Lecture Notes # 3 : Contrasts and Post Hoc Tests 3 - 1

• Introduce post hoc tests • Review assumptions and issues of power 1. Planned contrasts (a) Contrasts are the building blocks of most statistical tests: ANOVA, regression, MANOVA, discriminant analysis, factor analysis, etc. We will spend a lot of time on contrasts throughout the year. A contrast is a set of weights (a vector) that defines a specific comparison over scores or means. They are used, among other things, to test more focused hypotheses than the overall omnibus test of the ANOVA. For example, if there are four groups, and we want to make a comparison between the first two means, we could apply the following weights: 1,-1, 0, 0. That is, we could create a new statistic using the linear combination of the four meansˆI This contrast is the difference between the means of groups 1 and 2 ignoring groups 3 and 4 (those latter two groups receive weights of 0).