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I would like help deciding how to report my results.

I am looking at whether different demonstrations affect performance in a forced-choice binary task. Demonstrations were done either by a puppet or live (social conditions) or by the participant (individual condition). I used a GLMM in lme4 with a fixed effect of demonstration type, which was structured as a Helmert contrast: levels were puppet demo, live demo, and own demo.

The output of the GLMM indicated that there was a main effect of demonstration, with a difference between the puppet and live demos (but not between those two and the own demo).

To report this result most clearly & accurately, should I use the model output from lme4 and lmerTest (b, SE, Z, p)? Or should I explicitly run post hoc tests in e.g. multcomp or emmeans, and report the results of those? The comparisons of interest (puppet vs. live and puppet-live vs. own) seem to me to have already been made in the GLMM, in which case that should be sufficient. Is there some reason to do post hocs? Finally, is there an issue with multiple comparisons when doing GLMMs with Helmert contrasts?

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In most cases, I’d recommend displaying the estimated marginal means and their confidence intervals — e.g., via emmeans() — or displaying them graphically.

And also show the pairwise comparisons among them, with the Tukey adjusted P values. (Just show the P values, let people decide for themselves what’s important.)

If you do regard one particular factor level as a control, it may be enough to show just the comparisons with control, with a Dunnett adjustment. But that precludes making other comparisons among treatment levels.

I don’t think the Helmer’s comparisons are enough for most readers. And please avoid making careless statements like “there is no difference.” Null findings are weak; they do not imply equality.

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