How many of the digits in a mean of 12.3456789012 are worth reporting?

@article{Clymo2019HowMO,
title={How many of the digits in a mean of 12.3456789012 are worth reporting?},
author={R. S. Clymo},
journal={BMC Research Notes},
year={2019},
volume={12}
}

ObjectiveA computer program tells me that a mean value is 12.3456789012, but how many of these digits are significant (the rest being random junk)? Should I report: 12.3?, 12.3456?, or even 10 (if only the first digit is significant)? There are several rules-of-thumb but, surprisingly (given that the problem is so common in science), none seem to be evidence-based.ResultsHere I show how the significance of a digit in a particular decade of a mean depends on the standard error of the mean (SEM… Expand

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