# Levels of significance for a publication

I hope this is not outside the scope of this community - in case, just sorry me.

I am going through adapting my manuscript to some author guidelines. Regarding p values, they say:

p values should be given to two significant figures, unless p<0.0001

Now, I have some doubts regarding what does this means. Here is a table with some examples and my guess:

Actual p value Round according to the author guidelines (my guess)
0.532 0.53
0.048 0.048
0.061 0.06
0.00021 <0.001
0.003 0.003

Do you think my "guesses" are correct interpretation of what "two significant figures" means? Or instead I am misinterpreting the request?

• (1) Why would you leave .048 as it is, but round .061 to .06? (2) .00021 is larger than .0001, so per the instruction, it should also be given with two significant figures, as .00021. Sep 14, 2022 at 15:49
• These guidelines (which are common -- they echo the APA style manual) should not blindly be followed. In some circumstances and in some communities it's important to report many more than 2 s.f. and sometimes p-values as low as $10^{-8}$ or so should not be censored. You should decide on the precision with which you report your results and defend your decision to the editors.
– whuber
Sep 14, 2022 at 16:39
• @whuber that's a great comment and a great advice. Sep 14, 2022 at 16:50
• @StephanKolassa because - and please note, I try to refrain from this - p=0.048 rounded become 0.05 and people (i.e., reviewers) start questioning statistical significance. Again, I am pretty aware of the issue here regarding choosing a cut-off for significance... the problem is that not everyone seems to be aware... Sep 14, 2022 at 16:52

To have two significant figures, $$0.06$$ should be written as $$0.61$$ (to rule out something like $$0.062$$), and $$0.003$$ should be written as $$0.0030$$ (to rule out something like $$0.0031$$).
Additionally, $$0.00021>0.0001$$, so that should be written as $$0.00021$$.