My colleague has an experiment with a 2x2 all between subjects design with categorical variables predicting a three-level categorical dependent variable (choise between A, B, C/ coded as -1 0 1). Is this coding correct? Can a dependent variable have three levels? What kind of analysis can he best conduct?
A dependent variable can definitely be categorical and have multiple levels. These levels may be ordinal or not (briefly, it is ordinal if the levels have a definite order - e.g. none, some, a lot). If the dependent variable is ordinal, one choice is ordinal logistic regression. If it is not ordinal one choice is multinomial logistic regression. If you are using SAS, I made a presentation on this topic (actually, the start of the talk is not SAS-specific, so it may be helpful, regardless of what software you are using).