In article <[EMAIL PROTECTED]>, Steve <[EMAIL PROTECTED]> wrote: >The domain of interest is Psychology/Behavioral Sciences. The problem is >that many researchers will examine data for group mean differences across >factors that CANNOT be randomly assigned. This seems to violate a basic >assumption of ANOVA- random assignment to treatment groups.
Not necessarily. Randomization can be restricted (e.g. blocked designs). If absolutely *all* the assumptions of normality, linearity, form of the mean, etc. etc. hold, then the distributional results for the ANOVA hold even if you don't randomize. Randomization protects you against failures of these assumptions. (The quotation usually attributed to George Box that 'All models are wrong, but some are useful' is worth remembering.) You might find it interesting to read some of the early fundamental literature in experimantal design - e.g. Cox, Cochran & Cox, Kempthorne. I think that Kempthorne's book has a section where he derives the standard distributional results for one-way ANOVA as an approximation to the distribution under randomization only. >EXAMPLE (purely bogus- I'm making this up on the fly): Any ANOVA model with all fixed effects corresponds directly to a regression model, so use of MR does not guarantee anything. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
