Same value P-Values - Holm-Bonferroni When using a Holm-Bonferroni adjustment method or the like, how to you treat multiple p-values of the same value when ranking?
For instance, I have the unadjusted p-values:
2.20E-16
2.20E-16
0.001387
0.03591
0.148
0.4517

Should both 2.20E-16 values be treated as rank (1) and if so, should the 0.001387 value be rank (2) or (3)? Or should one of the 2.20E-16 values be (1) and the other (2), which would make the 0.001387 value (3)?
Cheers
 A: In the Holm approach, you immediately stop as soon a p value is above its treshold. So it does not matter.  
Since Holm-correction is just for decision making and not for creating p values, in your situation nothing changes anyway if you flip the order of the first. 
Here are two more interesting situations.
Situation 1
P values are 0.02, 0.02, 0.03
The smallest p value times 3 is above alpha 0.05. So the algo stops and all tests are non-significant. Same if you switch identical p values.
Situation 2
P values are 0.01, 0.01, 0.03
The smallest p value times 3 is below 0.05. So the algo continues with the next smallest p value times 2 (okay) etc. All tests are significant. Same if you switch identical p values.
A: The only difference it makes is in terms of the adjusted p-values, not in terms of whether the tests are significant. I have never seen a proposal for exactly how to do this and it probably does not matter too much (never mind getting too obsessed about statistical significance - getting into comparing the size of "significant" p-values is certainly completely pointless).
If you are in a situation, where two p-values are exactly the same and the associated null hypotheses are getting rejected, then I would be tempted to go with the option of adjusting each one as if it had been rejected before the other. This is in a sense the "conservative" approach in that it results in higher p-values compared to, say, randomly picking one of them to have been rejected first. Doing so does not change anything else for any other tests.
