Post Hoc Tests
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ANOVA Hypotheses:
You will recall, that in ANOVA the null and alternative hypotheses
are:
When the null hypothesis is rejected you conclude that
the means are not all the same. But we are left with the
question of which means are different?
T-Tests can't be used
We can't answer this question in the obvious way (using T-Tests
on the various pairs of groups) because we would get too "rosy"
a picture of the significance (for reasons I don't go into).
Post Hoc tests help give us an answer to the question
of which means are different. The Post Hoc tests gaurantee
we don't get too "rosy" a picture (actually, they provide
a picture that is too "glum"!).
Post Hoc tests
Post Hoc tests are done "after the fact": i.e., after the
ANOVA is done and has shown us that there are indeed differences
amongst the means. Specifically, Post Hoc tests are done when:
- you reject Ho, and
- there are 3 or more treatments (groups).
A Post Hoc test enables you to go back through the data and
compare the individual treatments two at a time, and to do
this in a way which provides the appropriate alpha level.
Two Post Hoc tests are commonly used (although ViSta doesn't
offer any Post Hoc tests):
- Tukey's HSD Test (thats HSD for Honestly Significant
Difference). This test can be used only when the groups
are all the same size. It determines a single value that
is the minimum difference between a pair of groups that
is needed for the difference to be significant at a specific
alpha level.
- Scheffe's Test is very conservative. It involves
computing an F-Ratio that has a numerator that is a mean-square
that is based on only the two groups being compared (the
denominator is the regular error variance term).
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