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I'm working on a scientific paper in which goodness-of-fit and a parameter are estimated by a $\chi^2$ minimization, and I'd like to know whether there is a general rule for how many significant figures one should quote for the value of the $\chi^2$ and its resulting P-value.

In particular I'm fitting one parameter from data in 31 bins, each with its contents in the gaussian regime. I'd guess the precision of my minimization algorithm is not the limiting factor (my code spits out $\chi^2$ = 38.8898 / 30, so the P-value is something like 0.1282) for signifcant figures, but what is? Is it the number of degrees of freedom? The degree to which the gaussian assumption is invalid in the least-populated bin(s)? Most papers I see typically quote to tenths in $\chi^2$ (so 38.9 / 30 in my case) and hundredths in P-value (0.13 for me), but I'm not sure if that's always reasonable.

P.S.- I'd like to apologize if any terminology I used is funny: in physics we use annoyingly non-standard terms when discussing statistics.

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  • $\begingroup$ "whether there is a general rule for how many significant figures one should quote for the value of the χ2 and its resulting P-value" - such things are likely to be specific to the journal. The defaults you suggest (1dp for χ2, 2 for p) seem fine to me. $\endgroup$ – Glen_b♦ Dec 15 '12 at 6:47
  • $\begingroup$ In my particular case I don't believe there is an explicit guideline, but I do appreciate that there is a degree of subjectivity here. However the main thrust of my question is really whether or not there is some theoretical way of determining the precision of those values. For example if you add two measured values 2.5 ± 0.2 and 3.03 ± 0.01, you are truly ignorant of the hundredths digit of the sum due to the larger uncertainty on 2.5. My main concern is whether there is a way to determine such a(n) (im)precision in the $\chi^2$ and P values based on the inputs. $\endgroup$ – Kevinismus Dec 15 '12 at 23:06
  • $\begingroup$ CLearly, if your data are only to a few figures, you have to understand the subsequent fuzziness in your results, and that may reduce the number of meaningful figures further. You can certainly carry such calculations through, but in any case, such errors tend to be small in effect compared to the fact that even precisely recorded data (say to 5 or 6 sig. figures) are noisy in the first place, and the models applied are wrong, and so even if you have precise calculations from such data, it still usually doesn't make any sense to quote more than a few figures. $\endgroup$ – Glen_b♦ Dec 15 '12 at 23:29
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Those things are data summaries, so one way to decide on significant figures is to keep whittling them down until the summary starts to lack adequate precision or seems unreasonable. I know that that response is not very specific, but consider this: no-one would respond differently to P = 0.13 from P=0.1282. For the Chisq value, I would whittle it down as far as you did, or further if the rounded value still yields the P = 0.13.

There is a paper in The American Statistician which talks about the precision of P-values. I don't agree with all that it says, but it is relevant to your question: Boos & Stefanski, The American Statistician, 2011, 65, 213

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