P-values

[Sidra Ilyas]

Hi Dear,

1) If a test e.g. a t-test is conducted at 95 % confidence level, and we get p-values such as 0.0519 and 0.0450, is it OK to round them to 2 decimal points to make an inference? Just in case if it matters, the inference would be related to some analysis in Economics field.

2) If we can possibly round them, then in case of the above mentioned values being exactly at 5 %, what is a common and most acceptable practice in terms of acceptance or rejection of null hypothesis? P-value exactly at 5 % accepts or rejects the null hypothesis of a test conducted at 95 % confidence level?

I have already done my google search, but I am still inclusive about it. Therefore, I request for the opinions here.

Thank you.

[Zhang xiangyang]

i meet the same question as you，（

p-values such as 0.0519 and 0.0450），0.0519≈0.05？

[Nick Cox]

Rounding from 0.0519 to 0.05 is to me defensible if you are just reporting but quite wrong if you have a decision rule to reject if P < 0.05. You chose a rule: no cheating even in borderline cases.

As discussed in earlier threads the P-value is dubious any way if the test assumptions don’t match the data, but that is a different issue.

You are working with a 5% significance level: dragging in extra wording about a 95% confidence level is at best awkward and indeed best avoided.

[Sidra Ilyas]

Thanks Nick.

Actually I personally use the term 5 % significance level. But the Stata document about t tests used confidence level that's why it came in my initial post. So, if I say it would be very basic to know for me, aren't they two different expressions for the same thing?

Also, if we choose a 5 % significance level, do we choose it ourselves whether we treat a p value exactly at 0.05 as rejecting or accepting the null. Is there no common or widely adopted practice for it?

Thanks again.

[Nick Cox]

Exactly 0.050000000000.... I will worry about if I ever see it reported. In practice asking for more decimal places usually resolves any issue. But this kind of question underlines the absurdity of sharp tests, another wider issue.

Sure, associated with t tests are confidence intervals for a difference between means — and indeed they often deserve more attention than the test result. But whenever I see in student writing and in papers for review wording phrases such as “testing at the 95% confidence level” I have to advise against it. Not the case here, but there are plenty of tests without associated confidence procedures.

[Nick Cox]

Here is a longer statement from a review of mine of a bad text at https://www.amazon.com/product-reviews/3540436030

Having presumably noted that a result significant at the 5% level often
corresponds to one lying outside a 95% confidence interval, Borradaile
uses expressions such as `significant at the 95% confidence level'.
There are several good reasons to avoid this usage completely. First,
there are significance tests not associated with a confidence interval
procedure. Second, it will seem at best sloppy and at worst wrong to
those familiar with standard usage. Third, any omission of the word
`confidence' produces talk of significance at the 95% level (pp. 149,
151, 153, 158, 161--162, 164--170, 191, 192, 284). Elsewhere occur
examples of the 5% confidence level (p.91) and the 5% significance level
(p.171). Naturally, some of these usages are possibly just typos, but
careless proof-reading has the same effect as careless writing.