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Started by jnewman
Thu, 15 Oct 1992 17:47
Are blocks fixed or random effects?
Author: jnewman
Date: Thu, 15 Oct 1992 17:47
Date: Thu, 15 Oct 1992 17:47
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Consider a two-way anova in which factor A has 4 levels and factor B has 8 levels and there are 3 replicates per treatment combination. If both treatments are fixed effects, then the error term for both main effects and the interaction is the subjects within treatments term which has 64 df. However, if treatment B is a random effect then the error term for testing A is the A*B interaction with 21 df, this is sometimes called a mixed model. Now, what if treatment B is really a blocking factor? Would B be considered a fixed or random effect. According to some psychology texts on the subject (e.g. Edwards: Experimental Design in Psychological Research, 5th ed, chapter 16) nearly all blocking factors must be considered random effects since we wish to draw inferences about the population of blocks, not just these particular blocks. On the other hand, experimental design texts in the agricultural field never mention the fact that blocks might be random effects. Our first question is: (1) Are there times in which blocks are clearly fixed effects and times in which they are clearly random effects? Following up on this are two questions relating to the case in which blocks are considered random effects: (2) Agricultural experimental design texts tend to recommend purposefully confounding the interaction and the subjects within treatments term by having only a single subject per treatment by block combination. This circumvents the issue of whether blocks are fixed or random effects because only one possible error term exists. Why is it `correct' to assume no interaction term in this case but not when the design is not confounded? Or, is it always our option to forget about the A*B interaction and use an error term with 85 df? (3) If the A*B interaction is included in the model but not found to be significant, can we substitute the subjects within treatment term in forming the F ratio? Thank you in advance for taking the time to answer these questions. Jonathan Newman Joy Bergelson Dept. of Zoology Dept. of Biology University of Oxford, UK Washington University, USA
Re: Are blocks fixed or random effects?
Author: Jerry Dallal
Date: Fri, 16 Oct 1992 17:13
Date: Fri, 16 Oct 1992 17:13
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In article <1992Oct15.184712.9572@vax.oxford.ac.uk>, jnewman@vax.oxford.ac.uk writes: > > (1) Are there times in which blocks are clearly fixed effects and > times in which they are clearly random effects? Yes. You stated the conditions. It depends on how you want to generalize. In my experience, they're almost always random. > > Following up on this are two questions relating to the case in which > blocks are considered random effects: > > (2) Agricultural experimental design texts tend to recommend > purposefully confounding the interaction and the subjects within > treatments term by having only a single subject per treatment by > block combination. This circumvents the issue of whether blocks are > fixed or random effects because only one possible error term exists. > Why is it `correct' to assume no interaction term in this case but not > when the design is not confounded? Or, is it always our option to > forget about the A*B interaction and use an error term with 85 df? > I'm not completely clear on what this says. In agricultural randomized blocks experiments there is one observation per combination of treatment and block, so the error term is the block*treatment interaction. Do *not* forget about the interaction unless you've got good reason to do so. > (3) If the A*B interaction is included in the model but not found to > be significant, can we substitute the subjects within treatment term > in forming the F ratio? > Do *not* pool unless you've got good reason to do so. You could try the analysis both ways. If pooling makes a difference, be wary. In theory, pooling in the absence of an interaction only increases your error df. They've got to be small to begin with for pooling to matter. Also, be wary of any technique that applies a significant test conditionally on the results of a prior test. Sorry for the "sound bite" answers but, as you've alredy noted, entire textbooks can be written about these issues. > Thank you in advance for taking the time to answer these questions. > > Jonathan Newman Joy Bergelson > Dept. of Zoology Dept. of Biology > University of Oxford, UK Washington University, USA
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