How it works
If every measurement is a multiple of some granularity g (questionnaire scores, rating scales, and counts are usually integers, g=1), then the true total of n observations must also be a multiple of g. A mean reported to d decimal places implies the true mean lies within M ± 0.5×10⁻ᵈ — so the true total must fall between n × (M − 0.5×10⁻ᵈ) and n × (M + 0.5×10⁻ᵈ).
If that interval contains no multiple of g, then no possible dataset of n observations could produce this mean — at least one of the mean, the sample size, or the reported precision is wrong.
A worked example
A paper reports: n = 20, mean M = 3.42 (integer-scored scale).
- Rounding tolerance on the mean: ±0.005
- Feasible-total interval: 20 × (3.415, 3.425) = (68.30, 68.50)
- No integer exists in that interval — GRIM-inconsistent: a sum of 20 integers must be an integer, and 68.3–68.5 contains none.
With M = 3.45 instead: the interval is (68.90, 69.10), which contains 69 → consistent.
Applicability
- Observations are multiples of the given granularity (integer scores, rating scales, counts)
- n is the final sample size included in the computation (use the post-exclusion n)
- The mean is an arithmetic mean, not a median or geometric mean
- Not applicable to continuous physical measurements (granularity far below reported precision)
What a GRIM failure actually means
GRIM flags mathematical inconsistency, not proof of fabrication. Possible causes: data fabrication, post-hoc sample exclusions without updating n, typos, non-standard rounding, or a wrong guess about the granularity. Its academic role is as a “line of questioning worth pursuing” — combined with terminal digit analysis, Benford's Law, and other statistical fingerprints for real screening value.
Source
Brown NJL, Heathers JAJ (2017). The GRIM Test: A Simple Technique Detects Numerous Anomalies in the Reporting of Results in Psychology. Social Psychological and Personality Science, 8(4), 363–369.
Related: GRIMMER (SD consistency), SPRITE (reconstructing plausible datasets from summary statistics), statcheck (recomputing reported p-values).
⚠️ Important: GRIM and every method on this site are screening aids. No single anomaly is sufficient to determine data fabrication. Final determinations must be made by competent institutions through due process.