Quick reality check: using correlation and Chi-square for hypotheses testing

I have two ordinal values on a 5 point Likert scale, let's say "Would you like flowers?" and "Would you like to go out to dinner with me?". My hypotheses is that there is a relationship between the two, i.e. people who would like flowers would also like to go out for dinner with me.

I can perform a Spearman's correlation to between ordinals to determine whether a relationship exists - that's all well and good (I hope). Then I can recode the Likert scale in a nominal Yes / No value using 'Agree' and 'Strongly Agree' as a 'Yes' and 'Strongly disagree', 'Disagree' and 'Neither' as a 'No'. Once that's done, I can then perform a chi-square test to determine whether this is a significant association. In effect I'm trying to test the efficacy of giving flowers for more dinner dates.

My question is whether this a good approach to test my hypotheses, using the correlation test to determine a relationship and then confirming the strength of the association?

• Something isn't right here. You said that you have two ordinal values on a 5 point scale such as "Do you like chocolate." The answer to this question should be "Yes" or "No" not an indication of agreement, so why are you having to recode data into Yes/No? I suspect that your original question isn't Do you like chocolate, but something like, "How much do you agree with the following statements. . . I like chocolate." Is that the case or am I missing something? Aug 1, 2015 at 14:38
• Sorry, I just tried to give a simple example. Your assertion is correct that the Likert ordinal is used for that type of question, but then recoded to determine the efficacy / strength of the association. I guess my question is whether the chi-square should be used within this context or am I over thinking things? I've re-edited the question, hopefully that makes things clearer... Aug 1, 2015 at 14:52
• So you can certainly used the Chi-Squared test, but the question is, what are you really trying to find out? If there is an association between those who agree/disagree with the chocolate and beer statements? If that's the case, there is no need to recode at all (unless you are doing this to make this a bit simpler). You could simply run a Chi-Squared test without any recoding at all (assuming you meet the Chi-Squared test assumptions as sufficient size and sufficiently large expected cell counts). Otherwise, an exact test, or category collapsing, would be preferable. Aug 1, 2015 at 15:06
• I'd also use the Yates' continuity correction when performing your Chi-Squared test if you use the 2x2 table approach. Aug 1, 2015 at 15:08
• Yes, the recode is the way to go. It sounds like your study might be underpowered and this may be way you are not seeing statistically significant results. A power analysis might warranted. Aug 1, 2015 at 15:52

I think the following is an important point and therefore I post it as an answer although I would have preferred to post it as a comment.

You say: "In effect I'm trying to test the efficacy of giving flowers for more dinner dates."

As I understand it, this implies causality which you cannot test with correlational data and running a Chi-Squared test does not change that.

• Extremely good point - I guess secretly I would like to point to a causal relationship, but ultimately I can only state that I've observed a correlation and that following a chi-square there is a statistically significant relationship. In effect, correlation to identify, chi-square to test, but caveat this is observational only. Does that sound about right? Aug 2, 2015 at 10:06
• Caveat this is correlational only, yes. But why do you use the Chi-Square to test the significance of the relationship anyway? With the Spearman Rank Correlation coefficient you get a p value that informs you about the statistical significance of your result. By collapsing groups you lose variance and I do not see what would be the advantage of a Chi-Square test here that would outweigh this loss.
– grey
Aug 2, 2015 at 10:17
• I guess it comes down to the size of the sample, that I'm getting weak correlations, and that chi-square (after recoding) provides a confirmatory factor for hypotheses testing. Is this a fundamentally wrong approach or a raising of eyebrows in a purist sense? (That's not implied in a derogatory way) Aug 2, 2015 at 10:34
• Maybe others can jump in here to comment on the legitimacy of such a procedure. IMHO it is not fundamentally wrong. If your N (=?) is that small, you may want to consider interpreting your results very cautiously anyway.
– grey
Aug 2, 2015 at 12:18
• I've just read that we seem to talk about N = 102 (did I get that right from your comment above?). If so, this is a large sample size for which I think the Spearman Rank correlation is well suited. If you do not observe a significant correlation with Spearman's Rank correlation coefficient, you may want to take a look at the distribution of the answers of the two variables. For instance, it is possible that most people would like to get flowers and you do not have enough diversity there for a significant correlation to emerge in the first place.
– grey
Aug 2, 2015 at 13:03