GRIM stands for Granularity Related Inconsistency of Means.

If you have a series of numbers given in whole units (A) and you divide them by a sample size (B) to get a mean, then that mean is a fraction A/B where both are integers.

Given that, any value described as "mean=A/16" must report decimals corresponding to 1/16th units. Where X is anything, the 2dp mean must be X.07, X.13, X.19, X.25, X.31, etc.

If a paper says , for example, 'mean=7.12' then the paper is wrong. 7.07 or 7.13 are possible. 7.12 is not.

Some additional fun points:

• GRIM sets a relationship between sample size and decimal places. Data rounded up may not be analyzable.

• GRIM is vulnerable to some types of subscales -- be careful to ensure that your 'whole integers' are in fact whole, not averages of other things.

• GRIM is particularly useful for percentages of whole numbers, because percentages given to 1dp '42.7%' are 3dp as decimals ie. '0.427'.

• GRIM was useful in the investigation of Brian Wansink, and was enumerated by Nick Brown when we were attempting to re-create data of Nicolas Gueguen.

• GRIM is available in the R package 'Scrutiny' -- just type install.packages("scrutiny")from your console. More information is on GitHub.

• GRIM is about ten years old.

• GRIM can be calculated in your browser through Lukas Jung's online portal here. So can GRIMMER (an extension of GRIM by Jordan Anaya)!

• GRIM has more uses than just means, and you can use it to calculate badly-described contingency tables (separate manuscript on that, here)

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