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I'm trying to find the right test for association for two likert scale, ordinal variables from a questionnaire I did:

  1. "How often do you recycle" - (1) Almost Daily, (2)2-3 times a week, (3)Once a week, (4) Less than once a week, (5)I don't recycle

  2. "Recycling can conserve the environment" - Ranges from (1)Strongly agree to (5)Strongly disagree, with (3)Neutral in the middle and a (6)I don't know option.

After graphing the data from my two variables together, it seems to that they don't have a monotonic relationship. From what I've searched, Kendall's tau c might suit my situation but I'm not sure if its a good idea since they don't have a monotonic relationship.

Edit: I'm aware that this seems like a duplicate from another similar question found here, but as I said in the below comments, Glen_b, who answered the question in the other post, mentioned that when one is looking for some general measure of non-monotonic association, you can look at nominal-nominal (such as Cramer's V), and nominal-ordinal association and he gave a reference to an article about that. But I want to know how does looking at nominal-nominal or nominal-ordinal association help me since I'm trying to do ordinal-ordinal association testing?

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  • $\begingroup$ Hmm, I wasn't able to comment on the answer to ask the following question: Glen_b mentioned that one approach you one is looking for some general measure of non-monotonic association is to look at nominal-nominal (such as Cramer's V), and nominal-ordinal association and he gave a reference to an article about that. But I want to know how does looking at nominal-nominal/nominal-ordinal association help me since I'm trying to do ordinal-ordinal association? $\endgroup$ – David Jr Gbadago May 12 '17 at 7:15
  • $\begingroup$ @David It might be prudent to edit the answer to include what you wrote in the comment by reference to the possible duplicate. That would decrease the chance that this is closed as duplicate $\endgroup$ – Momo May 12 '17 at 9:02
  • $\begingroup$ It sure seems like a duplicate to me. Both questions are about nonmonotonic relationships between Likert scale questions. $\endgroup$ – Peter Flom May 12 '17 at 11:27
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    $\begingroup$ The ordinality doesn't matter if you are trying to assess a nonmonotonic association. If you want to be able to capture any association between any levels of the 2 variables, that is equivalent to the nominal-nominal association. $\endgroup$ – gung - Reinstate Monica May 13 '17 at 11:58
  • $\begingroup$ Thanks! That was very helpful. But, now I need to figure out which nominal-nominal association test to use. Which one do you think I should use? I can't use chi-square because too many cells in my data would have expected counts less than 5 and some even have expected counts less than 1. That was a problem i was trying to fix in a previous question: stats.stackexchange.com/questions/278093/… $\endgroup$ – David Jr Gbadago May 13 '17 at 12:25