Bivariate tests with dummy variables

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Cookie G
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I'm not sure if this belongs in the Basic area or here.

I have a dataset with variables that I think it makes sense to make them into dummy variables (some are categories, some are ordinal). I've been asked to do bivariate tests and regression. I don't understand how I can do bivariate tests when I'm using dummy variables.

Thanks
 
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I guess I just use the dummy variables for the bivariate tests. It just seems less than ideal because in a sense one dummy variable has less information than the original variable.

For example, if I have geographic region and poverty level, I could do pairwise correlations. region 1 with pov level 1, region 1 with pov level 2, region 1 with pov level 3, region 2 with pov level 1, etc.

I've not been able to figure out any other way to do this. Please let me know if I'm missing something.