In my understanding, this is correlation issue between scale and categorical variable.There are a few options:
- Perform an analysis of variance (ANOVA) on the continuous variable separated into the modalities of the categorical variable. The idea is to look at the variance of the continuous variable within each class and compare it to the total variance.
- Perform a multimodal regression of the continuous variables, predicting for the categorical variable.
- Eta in SPSS measures the association between a scale (continuous) variable and a categorical variable. The limitation with the test is that it yields only the strenght of the association in a scale of 0-1 and which is interpreted just as you interprete correlation coeffcient for Pearson or Spearman. Logistic regression deals essentially with categorical variables. There are many other alternative tests that can apply if you intend to categorize the scale variable but I am making my proposition assuming that you want to keep your variables in their initial measurement levels.
- http://courses.ncssm.edu/math/Stat_Inst/PDFS/Categorical%20Data%20Analysis.pdf
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