April 25 - Testing Hypothesis with multiple group...

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April 25, 2008 Testing Hypothesis with multiple group means (ANOVA) Why analysis of variance (ANOVA)? o To compare means across more than 2 groups We have a continuous (interval or ratio level) dependent variable, and more than 2 groups Exactly like a t-test for independent sample, but for more than 2 groups The logic of ANOVA o When we compare means across groups, we need to think of how the scores vary: There is the total variance for the sample Then there is the between-group variance And there is the within-group variance o Total variance = between variance + within variance o We compare the differences across the groups to the differences within groups o Just like with a t-test, where we compare the difference between scores to the standard error Total variance (1) o Total variance measure how each case varies from the mean: Total variance : s 2 = (Σ (x1- ) 2 ) / n-1 o First we calculate the sum of squares : SS total = Σ i Σ k (x ik - grand ) 2 Total variance (2) o
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