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Unformatted text preview: an the baseline
Rejection of H0 : βP = 0 says there is evidence
that the Pet group is diﬀerent than the baseline
The overall F-test tests H0 : βF = βP = 0,
which is the same as H0 : µC = µF = µP .
16 General concept of 1-Way ANOVA 0.30 What matters is how far apart the sample means
are relative to variability. • Roughly speaking, we’ll consider an F -statistic
F= variation among the sample means
variation among individuals in the same sample 0.00 0.10 0.20 • When there is a lot of spread between the
group sample means and very little spread
within a group, we will have a large F -statistic.
0 5 10 15 20 25 • Compare F to an F -distribution for decision
0.8 1.2 Notation: 0.0 0.4 m = number of diﬀerent populations whose
means we are studying 0 5 10 15 20 25 The means of the three groups above is the same
in both pictures, but the variability is quite different.
17 F-distribution for 1-way ANOVA F -test
H 0 : µ1 = µ2 = . . . = µm
HA : not H0
• m − 1 numerator degrees of freedom
• N − m denominator degrees of freedom
(N data points, m parameters estimated) ni = number of observations in sample
from ith population
N = total # of observations, N = m i=1 ni 18 Assumptions for One-way ANOVA
• m i...
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