How to report a P-value? I am writing the results of my thesis, and I have a few questions on how to report P-values.

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*When is it appropriate to give the exact P-value, instead of writing e.g. P<0.05 (also in case of non-significant P-values)?

*If I have a P-value of e.g. 0.016, should I report it as P=0.01 or P=0.02? Or if it was 0.0167, should I write 0.016 or 0.017?

*When I have a very small P-value, e.g. 0.00000013, is it appropriate to report it as P<0.000001, or is it better to stop at e.g. P<0.001?


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*In practice, people report the exact p-value then declare whether the hypothesis test is statistically significant. Most statisticians don't advocate this. if the goal is hypothesis testing then reporting the p-value is moot because it doesn't make the test more significant, on the other hand the exact p-value matters if the result of the analysis doesn't boil down to a decision theoretic approach. So if the audience is not statisticians, they would probably expect you to do it the wrong way.


*The significant digits on a p-value matters. First, you have to follow whatever style guide there is for your thesis or publication. If there are no rules, you need to consider the variability of the analysis. In general, it's hard to say how "stable" a p-value is without simulation or bootstrapping, but you'll often find that even with a huge analysis, a p-value is only really stable out to two decimal places - hence reporting 3 decimal places conveys a level of precision that is not present in the analysis. Secondly, if there is a pre-specified "alpha" level, you need to show enough precision for the reader to know whether p < alpha. In other words, p=0.05 requires two decimal places of precision if p = 0.04 or lower, but borderline cases get awkward. Do you say p = 0.049994 or p = 0.05 but it was statistically significant.


*Don't cheat the incidental precision of the analysis. Use the prespecified precision following the rules above, and report out to the smallest decimal. Other aspects of the analysis should convey how striking the result is, a "really small p-value" in and of itself means nothing. And never never report p = 0.00.
