[R-sig-ME] repeated measures OR block with time covariate?

Prew, Paul Paul.Prew at ecolab.com
Wed May 20 03:51:44 CEST 2009

I've received helpful advice in the past from the readers of this list, and would like some more advice.  I think I understand that a blocking / nuisance factor in ANOVA will not affect the significance estimates of fixed factors / 'factors of interest', regardless of whether the blocking factor is designed as random or fixed --- the same sum-of-squares are taken off the top in ANOVA.  Other quantities may be affected, such as prediction intervals for specified levels of the fixed factor.  Fixed block effects are welcome, because virtually all the literature in experimental design treats Randomized Complete Block Designs as having fixed effects for blocks.
In a discussion with a colleague today, the following question was posed about repeated measures ~
A cleaning product is being tested at a sample of hospitals.  Micro-organism counts are taken over a period of weeks, for a control formulation and an experimental formulation.  The hospitals are not of interest, and can be considered blocking factors.  So my interpretation is that there's no harm in designating the hospitals as a fixed effect.  
Within the hospital, we can see week-over-week reductions in micro-organisms.    There's a slope related to time.  
*****   Could a fixed effect for the blocking factor Hospital and a fixed covariate Time take the place of what seems to be a good candidate for a repeated measures analysis (assuming that the repeated measures implies Hospital = random effect)?  *****
Any thought are greatly appreciated.  There's actually a Standard Operating Procedure being written for our scientists and engineers designating they use the repeated measures analysis.  I think it's over their heads, given that few could credibly define degrees of freedom, p-value, or other basic statistical concepts.  An approach that sticks to the "Randomized Complete Block Designs / fixed effects for blocks" is better suited, if it performs as well as the repeated measures design.
Regards, Paul
 Paul Prew  |  Statistician
 651-795-5942   |   fax 651-204-7504
 Ecolab Research Center  | Mail Stop ESC-F4412-A
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