adjusted means (aka LSMs) [Study Per­for­mance]

posted by Helmut Homepage – Vienna, Austria, 2014-07-27 04:23 (3994 d 11:46 ago) – Posting: # 13318
Views: 18,992

HI Khaoula,

❝ the software […] take this rule: [image] (it's false)


Yes, it’s wrong. Where did you find this formula? You would get a negative value for the root. Maybe Kinetica uses (also wrongly) CV% = 100√MSE² – 1 which would give 4.72% – at least closer to your original 3.47% – no idea. It’s not my job to un­veil all potential bugs in a software I neither seriously used nor validated myself…

❝ but for GMR, I'm really confused, It's an unbalenced cross over so you told me to use the least squares (or adjusted) means instead I read this post


❝ I have'nt found the same result (1,21), but 1,18 like kinetica v4... where is the problem?


Again, no idea. How did you calculate a GMR of 1.21? Your corrected log-transformed data gives a LSM for the reference of 6.1477 and for the test 6.3125. These values are derived exactly as I stated in my old post.

subj seq form per logCmax  subj seq form per logCmax
────────────────────────────────────────────────────
  1   RT   R   1   6.6399    3   TR   R   2   6.4505
  2   RT   R   1   5.7104    4   TR   R   2   6.1485
  7   RT   R   1   5.7268    5   TR   R   2   6.3439
  8   RT   R   1   5.8944    6   TR   R   2   6.2634
  9   RT   R   1   5.4931   11   TR   R   2   5.9162
 10   RT   R   1   6.0379   12   TR   R   2   6.5582
 14   RT   R   1   6.6399   13   TR   R   2   7.0733
 15   RT?                   16   TR   R   2   5.4467
────────────────────────────────────────────────────
               x   6.0203                 x   6.2751


subj seq form per logCmax  subj seq form per logCmax
────────────────────────────────────────────────────
  1   RT   T   2   6.6134    3   TR   T   1   6.6529
  2   RT   T   2   5.3753    4   TR   T   1   6.4425
  7   RT   T   2   5.4806    5   TR   T   1   6.3386
  8   RT   T   2   6.2748    6   TR   T   1   6.3026
  9   RT   T   2   6.2500   11   TR   T   1   6.5568
 10   RT   T   2   6.3491   12   TR   T   1   6.5425
 14   RT   T   2   6.6134   13   TR   T   1   7.2442
 15   RT?                   16   TR   T   1   5.8260
────────────────────────────────────────────────────
               x   6.1367                 x   6.4883


Mean of R in sequence RT is 6.0203 and in sequence TR is 6.2751. LSM = (xRT+xTR)/2 = 6.1477. 
Similarily we get the LSM of the test 6.3125.
Backtransformed LSMs are ℯ6.1477 = 467.64 (R) and ℯ6.3125 = 551.40 (T). Therefore, the GMR is 551.40/467.64 = 1.1791, agreeing with what PHX/WNL reports.


PS: Sometimes in study reports the geometric means of treatments and results of the ANOVA are given in the same table (without the LSMs). Then – if the study was not balanced – people are confused, since the ratio of geometric means does not match the point estimate (calculated from the LSMs). Here the backtransformed geometric means are 471.64 (R) and 557.90 (T). Wrongly calculating the ratio 557.90/471.64 = 1.1829 1.1791…

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