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Lecture 12

ADM2304 Lecture 12: 12

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Tony Quon

Rationale: > If the variation between groups is signicantly larger than the variation within groups (i.e., F is large) then there is reason to believe that there is a difference in the treatment populations that cannot be explained simply by sample variation > How large is large enough? Again, we will use tables to determine if our Fstatistic is large enough to reject at the prespecied signicance level Hypotheses: > Again, the null hypothesis is that there is no effect > If the means from the different treatment groups are different enough we conclude that the treatment did in fact have an effect > The aim is to show a relationship between treatment and effect One Way Analysis of Variance: Hypotheses: H 0Allmeansareequal H aAtleast onemeandiffersfrom theothers > For OneWay ANOVA, we assume that the response, X, will be a random variable centered around some mean. That is, X =ij + i ij > for i = 1,,I (the populations) and j = 1, . , ni. So Xij is the jth observation from the ith population (or treatment). If the null hypothesis is true then > X = + ij ij
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