00 010 020 when there is a lot of spread between the

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Unformatted text preview: an the baseline group. Rejection of H0 : βP = 0 says there is evidence that the Pet group is different than the baseline group. 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 where... 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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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.

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