## Even in 2x2... [General Sta­tis­tics]

❝ ... But we see a similar effect with the EMA’s Method A above, which is a bloody ANOVA and all effects fixed. I don’t get it.

Dear all,

the reason of the difference is that sequences were unbalanced (not equal number of subjects in each of the sequences).
As you know (for ln-transformed data) the estimated marginal means (i.e. least squares means in SAS terminology) differ from arithmetic means of T and R if sequences are unbalanced.
The way of calculation of the estimated marginal means involves some modification of "standard" marginal means. I'm lazy to go through the matrix algebra (which is used by most of the softwares), so simply: marginal means are "corrected" to estimated marginal means by using a difference between mean of all data and mean of marginal means of T and R (when the sequences are balanced then this difference is zero).

Personally I would not report these least squares means at all. If you are calculating ANOVA (e.g. by GLM) you get point estimate directly, i.e. without calculation of least squares means.

For unbalanced sequences there might be more questions ... together with misleading terminology - e.g. geometric means ratio - for unbalanced sequences, the ratio of geometric means reported in descriptive statistics differ from geometric means ratio reported with 90% confidence interval which is also very, very strange. As these ratios are different, somoone wants to have the "correct" geometric means of T and R for which the ratio T/R is equal to point estimate (i.e. somoone wants "geometric least squares means"). Nevertheless geometric means are geometric means! Behind geometric least squares means I see only values of "T" and "R", for which (by dividing) we get the point estimate. But as it was pointed out, least squares mean of T can be affected by R, and vice versa.

Best regards,
zizou  Ing. Helmut Schütz 