Starting at the top: The solution vector is what is used to create the least squares means.  I find it useful if I need an estimate and standard error of a continuous covariate.  Otherwise, the latter two are more useful. The Type3 F tests are testing to see if at least one mean is different from all the others in that effect (main or interaction). This is the primary test of "significance' for an effect. The LSM (least squares means) tells you what the expected values are for each of the levels of the effects.  Using the diffs option allows you to test if one particular mean is "significantly' different from another.   I don't know what you mean by more powerful.  Do you mean which had a greater effect on the mean?  That is generally what Cohen's D is all about.  However, mixed models don't really lend themselves to calculating effect sizes. If you really want to look at something like it, add the /diff option to the lsmeans statement. The results table should present the t values for each comparison.  This is a ratio of the difference to the standard error of the difference.  Cohen's D is a ratio of the difference to the standard deviation of the reference group, so they should be analogous in direction.   SteveDenham ... View more