Post Hoc Tests

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?
TTests can't be used
We can't answer this question in the obvious way (using TTests
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 FRatio that has a numerator that is a meansquare
that is based on only the two groups being compared (the
denominator is the regular error variance term).
