How it works
If every observation is a multiple of some granularity g (questionnaire scores and rating scales are usually integers, g=1), then fixing the sample size n and the mean M leaves the data very little freedom: with the total fixed, Σx² is minimized by squeezing all observations onto the two grid points adjacent to the mean, and maximized by pushing as many observations as possible to the two ends of the scale — a consequence of the convexity of Σx².
This yields an exact achievable-SD interval [SD_min, SD_max]:
- SD too small (< SD_min): no such dataset exists — 20 integers averaging 3.5 cannot have an SD below 0.5, because 10 threes and 10 fours is already the “tightest” possible distribution.
- SD too large (> SD_max, requires scale bounds): the data would have to exceed the scale to produce that much spread.
If the reported SD (within its rounding tolerance) does not intersect the achievable interval, then at least one of n, M, SD, the granularity, or the scale bounds must be wrong — the same logic as GRIM, with one more dimension of evidence.
A worked example
A paper reports: n = 20, mean M = 3.50, SD = 0.20 (1-7 integer scale).
- Mean feasible: 20 × 3.50 = 70, an integer ✓ (GRIM passes)
- But the “tightest” integer distribution around a mean of 3.5 is ten 3s and ten 4s, giving SD = 0.51
- Reported SD = 0.20 < 0.51 — mathematically impossible ✗
This “too-consistent statistics” pattern is one of the classic fingerprints of fabricated data: invented numbers often come with a plausible-looking SD that ignores the coupling between SD and granularity.
Applicability
- Each observation is a multiple of the given granularity (integer scores, 0.1/0.01-precision scale scores, etc.)
- The mean is an arithmetic mean; n is the final sample size included in the computation
- Scale bounds (e.g., Likert 1-7) are needed to assess the “SD too large” side; without them only “SD too small” is tested
- Not applicable to continuous physical measurements (granularity far below reported precision)
What a SPRITE failure actually means
SPRITE flags mathematical inconsistency between the summary statistics, not proof of fabrication. Possible causes: data fabrication, typos in M/SD/n, non-standard rounding, post-hoc exclusions, or a wrong guess about the granularity or scale. Its role is to generate specific, concrete questions worth asking the authors — cross-check with GRIM, statcheck, and the statistical fingerprints for real screening value.
Source
Peeters CFW et al. (2016). SPRITE (Sample Parameter Reconstruction via Iterative TEchniques): Assessing the plausibility of reported means and standard deviations. The Quantitative Methods for Psychology, 12(3), 253–268.
This tool implements SPRITE's feasibility core (exact closed-form computation of the achievable SD interval) and displays example distributions at both ends of the feasible region as evidence.
⚠️ Important: SPRITE 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.