total (pooled) variance: examples [Power / Sample Size]

posted by zizou – Plzeň, Czech Republic, 2023-04-26 00:43 (159 d 06:46 ago) – Posting: # 23540
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(edited by on 2023-04-26 19:05)

Dear BEQool, well done! :thumb up:

❝ So it seems that the denominator is affected by whether the model is complete or incomplete.

Thank you for correcting me. I didn’t remember it correctly. I was sure about denominator equal to 3 in “All at Once” approach (i.e. one ANOVA). The another (better) approach I didn’t use for past several years and I forgot the details like the denominator used. Sorry for the confusion. So it seems the denominator is equal to the number of treatments in evaluation. :ok:

Btw. total (pooled) CV in 2x2x2 can also be obtained by fitting the model with factors Formulations, Periods, Sequences (i.e. without Subjects(Sequences)). Then use MSE in equation:
CV=sqrt(e^(MSE)-1) (multiplicative model with residual variance sigma^2 which is estimated by MSE from ANOVA)
For parallel design, it's trivial and only the total (pooled) CV can be obtained.
For higher-order designs with more than two formulations I never tried it but it could be another option for recalculation.

❝ ... it could happen with real-world data as well?

Sometimes (not often) it happens. It was discussed e.g. in this thread.

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