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I remember that I heard something like this, that for a certain sample size one should not give more than $n$ decimal places for location and dispersion parameters e.g. for small samples sizes only one decimal place, for larger ones two or even more.

But I can absolutely find no information on this topic. There is this article: http://adc.bmj.com/content/early/2015/04/15/archdischild-2014-307149.full which has some rules as a table but there is no hints about the sample size.

One interesting thing here is also that the paper states for test statistic, only one decimal place and max. 2 significant places should be given. In a statistics course we were taught to give test statistic results to at least 6 decimal places.

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From a purely statistical standpoint I see no reason for a rule like this, since your point estimate is technically known to whatever precision you like. The idea is just to acknowledge that it's only a point estimate (and not the underlying thing you're trying to estimate), and the way you account for that is by also measuring the uncertainty in that estimate. But the way you do that is with something like a standard error or a confidence interval, not by rounding to some special number of digits.

The link you provided seems to be more interested in presentation than any serious statistical considerations. One might argue for instance that if you're estimating a dollar value you may not want to report more than two decimal places because fractions of a cent seem a bit strange and the reader may not care about this much precision. But again this more about communication than statistics.

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    $\begingroup$ Yes, I thought the same, but I remember that someone said it is useless to give 6 decimal places for the mean if you only have 200 samples, even if the number you calculated has 20 decimal places. I remember it in a way, that he meant you can not even calculate with the precision because you have so less samples. Maybe he meant that it is useless to present them to the reader? I looked into my course records and one book i own but could not find the line I'm looking for... $\endgroup$ – reox Nov 26 '16 at 22:47

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