CI = LSM ratio ± something [General Sta­tis­tics]

posted by Helmut Homepage – Vienna, Austria, 2011-12-30 16:49 (5282 d 09:04 ago) – Posting: # 7831
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Dear Paul!

❝ Could it be possible that the Least Squares Mean Ratio can fall outside the 90% confidence limits.


No, since the CI is calculated as (in log scale) \(\mathbf{{\color{Red} \mp}} \;t_{\alpha,df}\sqrt{\frac{2MSE}{(n_1+n_2)}}\).
\(\mathit{\Delta} = \bar{x}_T - \bar{x}_R\), where \(\bar{x}\) are the Least Squares Means (SAS-lingo; textbooks: adjusted means) of Test and Reference, \(t_{\alpha,df}\) is the tabulated value of the t-distribution (at α 0.05 and n1+n2–2 degrees of freedom), n1,2 the numbers of subjects in sequences 1 and 2, and MSE the estimated residual variance from ANOVA.
Note the !

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