I have been struggling to reconcile my (very basic) understanding of P-values with the approach of one of my colleagues and it appears to come down to interpretation of p-value terminology. This is having a knock-on effect on the correct implementation of a Holm-Bonferroni correction - any advice would be welcome!
The problem is this:
We have run a statistical test to look at whether the expected number of observations is higher or lower than expected - thus it is a two tailed test (<2.5% or >97.5%). The number of observations was converted to a z-score (<-1.96 or >1.96) and then into a probability (P). For our reporting we had two options:
- Report the P-value as rejected if P<2.5% or P>97.5%
- Convert the P-value into a one-tailed value and reject if its P<5%
The issue arises because my colleague believes the following:
Option 2 is the more widely used definition. When we see "two-tailed p-value" referred to, this is usually what is meant. And when we apply Holm-Bonferroni, it is expecting rejection to correspond to p-value below 5%, so we need this form of the p-value.
What we report as a p-value under option 1 is what would universally be reported as the p-value for a one-tailed test, so can be referred to as a "one-tailed" p-value. The p-value under option 2 is what would generally be referred to as a "two-tailed" p-value, i.e. a p-value which has been converted to reflect the fact that the test is being run as a two-tailed test.
This is something I am struggling with - is this actually true because it seems completely counter-intuitive to me? I can find nothing on the internet to suggest that this is the case either.
This interpretation is critical because we go on to perform a Holm-Bonferroni correction (there are > 50 tests in total), which requires (what I understand to be) one-sided style P-values (P<5%) - thus I believe that our 'two-sided' p-value from option 1 should be divided by 2 (0.5*P or 0.5*(1-P)) to convert it appropriately before running the test. however my colleague believes it should be multiplied by 2 (2*P or 2*(1-P)) because Option 1 is actually known as a 'one-sided' value...
Can anyone offer any guidance on this to me as what I thought was a relatively simple concept is now confusing me greatly!