# PMean: The unthinking approach to borderline p-values

## 2017-10-19

I ran across a nice discussion of how to write the results section of a research paper, but it has one comment about the phrase “trend towards significance” that I had to disagree with. So I wrote a comment that they may or may not end up publishing (note: it did look like the published my comment, but it’s a bit tricky to find).

Here’s what I submitted.

I have to disagree with one comment. “Never attempt to describe results that fail to achieve significance at the a priori threshold for statistical significance, such as suggesting that the results ‘approached significance’ or displayed a ‘trend towards significance.'” There is a belief in some circles that a p-value of 0.04 tells you something that is radically different than a p-value of 0.06. Both represent findings that should be reported, but treated with caution. I would much rather put my faith in a p-value of 0.06 that has a solid mechanistic explanation than one of 0.04 that appears to defy any scientific rationale. Similarly, I would trust a p-value of 0.06 that was associated with other closely related outcome measures that did achieve statistical significance than a p-value of 0.04 that was surrounded by other similar outcome measures that failed to achieve statistical significance.

Context is critical in interpretation of p-values. Unfortunately most scientists do not allow the context of a finding to enter into the discussion of borderline p-values (either the 0.06 p-value or the 0.04 p-value) out of a fear of violating some sacrosanct edict of research conduct.

It seems that every scientist has a p-value receptor in their brain. It stimulates the pleasure center when it encounters a p-value less than 0.05 and it stimulates the pain center when it encounters a p-value greater than 0.05. But no matter what the value, the p-value receptor also shuts down all other areas of the scientist’s brain once it encounters a p-value of any size. And arguing that p-values on the “wrong” side of an arbitrary Type I error rate of 0.05 should be discussed only as a negative result encourages this sort of unthinking approach to p-values.

At a minimum, look at the confidence interval for a “negative” finding. If it includes the null value but also includes values that are considered clinically important, then you should describe the result as being one that warrants further study with a larger sample size.

Other than this one complaint, I think it is a very good article.