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 ;) ?
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asked Dec 19, 2012 at 1:31
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1$\begingroup$ Readers may also find this thread: number-of-significant-figures-to-put-in-a-table of interest. $\endgroup$– gung - Reinstate MonicaDec 28, 2012 at 22:17
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$\begingroup$ I found this informative: davegiles.blogspot.com/2011/12/… $\endgroup$– JohnJan 2, 2013 at 21:41
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$\begingroup$ An example of where paying attention to significant digits really matters appears at 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. $\endgroup$– whuber ♦Sep 1, 2014 at 19:16
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4 Answers
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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, 2012 at 2:32
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$\begingroup$ (The last part is tongue in cheek, sorry for my irreverence ;-). $\endgroup$ Dec 19, 2012 at 2:34
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2$\begingroup$ +1. Large numbers of digits seem to generate irreverent responses: see the last few lines of my reply to a similar question on another SE site. $\endgroup$– whuber ♦May 30, 2013 at 17:01
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$\begingroup$ @gung How do you decide to represent the endpoints of the CI with two decimals? $\endgroup$ Oct 28, 2015 at 21:17
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$\begingroup$ @user765195, I made those numbers up. The don't actually refer to anything. $\endgroup$ Oct 28, 2015 at 21:28
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1$\begingroup$ @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? $\endgroup$ Oct 28, 2015 at 21:30
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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.
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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.
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$\begingroup$ I mean both final answers and mid-calculations are typically rounded even in textbooks. $\endgroup$ May 30, 2013 at 16:56
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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, 2012 at 10:55
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$\begingroup$ For further elucidation, Wikipedia's article on Accuracy and Precision would make good reading for the original poster. $\endgroup$ Jan 3, 2013 at 14:14
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$\begingroup$ that's a good point, but even when 𝛂 = .05 rounding in certain calculations can have a large effect on the outcome. $\endgroup$ May 30, 2013 at 16:59