Analysis of Variance II Interactions Post-Hoc

ANOVA What question are we asking? On a dependent variable, are several group means different from one another? Differently: Do we need just the grand mean, or all of the sample means?

Grand Mean One Way to do Variance

Another Way to do Variance

ANOVA This type of question is called a “One Way ANOVA” This really means there is one (categorical) independent variable and one (continuous) dependent variable But we can actually ask questions about more than one variable with ANOVA

Example: Treatment Effects Imagine we have a treatment that is designed to reduce depression. We randomize subjects into two groups: Treatment and Control But in both of these groups there are males and females We run a t-test to see if there are differences between treatment and control groups….we find NO DIFFERENCE Another researcher analyzes our data and declares there is a tremendous treatment effect What happened?

The Magical Interaction Effect DepressionDepression Treatment Control Males Females

Some Terminology Main Effects: This is just the mean differences between two groups In our example: There is a main effect of treatment vs. control and another main effect of males vs. females Interaction: This is the means of combined groups. In Our Example: Gender x Treatment has four means: Male treatment, male control, female treatment, female control We say that the level of one variable depends on the level of the second variable

Post Hoc Tests

Effect Size