What Patrick is getting at is; suppose that you have data that ranges from 0 to 100. If you break this group into quantiles, say 4, you just decided that there IS a difference between a '23' and a '26'. But, there is NO DIFFERENCE between '2' and '23'. If this idea is true, then carry on with our blessing. If not, you should rethink what it is you want to do. 

If I understand correctly, your DV is nominal and your predictor is ordinal. Is that correct? In that case, you may want to use ordered multinominal logistic regression.

There is plenty of casestudies online.

In the link below, you can find other types of test in case your variables are of a different level.

I also added a link about how to perform an ordinal regression in spss, in case you have both variables ordinal.

http://www.ats.ucla.edu/stat/mult_pkg/whatstat/

https://statistics.laerd.com/spss-tutorials/ordinal-regression-using-spss-statistics.php

Simin,

Gerine is right on target. I understood the dependent variable to be ordinal, in which case her pointers will take you to cumulative logistic regression.

But I want to back up a bit: What was the reasoning for dividing/setting tertiles? In most circumstances, you're going to be losing information and precision by doing that.

Pat

What Patrick is getting at is; suppose that you have data that ranges from 0 to 100. If you break this group into quantiles, say 4, you just decided that there IS a difference between a '23' and a '26'. But, there is NO DIFFERENCE between '2' and '23'. If this idea is true, then carry on with our blessing. If not, you should rethink what it is you want to do. 

I totally agree that in most cases this would not work. Maybe you should also think about your dependent variable, as you state that it is "divided" in three categories, the same may go for this variable.