Fig. 2
From: How many of the digits in a mean of 12.3456789012 are worth reporting?
Experimental dependence of sig-digs in the SEM, DSEM, on the SEM sample size, NS. For samples from a Gaussian population of 107 with mean 39.5681 and the arbitrary standard deviation (SD) = 21.60 (empty squares) the points are close to a series of segments of lines DSEM = log10 (NS) + c. The squares with a cross inside show a similar pattern for a SD half that used for the empty squares. The line through the mean for one sawtooth has a slope of 1.0. The longer sloping line y = log10 (NS)/2 + 1, with half the slope of the sawtooth lines, summarizes the upper bound of sawtooth lines and sets the boundary between significant and random digits. The staircase ending in a broken line, with a step every 100-fold increase in NS shows the simplest rule for significant digits in an SEM. The staircase with continuous lines and a short step at the bottom shows Rule 2 in Rules Box, taking account of the difference in behaviour for very small NS