9.5 - ANOVA and Regression

These models can get a lot more complicated, but in the end, they all revert back to a linear model, just as a regression does. The first thing to notice is the assumptions for regression and ANOVA are very similar. Other than linearity they are exactly the same. The fact that linearity is not included in the assumptions for ANOVA makes sense if we recall that in the regression example we used a quantitative predictor variable, and in Moriah’s example we use a categorical variable. Recalling how we make a scatterplot, it is very reasonable to NOT be able (or needing) to look at linearity as an assumption for a relationship between a categorical predictor variable and a quantitative response variable.

The more meaningful parallel is the mechanics of the two statistical techniques. If we created a dummy variable for the food insecurity levels in Moriah’s study, we would then have the model:

Test score = Low Food Insecurity + Medium Food Insecurity + High Food Insecurity

This results in each level of food insecurity having a different slope. Our test is simply one of testing the differences of each slope. Viola a regression! If this is too confusing, it is okay. Just remember that the label of “regression” and “ANOVA” are really for convenience sake. Before powerful computing a linear model with quantitative variables was a regression and a linear model with categorical variables was an ANOVA. Now, we have so many kinds of models with so many processing options the distinction is very trivial!