The Analysis of Variance ANOVA The Analysis of Variance ANOVA

μ-3σ μ-2σ μ-σ μ μ+σ μ+2σ μ+3σ
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Test-statistic (Reprise)
What value of F provides information regarding rejecting H 0 ?
Again, recall that if H 0 is true, then μ 1=μ 2=μ 3=…=μ I , and therefore,
should be reasonable close to each other, and also to the grand mean x . Then, the
differences between individual sample means and grand mean would be small,
resulting in a small MSTr. Otherwise, the differences would be large resulting in a
large MSTr.
MSE, however, is independent of whether H0 is true, as it relies on the underlying
value of the sample variance. Therefore, we can assert that:
When H 0 is true,
When H 0 is false,
Therefore, an F value >>1 indicating that MSTr >> MSE provides justifiable
skepticism on H 0. The form of the rejection region is therefore, f ≥ c where, f is
the observed value of the F statistic, c is the cutoff chosen to give enough benefit
of the doubt to H 0. That is c is chosen such that P ( F ≥ c, when H 0 is indeed
true) ≤ α, the desired significance level .
E(MSTr) = E(MSE) = σ
E(MSTr) > E(MSE) =
σ
x
. . I . x x , , 1 2
© 2006 All Rights Reserved, Robi Polikar, Rowan University, Dept. of Electrical and Computer Engineering
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