAR, MAR, MNAR)
• Missing data mechanism discussed
• Handling method stated (complete case, imputation, maximum likelihood)
• If imputation used: method described (MICE, single imputation, last observation carried forward)
• Sensitivity analysis comparing complete-case and imputed results

Red flags:

• No mention of missing data at all
• Complete-case analysis without reporting how much data was lost
• Last observation carried forward (LOCF) without justification (generally discouraged)
• Listwise deletion resulting in substantial sample reduction without discussion

8. P-Hacking and Selective Reporting Red Flags

P-hacking is the practice of manipulating data analysis to produce statistically significant results. Watch for:

Analysis Red Flags

• Suspicious p-value clustering -- many p-values just below 0.05 (e.g., 0.048, 0.043, 0.049)
• Outcome switching -- primary outcome in registration differs from primary outcome in paper
• Flexible exclusion criteria -- post-hoc exclusion of participants that changes results
• Unplanned subgroups -- subgroup analyses not pre-specified but presented as primary findings
• Optional stopping -- data collection appears to have stopped when significance was reached
• Transformation shopping -- multiple transformations tried until one yields significance
• Covariate fishing -- adding/removing covariates until the desired result appears
• Rounding down -- reporting p = 0.05 when actual value is slightly above (e.g., p = 0.054)

Reporting Red Flags

• Selective outcome reporting -- registered outcomes missing from the paper
• Absence of non-significant results -- only significant findings reported from multiple tests
• HARKing (Hypothesizing After Results are Known) -- exploratory findings presented as confirmatory hypotheses
• Narrative spinning -- emphasizing subgroup results or secondary outcomes when primary outcome is non-significant
• Vague methods -- analysis plan described in vague terms that could accommodate multiple approaches

What to Do

1. Check trial/study registration (ClinicalTrials.gov, PROSPERO, OSF) for pre-registered outcomes and analysis plan
2. Compare registered outcomes with reported outcomes
3. Look for discrepancies between methods and results sections
4. Examine whether non-significant results are reported and discussed
5. Check if the number of reported comparisons matches what the design would produce

9. Additional Statistical Quality Checks

• Baseline comparisons in RCTs -- p-values for baseline characteristics are unnecessary (randomization ensures comparability in expectation). If present, they should not drive covariate selection.
• Percentage precision -- percentages with excessive decimal places for small samples (e.g., "33.33%" when N = 3)
• Standard deviation vs. standard error -- SD used for describing data, SE (or CI) for describing precision of estimates. Verify correct usage.
• Appropriate denominators -- percentages calculated from the correct denominator (ITT population vs. completers)
• Consistency -- numbers in text match numbers in tables and figures
• Degrees of freedom -- reported and consistent with sample sizes

Output Format

## Statistical Review Report

### Overall Statistical Quality: [Adequate / Needs Improvement / Serious Concerns]

### Test Appropriateness
| Analysis | Test Used | Appropriate? | Issue (if any) |
|----------|----------|-------------|----------------|
| [description] | [test] | Yes/No | [issue] |

### Assumption Verification
- [Finding 1]
- [Finding 2]

### Effect Size and CI Reporting
- [Finding]

### Multiple Testing
- [Finding]

### Sample Size Adequacy
- [Finding]

### Missing Data
- [Finding]

### P-Hacking Indicators
- [None detected / Concerns identified: ...]

### Recommendations
1. **Critical:** [...]
2. **Major:** [...]
3. **Minor:** [...]

Checklist

Test Selection and Assumptions

• Each statistical test appropriate for the data type and design
• Parametric assumptions checked and reported
• Non-parametric alternatives used when assumptions violated
• Correct handling of paired/clustered data

Reporting Quality

• Effect sizes reported for all comparisons
• 95% confidence intervals provided
• Exact p-values reported (not "NS" or "p < 0.05")
• Multiple testing correction applied and stated
• Sample size justified with power analysis

Data Integrity

• Missing data quantified and handled appropriately
• Numbers consistent across text, tables, and figures
• Denominators correct for all percentages
• SD vs. SE used correctly

Bias Assessment

• No evidence of p-hacking or selective reporting
• Registered outcomes match reported outcomes
• Non-significant results reported
• Subgroup analyses labeled as exploratory (unless pre-specified)

References

• Wasserstein RL, Lazar NA. The ASA's Statement on p-Values: Context, Process, and Purpose. The American Statistician. 2016;70(2):129-133. doi:10.1080/00031305.2016.1154108
• Wasserstein RL, Schirm AL, Lazar NA. Moving to a World Beyond "p < 0.05." The American Statistician. 2019;73(sup1):1-19. doi:10.1080/00031305.2019.1583913
• Simmons JP, Nelson LD, Simonsohn U. False-Positive Psychology: Undisclosed Flexibility in Data Collection and Analysis Allows Presenting Anything as Significant. Psychological Science. 2011;22(11):1359-1366. doi:10.1177/0956797611417632
• Head ML, Holman L, Lanfear R, Kahn AT, Jennions MD. The Extent and Consequences of P-Hacking in Science. PLoS Biol. 2015;13(3):e1002106. doi:10.1371/journal.pbio.1002106
• Kerr NL. HARKing: Hypothesizing After the Results are Known. Pers Soc Psychol Rev. 1998;2(3):196-217. doi:10.1207/s15327957pspr0203_4
• Lang TA, Altman DG. Basic Statistical Reporting for Articles Published in Biomedical Journals: The "Statistical Analyses and Methods in the Published Literature" or The SAMPL Guidelines. Int J Nurs Stud. 2015;52(1):5-9. doi:10.1016/j.ijnurstu.2014.09.006
• Greenland S, Senn SJ, Rothman KJ, et al. Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations. Eur J Epidemiol. 2016;31(4):337-350. doi:10.1007/s10654-016-0149-3