[carbor1]

No, not necessarily. It's standard practice to pick a p-value significance cut-off (0.05), but report the smallest such standard cut-off that any particular value meets. So "p < 0.001" is reported for values that meet that threshold. Anything over the cut-off is just not reported as significant.

[j2kun]

That seems dishonest to me. They're saying that some results are more significant after the fact. Is there any mathematical justification for why this is OK?

[dx034]

As far as I know there is not. There is no such thing as "more significant", results either are significant or they're not.

[carbor1]

That being said, the authors are doing a lot of comparisons here! They ought to be reporting Dunn-Bonferroni corrected p-values.