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Let's say I am performing a three-way ANOVA to reveal the effects of "age" (5 levels), "gender" (2 levels), and "study time" (10 levels) on a test score.

I can perform this three-way ANOVA using MATLAB's anovan function (I am using sums of squares type II, because I am only interested in main effects):

[p, tbl, stats, terms] = anovan(testScore, [age, gender, studyTime], 'varnames', {'age'; 'gender'; 'studyTime'}, 'sstype', 2, 'model', 'linear');

Afterwards, I can use MATLAB's multcompare function to perform post-hoc tests:

[comparison, m] = multcompare(stats, 'display', 'off', 'dimension', 1);

Could someone explain to me in detail, what the first column of the output "m" contains? MATLAB's help says that "m" contains the "estimates and their standard errors" - but how are these estimates actually computed? Would it be correct to say that they are the level means of a given factor when accounting for the influence of the other factors?

Thanks in advance!

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