Estimated marginal means refer to the estimated means for each level of a factor, adjusted for any other variables in the model.

Some key points about estimated marginal means:

- In a simple one-way ANOVA with no covariates, the estimated marginal means will be identical to the observed means for each group. But with unbalanced designs or inclusion of covariates, the estimated and observed means may differ ([2], [3], [4]).
- Estimated marginal means represent the model-based means for each level of a factor, adjusted for any other factors and covariates in the model. So they account for those other variables ([1], [4], [5]).
- The standard errors of the estimated marginal means are based on the Mean Squared Error from the ANOVA table, allowing for statistical tests and confidence intervals ([4]).
- Estimated marginal means can be obtained for complex designs with multiple factors and covariates. They provide a way to test differences among factor level means while accounting for other variables ([1], [5]).
- For reporting results, estimated marginal means are generally preferred over descriptive means, since they represent the factor level means adjusted for other modeled variables ([3], [4]).

So in summary, estimated marginal means provide a model-based estimate of the marginal means for each level of a factor, adjusted for any other variables included in the analysis. They allow for statistical tests of differences not confounded by correlations with other factors or covariates.

Citations:

[1] https://psych.hanover.edu/classes/ResearchMethods/jamovi/oneway/one-way-stats2.html

[2] https://stats.stackexchange.com/questions/404691/is-it-appropriate-to-use-estimated-marginal-means-when-model-estimates-are-not-s

[3] https://stats.stackexchange.com/questions/25276/estimated-marginal-means-or-means-from-descriptives

[4] https://www.theanalysisfactor.com/why-report-estimated-marginal-means-in-spss-glm/

[5] https://aaroncaldwell.us/SuperpowerBook/estimated-marginal-means.html

[6] https://www.youtube.com/watch?v=y-eHngU_rCg

[7] https://www.reddit.com/r/AcademicPsychology/comments/tu8180/estimated_marginal_means/?rdt=50632

[8] https://psych.unl.edu/psycrs/942/q2/2x2_factorial_142.pdf

[9] https://forum.jamovi.org/viewtopic.php?t=1646

[10] https://easystats.github.io/modelbased/articles/estimate_means.html

[11] https://cran.r-project.org/web/packages/emmeans/vignettes/basics.html

[12] https://jasp-stats.org/2020/04/14/the-wonderful-world-of-marginal-means/

[13] https://core.ecu.edu/wuenschk/spss/ANOVA2-SPSS.pdf