GRIM Test (mean–granularity consistency)
The lightest possible check: using only the sample size n and mean M printed in the paper, test whether that mean is mathematically possible. No raw data, results in 30 seconds. Ideal for quickly vetting papers while reading, reviewing, or running a systematic review.
Reference: Brown & Heathers (2017), “The GRIM Test”.→ GRIM explainer & online test
SPRITE Test (mean–SD consistency)
GRIM's natural extension: add the standard deviation SD and test whether the n + M + SD combination is possible under the measurement granularity (and scale bounds). Purpose-built to catch summary statistics whose spread is too small or too large to be real.
Reference: Peeters et al. (2016), “SPRITE”.→ SPRITE explainer & online test
Statcheck (reported p-value recomputation)
Scan a results section for t/F/χ²/r/z statistics, recompute the exact p-value from each statistic and its degrees of freedom, and compare it with the reported value — flagging reporting inconsistencies and significance decision errors.
Reference: Nuijten et al. (2016), statcheck.→ Statcheck explainer & online tool
Citation Verification (Crossref check)
Non-existent references are the paper mill's most common flaw. Paste a reference list and automatically verify every entry against the public Crossref database.
Benford's Law (leading digits)
Natural data's leading digits follow a specific distribution: 1 appears ~30.1% of the time, 2 ~17.6%, down to 9 at ~4.6%. Hand-made “random” data often deviates — fabricators tend to make leading digits look uniform, which is itself unnatural.
Reference: Newcomb (1881), Benford (1938), Nigrini (1996).→ Benford explainer & online test
Terminal Digit Analysis (last digits)
Real measurements' terminal digits should be roughly uniform across 0-9. Mosimann et al. (1995) found that hand-fabricated data often favors 0 and 5 — people instinctively pick numbers that “look round” when asked to think of random digits.
Reference: Mosimann, JE et al. (1995), “Data fabrication: Can people generate random digits?”→ Terminal digit explainer & online test
Variance Anomaly (too-clean data)
Real biological, psychological, and social data have natural variability. Fabricated data is often “too clean” — suspiciously small variance, perfect fits, and p-values clustered in the 0.04-0.05 significance zone. Such patterns are typical fingerprints of mass-produced data.
Reference: Hartgerink CHJ (2016), “The value of statistical tools to detect data fabrication.”→ Try the variance screen
Digit Pair Frequency (adjacent repeats)
Adjacent digit pairs follow natural patterns. Fabricators often deliberately avoid adjacent repeats (like 11, 22) because they think repeats “look non-random” — but that very avoidance betrays fabrication: in real data, adjacent repeats are perfectly normal.
⚠️ Important: All of these methods are screening aids. No single anomaly is sufficient to determine data fabrication. Anomalies can arise from data characteristics, sample size, measurement methods, and other factors. Final determinations must be made by competent institutions through due process.
Case Studies (classic retractions)
Walk through publicly documented cases with official findings (Schön, Stapel, Wansink, the paper-mill retraction wave): which statistical signals could have been flagged earlier?