# Solved – What does the sum to zero constraint mean

In an ANOVA model, there is a constraint that the coefficients must sum to zero. What does this actually mean? I do understand the reason why you might want to make them sum to zero, i.e. to have two degrees of freedom to estimate two parameters for instance, and not 3 df for estimating 2 parameters.

What parameters actually sum to zero?

Contents

$$begin{array}{l|ccc} & C_0 & C_1 & C_2 \ hline text{Less than High School} & 1 & -1 & -1 \ text{High School} & 0 & 1 & 0 \ text{Some College} & 0 & 0 & 1\ end{array}$$
So with the exception of the intercept term ($$C_0$$) the contrasts add up to 0 columnwise. That means that the interpretation of $$C_1$$ is a mean difference between high school and less than high school and $$C_2$$ a mean difference from some college to less than high school.