The Logic of Anova

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THE LOGIC OF ANOVA

ANalysis Of VAriance (commonly abbreviated as ANOVA), more specifically, we will take up an application known as one-way ANOVA. Many statisticians think of ANOVA as an extension of the difference of means test because it’s based, in part, on a comparison of sample means. At the same time, however, the procedure involves a comparison of different estimates of population variance—hence the name analysis of variance. Because ANOVA is appropriate for research involving three or more samples, it has wide applicability. Imagine for a moment that we want to know if scores on an aptitude test actually vary for students in different types of schooling environments—home schooling, public schooling, and private schooling. This research question involves a comparison of more than two groups. Assuming that the aptitude test scores are measured at the interval/ratio level, the situation is tailor-made for an application of ANOVA. We could easily think of our study as one that asks whether or not aptitude test scores vary on the basis of school environment. Another way to look at the question is whether or not type of school environment is a legitimate classification scheme when it comes to the matter of aptitude test scores. After all, to refer to students in terms of home, public, and private schooling is to speak in terms of a classification scheme. If aptitude test scores really do vary on the basis of school environment—if there is a significant difference between the scores in the three environments—then it’s probably legitimate to speak in terms of school environments when looking at test scores. If there isn’t a significant difference between the scores, however, we have to question the legitimacy of the classification scheme. To suggest that two groups are different with respect to some variable is, in fact, a way of suggesting that the members of the group or cases can reasonably be classified on the basis of the variable in question. That said;...
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