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then, to test if any of the groups have a diﬀerent heart rate, we would consider the ‘overall’
null hypothesis
H 0 : µ1 = µ2 = µ3
HA : at least one µi is diﬀerent for i=1,2,3
7 6 Why not just do 3 pairwise comparisons?
• H 0 : µ1 = µ2
• H 0 : µ1 = µ3
• H 0 : µ2 = µ3
Problems:
• 3 separate pvalues for 3 diﬀerent tests don’t
tell us how likely it is that three sample means
¯¯¯
(Y1, Y2, Y3) are spread apart as far as these
by chance (i.e. when µ1 = µ2 = µ3).
¯
¯
• It might be that Y1 = 73.48 and Y2 = 91.32
are signiﬁcantly diﬀerent when only looking
at 2 populations, but not signiﬁcantly diﬀerent if we look at 3 populations
– as more and more groups are added, we expect the gap between smallest and largest
sample means to get larger (even if the
population means are the same).
8 • The probability of a Type I error (rejecting
H0 when it was true) for the whole set of
three ttests will be larger than α.
– For example,
∗ Set the chance of making a Type I error
on an individual ttest at α = 0.05
∗ The chance of NOT making a mistake
on an individual ttest is (1 − α) = 0.95 These ttests are not independent, bu...
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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

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