# What does “pairwise p-value” mean without any specified tests?

I am reading a paper that reports "pairwise p-value"s. If someone reports "pairwise p-value" for 4 pair of values without telling anything about the performed statistical tests, does this make any sense? Is there an assumption of a specific test that automatically comes with the "pairwise p-value" terminology?

Additional info from my comment below: The authors of the paper mention that they are testing whether the mean of the first set in the pair is smaller than the mean of the second set in the pair. Maybe then "pairwise p-value" automatically means the p-value from a paired t-test since t-test is the simplest thing to test for whether the means of two pair of values are different or not?

• Is the author perhaps implying a multiple testing correction has been applied (e.g. Bonferroni)? – Frans Rodenburg Oct 6 '17 at 3:30
• I think there are no multiple hypothesis here, just one, so I think they don't mean Bonferroni. They mention that they are testing whether the mean of the first set in the pair is smaller than the mean of the second set in the pair. Maybe then "pairwise p-value" automatically means the p-value from a paired t-test since t-test is the simplest thing to test for whether the means of two pair of values are different or not? – user5054 Oct 6 '17 at 3:34

Without mention of the type of test performed and without multiple 'pairs' of comparisons, a 'pairwise $p$-value' could describe any $p$-value arising from a test for location shift between two groups. Most commonly, this is a $t$-test, which compares means (as you pointed out in the comments, means are compared). Other tests for location shift include non-parametric alternatives, such as the Wilcoxon rank sum test.

Since you mentioned the author indicates testing for whether one group is smaller than the other, this would be the $p$-value of a one-sided test. But it could still be a paired/ unpaired, equal variance/Welch $t$-test or even a different test entirely.

Pairwise vs Paired
The word pairwise refers to the pair of groups being compared, so without further information, I do not believe there is a reason to assume this concerns a paired test, where both samples are measurements from the same group.

Edit
As David Ernst pointed out, the use of pairwise instead of paired may simply have been a mistake on the author's side.

• Perhaps mention more explicitly the possibility that the author of the paper got the notions of paired and pairwise confused or made a simple typo. – David Ernst Oct 6 '17 at 8:16

It does make sense, but there's not much information:

• You know the author made four pairwise tests, but you don't know they are independent or not
• You don't know anything about the null hypothesis
• You can't assume any specific test, there're many pairwise tests in statistics!

Generally, it means something like post-hoc test in ANOVA (https://onlinecourses.science.psu.edu/stat200/node/158) in the litetature, but you should double check.

• I edited my question. They are in fact comparing means, they state that. Does that modify your response? – user5054 Oct 6 '17 at 6:09