Why do you have to recode a categorical variable into dummy variables?

Answer 1

To capture and express differences between group means produced by categorical predictors (independent variables) using correlational/regression techniques, one typically encodes categorical variables vis-a-vis dummy, contrast or effects coding to produce vectors, each of which define a group difference in the form of a slope coefficient. Each vector can be thought of as a predictor variable which targets a single degree of freedom difference (or the difference between two group means). The correlation between a vector and the criterion (dependent variable), when squared, expresses the difference between two group means as a proportion of variance accounted for (the proportion of variance in DV accounted for by being either in grp1 or grp2). Coding allows one to easily partition the between groups variance. The vectors are always single degree of freedom values (two coded values for two groups). How many vectors? The number is equal to the degrees of freedom of the between groups term or one less than the number of groups. Take a look at Kepple & Zeddeck 1989 "data analysis for research designs". Hope this helps.