I don't know if this is the main cause, but it sounds like you're conflating binary outcomes and continuous outcomes. Your logit model is working on binary outcomes, but a t-test works on continuous outcomes. ... The difference between estimated means and arithmetic means may have to do with what the estimated means are reporting. That is, if they are being reported on the "link" scale, or on the "response" scale. Probably the best approach for this forum, would be to present a small reproducible example that shows the effect you are seeing.

Jonathan,

first of all I am wondering you have 16(!) readouts per subject, is that 8 per visit? If so, you need to consider aggregation before you run any descriptive statistics per visit. Otherwise you have way too small Stnadrda errors in the t-test since that test handles all observatiosn as independent ones, thus you have an inflation of the n used in the t-test.

Same time, the GLMM can handle the multiplemeasures per visit per subject if modelled accurately and you need to take care of that.

Note that GLMM appled to binomial using a logit link function (which is the right way to do) gives back estimated probilities for a certain outcome of the binary variable. Firstly, the discrepancy you see may arise from the fact that the GLMM does model the 0 outcome, rather than the 1 outcome (which is consider for the t-test) - check what is done in GLMM. Secondly, the GLMM estimates the probs taking the visits into account and therefore can be differnt from the crude rates. Thridly, should be set up as repeated measures analysis to account for the 2 visits analyzed within each subject. Check on that, too.

I would assume the difference stems from the 1st point, but the others should be checked too to get valid results.

Best,

John

J.-P. Lawo I have added more details to the question to make it clearer. It was 16 items per subject, in a single test.

The EMM's are reporting (approximately) the proportion incorrect.

515/(269+515)

# = 0.657

596/(172+596)

# = 0.776

Sal Mangiafico that's the proportion of incorrect.

The problem was that I had it set to ascending instead of descending. It's all resolved now!