Look into ordinal regression analysis. I know Conover's book is a start here. Could you assign a k-1 dummy ton it making it immediately testable. If it a regressand, then you will need Tobit or Probit regression approach. These are available in most softwares.
There are regression models for ordinal response variables (-> ordinal logistic regression). However, there are no models for ordinal predictors. The only chance is to treat the ordinal predictor as nominal.