This preview shows page 1. Sign up to view the full content.
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
in statistics
• 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
F test
– if so, do a follow up analysis to decide
which groups diﬀer and to estimate the
size of diﬀerences 10 • Step one: 1Way ANOVA Ftest
We perform the overall Ftest:
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
for us.
>...
View
Full
Document
This note was uploaded on 06/12/2013 for the course MATHEMATIC MAT7870 taught by Professor Sun during the Winter '13 term at Wayne State University.
 Winter '13
 Sun
 Statistics, Linear Regression, Variance

Click to edit the document details