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

TL;DR

This paper proposes an evidence-based rule for determining the number of significant digits to report in a mean, based on the standard error, to ensure accuracy and credibility in scientific reporting.

Contribution

It introduces a simple, data-driven rule for reporting significant digits in a mean based on the standard error, addressing a common but unsubstantiated practice.

Findings

The significance of a digit depends on the SEM.

The DM index helps determine the last significant digit.

Reporting beyond the rule reduces credibility.

Abstract

OBJECTIVE. A 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. RESULTS. Here I show how the significance of a digit in a particular decade of a mean depends on the standard error of the mean (SEM). I define an index, DM that can be plotted in graphs. From these a simple evidence-based rule for the number of significant digits ("sigdigs") is distilled: the last sigdig in the mean is in the same decade as the first or second non-zero digit in the SEM. As example, for mean 34.63 (SEM 25.62), with n = 17, the reported value should be 35 (SEM 26). Digits beyond these contain little or no useful information, and should not be reported lest they damage your credibility.