## Huge gap in my understanding [General Sta­tis­tics]

Dear ElMaestro,

Likely best to consider “lsmeans” as a predictor for a population value based on estimates from a model where the latter can be derived via maximum likelihood estimation.

“Lsmeans” allow making predictions for an average value of a co-variate (i.e. adjusted for the average value)
- see example above where predictions (i.e. “lsmeans” in SAS speak) for strength grouped by Machine were provided condition at diameter equal to 24.133 (i.e. adjusted for the average of diameter).

Prediction (i.e. lsmeans in SAS speak) can be also obtained for any a value of diameter (e.g. diameter=100) if this would make sense in a specific situation (e.g. consider a co-variate modeling a time course where you are interested in predictions at weeks 1, 2, or 3 at which no observations are available)

Best regards & hope this helps

Martin

PS.: A very nice summary is given here: https://cran.r-project.org/web/packages/doBy/vignettes/LSmeans.pdf

PPS.: In balanced multi-way designs or unbalanced 1-way designs I would expect identical values for observed means and "lsmeans"