Robert A LaBudde wrote:
At 05:49 PM 5/13/2009, Rob Knell wrote:
People
I apologise for asking a general stats question, but I'm at a bit of a
loss as to what to do following some hostile referees' comments. If I
have a fully randomised blocked design, with only three blocks, should
I treat block as a random or fixed effect? I have read comments about
not treating block as a random effect if the number of blocks is less
than 6 or 7: is this right?
Any advice much appreciated
Rob Knell
If you treat the variable as fixed effects, then inference will only
apply to those particular choices of blocks. If you treat the
variable as a random effect, you are probably going to estimate a
variance for a population distribution plus a mean effect, so
inference can be made to the population of all possible blocks.
The rule you've probably seen quoted could be paraphrased to say: If
you're trying to estimate a random effect (i.e., variance), you will
need at least 6 subjects, or you won't get any precision on the
estimate. For fewer than 6 subjects, you might as well give up on
modeling a random effect, and just settle for doing the fixed effects
model.
That being said, if you really need inferences on the population of
blocks, model the random effect and bite the bullet on the imprecision.
Also, remember the assumption that the blocks are chosen randomly
(from a normal distribution). If they're not, stick with the fixed
effects model.
It depends what you're doing.
If everything is normally distributed, (nearly) balanced, orthogonal, etc.,
and you can successfully use classical method-of-moments approaches to
ANOVA, then you have the choice whether to treat the 3 blocks as random or
fixed (although you will have a really bad estimate of the block variance).
If all of the above are not true, then you are almost guaranteed not to be
able to estimate the variance properly -- symptoms will range from an
estimated block variance of 0, to various warnings and errors. (The rule of
thumb quoted above applies.) See also Andrew Gelman, Analysis of variance:
why it is more important than ever for ammunition, if you need it ...
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