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Lecture 9

Political Science 3N06 2014 Lecture 9a ANOVA .doc

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Political Science
Todd Alway

Political Science 3N06 2014 Lecture 9a: ANOVA - How do we test whether sample differences indicate population differences when there are more than two groups being measured on a given variable? - After all, many independent variables have more than 2 attributes – social class (high, middle, low), provinces (10), ethnicities (many) - If you want to see whether, for example, opinion on abortion varies according to Province, how do you do so? - Why not multiple paired t-tests? o Problem of accumulating Type I errors - What we require is a single test of difference that can incorporate three or more different groups - ANOVA – Analysis of Variance - Recollect our discussion of variance - - A measure of dispersion – the standard deviation squared - With ANOVA, you are dealing with two types of variance - There is the variance within each sample (i.e. variability within each group) - And there is the variance between the samples (i.e. variability between the groups) - ANOVA tests whether the variation between the groups is significantly greater than the variation within the groups - If this is the case, then (depending upon the size of the difference) it is probable that these samples do not come from the same population - The groups are significantly different with respect to the dependent variable - These variances are expressed as ‘sum of squares’ - The Sum of Squares Within (SSW) o Which is a measure of the deviations between individual sample scores and sample means - The Sum of Squares Between (SSB) o Which is a measure of the deviations between sample means and the total mean of all samples combined 1 - This culminates in a new statistic, the F statistic, using a new distribution, the F dist
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