Is there a more scientific way of determining the number of significant digits to report for a mean or a confidence interval in a situation which is fairly standard - e.g. first year class at college.
I have seen Number of significant figures to put in a table, Why don't we use significant digits and Number of significant figures in a chi square fit, but these don't seem to put their finger on the problem.
In my classes I try to explain to my students that it is a waste of ink to report 15 significant digits when they have such a wide standard error in their results - my gut feeling was that it should be rounded to about somewhere of the order of $0.25\sigma$. This is not too different from what is said by ASTM - Reporting Test Results referring to E29 where they say it should be between $0.05\sigma$ and $0.5\sigma$.
When I have a set of numbers like
x below, how many digits should I use to print the mean and standard deviation?
set.seed(123) x <- rnorm(30) # default mean=0, sd=1 # R defaults to 7 digits of precision options(digits=7) mean(x) # -0.04710376 - not far off theoretical 0 sd(x) # 0.9810307 - not far from theoretical 1 sd(x)/sqrt(length(x)) # standard error of mean 0.1791109
QUESTION: Spell out in detail what the precision is (when there is a vector of double precision numbers) for mean and standard deviation in this and write a simple R pedagogical function which will print the mean and standard deviation to the significant number of digits that is reflected in the vector