Why don't we use significant digits?

Question

Any idea why we don't use significant digits in statistics? Something along the line of we are using estimates so rules about precision don't apply ;) ?

Readers may also find this thread: [number-of-significant-figures-to-put-in-a-table](http://stats.stackexchange.com/questions/8734/) of interest. — gung - Reinstate Monica, Dec 28 '12 at 22:17
I found this informative: http://davegiles.blogspot.com/2011/12/reported-accuracy-for-regression.html — John, Jan 02 '13 at 21:41
An example of where paying attention to significant digits really matters appears at http://stats.stackexchange.com/questions/113314, where the OP obtained noticeably different regression results traceable to differences in the precision with which data were input to regression procedures. — whuber, Sep 01 '14 at 19:16

score 19 · Accepted Answer · answered Dec 19 '12 at 02:32

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Significant digits are used in some fields (I learned about them in Chemistry) to indicate the degree of meaningful precision that exists in a number. This is an important topic in statistics as well, so in fact we report this constantly--we just report it in a different form. Specifically, we report confidence intervals, which indicate the level of precision of an estimate (such as a mean).

Once you've listed the 95% CI for an estimate, such as $(-0.12, 1.12)$, you can list as many digits for your mean as you might like, such as $0.50129519823975923$, and there is no problem. In fact, the statistician Andrew Gelman has recommended that you list at least four (2009, p. 4).

answered Dec 19 '12 at 02:32

gung - Reinstate Monica

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*(The last part is tongue in cheek, sorry for my irreverence ;-).* – gung - Reinstate Monica Dec 19 '12 at 02:34
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+1. Large numbers of digits seem to generate irreverent responses: see the last few lines of [my reply to a similar question](http://gis.stackexchange.com/questions/8650/how-to-measure-the-accuracy-of-latitude-and-longitude/8674#8674) on another SE site. – whuber May 30 '13 at 17:01
@gung How do you decide to represent the endpoints of the CI with two decimals? – user765195 Oct 28 '15 at 21:17
@user765195, I made those numbers up. The don't actually refer to anything. – gung - Reinstate Monica Oct 28 '15 at 21:28
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@gung What I was meaning to ask was that what is the precision of the end points of a CI? How many digits are valid, say, when you're calculating a Wilson CI for a binomial proportion? – user765195 Oct 28 '15 at 21:30
@user765195, I would just use however many seem reasonable at the time you're making the CI. – gung - Reinstate Monica Oct 28 '15 at 21:54
@gung Could you please explain for the case when the $p$ value is known, but the CI is not known? – caveman Dec 06 '16 at 05:11
@caveman, a p-value in isolation (ie w/o a CI) does not provide a direct estimate of precision. – gung - Reinstate Monica Dec 06 '16 at 12:20

score 12 · Answer 2 · answered Dec 19 '12 at 01:48

One reason for restricting the number of digits reported in many estimates, p-values, etc. is based on perception. Reporting something like p = 0.04872429 implies a level of precision in the results that causes them to be perceived as more accurate.

Essentially, the use of high numbers of digits in reporting statistical results tastes too many of trying to cloak your findings in an undeserved air of authority.

score 1 · Answer 3 · answered Dec 19 '12 at 10:55

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I think it really depends upon the level of confidence required, fewer digits for significance are appropriate for 95%, as opposed to 99.999% or greater, for example, as used by CERN for many of their results.

answered Dec 19 '12 at 10:55

Robert Jones

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For further elucidation, Wikipedia's article on Accuracy and Precision would make good reading for the original poster. – Robert Jones Jan 03 '13 at 14:14
that's a good point, but even when = .05 rounding in certain calculations can have a large effect on the outcome. – timothy.s.lau May 30 '13 at 16:59

score 1 · Answer 4 · answered Jan 02 '13 at 20:50

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Are you talking about rounding your data to some number of significant digits or rounding your final answer? If you round your data you can get into situations where you've thrown away noise that statistical calculations need to use.

answered Jan 02 '13 at 20:50

Emil Friedman

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I mean both final answers and mid-calculations are typically rounded even in textbooks. – timothy.s.lau May 30 '13 at 16:56

Why don't we use significant digits?

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