In the manuscript of a recent study we describe some post hoc tests, looking at the estimated marginal means of our linear mixed model in SPSS, applying a bonferroni correction.
Now our reviewers are asking us to specify what "test" was used. Is it correct to simply call these comparisons t-tests?
I believe they are conditional F tests:
https://books.google.co.uk/books?id=y54QDUTmvDcC&pg=PA91&lpg=PA91&dq=Conditional+F-tests+are+preferred+for+LMMs&source=bl&ots=L_RVeumUQV&sig=WlHM0ZNHY_ahZYqPU3Y0PbFaUxs&hl=en&sa=X&ved=2ahUKEwiAyIuQkNHeAhVRfMAKHaL_BrgQ6AEwAnoECAcQAQ#v=onepage&q&f=false
However, I believe they use a potential very liberal heuristic for determining df. Because the LMM test statistic doesn't really have an F distribution and because the df are inaccurate these tests may not be very accurate for inference. The exception is a fully balanced ANOVA fitted withe REML when they should be equivalent to an ANOVA F test assuming sphericity.
Thom Baguley
Thank you for your answer. I believe the conditional F test refers to the test ran by the LMM directly. I am wondering exactly what test is ran by the post hoc pairwise comparisons. These results do not provide a test statistic.
I have seen people suggest simply computing the test statistic using the mean difference and standard error. The resulting values do seem to somewhat match the p values on a t distribution but somehow I am unable to find a conclusive answer regarding the actual test used.
Yes - I think they are likely to be Wald-style t tests. As you suggest these are formed by the estimate / SE. The same issue applies in relation to the error df calculation - the true df is somewhere between 1 and n - k (where k is number of parameters) but not straightforward to infer.
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