So I was trying to find an article with statistics in it that I could have my intro stats students reproduce as an assignment.  So I went to PloS Medicine and randomly chose a recent paper.  I can across this one: http://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.1001807#pmed-1001807-t001

I was going to have my student reproduce the numbers in this paragraph in the results section:

As described above, GII VLPs were distinct from the GI VLPs at 7 d post-vaccination. Interestingly, the GII.4C VLP (representing the vaccine component) associated much more closely with the early GII.4 VLPs than with either the late GII.4 VLPs or the GII VLPs from other genotypes (ANOVA: F_2,4 = 14.74, p = 0.0143), showing that the IgG response to GII.4C vaccination is highly cross-reactive with the early GII.4 VLPs but not the antigenically distinct contemporary GII.4 VLPs or other GII VLPs. Even as late as 180 d post-vaccination (Fig. 9G–I), clustering by genogroup (or by subclades within genogroups) remained (t-test: t₅₃ = 23.96, p < 0.001), although overall distances (dissimilarities) in IgG responses differentiating between VLPs had decreased compared to day 7. Specifically, the GI viruses clustered relative to the other virus strains (t₂₅ = 11.32, p = 0.0024), GII.4C continued to cluster with GII.4.1997 and GII.4.2002 (t₂₅ = 8.973, p = 0.0061), and the contemporary GII.4 VLPs remained tightly clustered with the other GII genotypes (t₃₈ = 19.24, p < 0.001). Interestingly, and echoing our findings above, GII.4.1997 remained somewhat distinct from GII.4C and GII.4.2002 (Fig. 9G–I) because of the elevated levels of IgG against GII.4.1997 VLP still found in several of the vaccine recipients 6 mo post-vaccination.

…but I can’t reproduce the numbers myself.  I can reproduce the p-value for the ANOVA (0.0143), but I can’t reproduce any of the p-values for the t-tests.  For instance, with a t-test statistic of 8.973 with 25 degrees of freedom, I get a two-sided p-value of 0.00000000272 as opposed to the stated p-value of 0.0061.  Am I missing something obvious?  Or are these p-values all wrong?

Follow-up question: If (IF!) the p-values are all wrong, as I suspect, should I still assign it to my students and ask them to reproduce the numbers as a lesson that they shouldn’t trust every statistics they see?

Cheers!