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Unformatted text preview: t the
general idea of doing multiple tests at a
certain controlled error rate still stands.
This is a multiple comparison issue.
– How do we control the error rate on a
‘group’ of tests? ∗ What is the probability of not making a
mistake on any of the three tests?
Well, if the tests were independent,
(1 − α)(1 − α)(1 − α) = (0.95)3 = 0.8574
Thus, there’s a 0.1426 chance of making
at least 1 mistake (deﬁnitely larger than
α = 0.05 for the whole set of three tests) 9 Multiple comparisons procedures
• How do we do numerous comparisons of interest simultaneously while maintaining a certain overall error rate (like α = 0.05)?
• Two steps
– start with an overall test to see if anything
is interesting... i.e. test if any of the means
are signiﬁcantly diﬀerent using an overall
– if so, do a follow up analysis to decide
which groups diﬀer and to estimate the
size of diﬀerences 10 • Step one: 1-Way ANOVA F-test
We perform the overall F-test:
H 0 : µ1 = µ2 = µ3
HA : at least one µi is diﬀerent for i=1,2,3
Though we can do coding of two dummy
variables to represent group, R will do this
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