Often quantitative data in the social sciences have only ordinal justification. Problems of interpretation can arise when least squares multiple regression (LSMR) is used with ordinal data. Two ordinal alternatives are discussed, dominance-based ordinal multiple regression (DOMR) and proportional odds multiple regression. The Q[superscript 2] statistic is introduced for testing the omnibus null hypothesis in DOMR. A simulation study is discussed that examines the actual Type I error rate and power of Q[superscript 2] in comparison to the LSMR omnibus F test under normality and non-normality. Results suggest that Q[superscript 2] has favorable sampling properties as long as the sample size-to-predictors ratio is not too small, and Q[superscript 2] can be a good alternative to the omnibus F test when the response variable is non-normal.