GRIM test for reported means

Can this mean arise from whole-number responses with this sample size? A flag is a prompt for human review, not a verdict.

How it works

With N participants answering k whole-number items and the item scores averaged, the sum of all responses is an integer S, so the mean is S / (N × k). The tool asks, with exact integer arithmetic, whether some integer S rounds to the reported mean at the reported number of decimals. When N × k is at least 10^decimals, nearly every reported mean is attainable and the test is uninformative; the tool tells you so.

Rounding. When S / (N × k) lands exactly halfway between two reportable values (for example 1.125 at two decimals), software disagrees: SPSS and Excel round half up (1.13), R and Python round half to even (1.12). By default this tool accepts either result, which is also the default of the R package scrutiny (rounding = "up_or_down") and avoids flagging a correct mean because of a rounding convention. Tick “Strict” to accept only round-half-up; strict mode flags more means (in a 2,500-case random comparison with scrutiny, about 1.5% of the attainable means were attainable only through a half-down tie). Exact ties need N × k whose only prime factors are 2 and 5.

Limits: GRIM assumes integer data, a single N for the mean, and standard rounding. Missing data, weighted or transformed scores, and means of means can make a correct mean look impossible, so a flag asks for a look at the methods, not a conclusion.