Bioequivalence and Bioavailability Forum

Hello Angus,

❝ That leads me to question about Least Square Geometric Means. How is that determined then? Is that from "the mode" or the ANOVA. I am thinking it is from the ANOVA?

LS Means (it is questionable to call them LS Geometric Means) are determined from the b-vector of the model but only when you construct the model matrix as described above with 1's and 0's and when you opt out of the intercept and fit the factor of interest first; yes, I know, this is a cosmic mindf%cker but the sexy key word is 'contrast coding'.; try and look it up. I never found an explanation of it that made much sense to me, to be honest.
The LS Means can also be calculated directly - simple formula given by Chow & Liu.
Just think about it this way: For our purposes ls means for factor XYZ are the b-vector estimates that correspond to minimisation of the residual sums of squares.
Remember: The b-vector conveys an estimate of all the effects (constants) we work with: treatments, periods, sequences, subjects. Minus those lost to df-considerations.

Note also that the anova never determines effects (ls means or otherwise); those just come from the b-vector. A common -but not bad- misconception is also that the residual comes from the anova. It too comes from the model. The anova takes all the variance (all the variability) and tries to tell us where that variability comes from: treatment, sequence, subject, sequence or unaccounted for. Type I and Type III anova's are two different ways of getting the observed variability assigned to the factors. When things are balanced they are identical, by the way.