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Ch. 28  Comparing Several Means
Use
t
tools?
NO!
Æ
Reason?
Compound uncertainty
 In any test, there is uncertainty such that we reject H
0
when it’s true, or Type
I error.
By comparing multiple means and using ONE
t
test for each pair, the
“overall” Type I error will compound.
 For example, consider 3 means that are equal and each
t
test uses
α
= 0.05.
Thus, there’s a 5% chance to show a difference when there isn’t (recall H
0
assumes no diff.).
The chance of detecting
at least
one difference among the
three means is roughly 1 – 0.95
3
= 0.143 or 14.3% when the means are
EQUAL!
(Note: 14.3% is the “overall” Type I error.)
 For 5 means, the “overall” Type I error becomes approx. 40%.
Def’n: ANalysis Of VAriance (ANOVA)
is a procedure to test the equality of three or
more population means.
NOTE: the name of the test refers to comparing different
sources of variability; it WILL test differences among means.
Test requires the following assumptions:
1.
The populations are all normally distributed.
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 Winter '10
 PaulCartledge

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