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Many stats packages allow you to view the adjusted means/marginal means/predicted values of a model (e.g., R's lsmeans, Stata's 'margins', SPSS's 'Estimated Marginal Means'; for more info., see https://www3.nd.edu/~rwilliam/stats/Margins01.pdf).

Marginal means are often presented with a t/z value, a p value, and confidence intervals.

1) Are these one-sample tests?

2) What is their importance? If, for instance, I have a marginal mean which does not reach the threshold of significance, can I still use it to describe my data? What does it mean if it is not significant? (ignore the dubiousness of null hypothesis significance testing for the sake of the question, since they still dominate many journals in the psychological sciences).

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    $\begingroup$ 1. Probably not; most programs report two-sided P values by default (if not, how would it guess which tail you want to test?) 2. There is no law that says you have to test anything; you can just report estimates; I suggest including confidence limits as well, and explaining exactly what you are showing. $\endgroup$
    – Russ Lenth
    May 23 '17 at 1:46
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    $\begingroup$ OK. I tend to hesitate posting answers, but I'll see how it flies. $\endgroup$
    – Russ Lenth
    May 23 '17 at 12:50
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There is no law that says you have to test anything; you can just report estimates. I suggest including confidence limits as well, and explaining exactly what you are showing.

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  • $\begingroup$ Thanks for that, Russel. If that is the case, why include them as defaults across stats packages? (including lsmeans ;-)) It gives me the impression that non-significant marginal means should be viewed critically. I just wondered what the significance test means in the broader sense of the model, e.g., this mean has been adjusted for the intercept and covariates in the model. $\endgroup$ May 23 '17 at 20:49
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    $\begingroup$ I don't think a significance test or CI of an EMM means much of anything in terms of assessing he model. It is just a prediction (or average of predictions) from the model at each level of a factor, with covariate(s) set at their average values. The vignette in the R lsmeans package discusses this some and provides some references. Also look at the section on mediating covariates for discussion of cases where such adjusted means are inappropriate. $\endgroup$
    – Russ Lenth
    May 24 '17 at 1:46
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    $\begingroup$ I'll also mention that the defaults in R lsmeans are to show CIs (not tests) for the EMMs, and to show tests (not CIs) for contrasts thereof. Those defaults were chosen based on perceptions of what most users want. $\endgroup$
    – Russ Lenth
    May 24 '17 at 13:38

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