Kempthorne uses the randomization-distribution and the assumption of unit treatment additivity to produce a derived linear model , very similar to the textbook model discussed previously.  The test statistics of this derived linear model are closely approximated by the test statistics of an appropriate normal linear model, according to approximation theorems and simulation studies.  However, there are differences. For example, the randomization-based analysis results in a small but (strictly) negative correlation between the observations.   In the randomization-based analysis, there is no assumption of a normal distribution and certainly no assumption of independence . On the contrary, the observations are dependent !
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One approach to controlling the Type I error rate with multiple contrasts is
simply not to perform the contrasts unless the overall effect is significant.
In other words, you don't ask where the differences are between groups
unless there is an overall difference between groups. Sounds reasonable,
but wait a moment! If there is no overall statistically significant difference
between groups, surely none of the contrasts will turn up significant? Yes,
it can happen! There's jitter in the p values, and there's nothing to say that
the p value for the overall effect is any more valid than the p value for individual
contrasts. So if you've set up your study with a particular contrast in mind--a
pre-planned contrast --go ahead and do that
contrast, regardless of the p value for the overall effect. Performing the pre-planned
contrast does not have to be contingent upon obtaining significance for the
overall effect. Those of us who prefer confidence intervals to p values can
understand why: the estimate of the difference between groups has a confidence
interval that may or may not overlap zero, and the confidence interval for the
overall effect (expressed in some measure of goodness of fit) may or may not
overlap zero. There is no need to reconcile the two.
Goodness of Fit
W hat statistic do we use to talk about how well the ANOVA model fits the data? It's not used that frequently, but you can extract an R 2 just like you do for a straight line. The R 2 represents how well all the levels of the grouping (nominal) variable fit the data. More about goodness of fit soon. Go to: Next · Previous · Contents · Search · Home editor
Last updated 2 Nov 03