Hi all, I am trying to find the relationship between two ordinal variables (5-point likert scale).
The variables are:
1) Importance of attribute (not at all important, slightly important, moderately important, very important, extremely important)
2) Likeliness to visit if the said attribute is present (extremely unlikely, somewhat unlikely, neither likely nor unlikely, somewhat likely, extremely likely)
I want to see if the importance of the attribute has any correlation with their likeliness to visit if the attribute was present. I did my research and found that I could potentially use both the Spearman rank-order correlation and the Chi-sq test for independence. Can someone explain to me in simple terms the difference between the two, and recommend the test that I should use?
If you are interested in finding the correlation between the two ordinal variables Spearman's correlation index will give you the exact value which may be tested for significance. The chi-square goodness of fit test is used to test for independence. Therefore the Spearman's rank correlation is the better approach here.
The chi-square test is also applicable, if you only have categorical data and not ordinal. So it seems more appropriate to use rank correlations. In short: With the chi-suare test, the observed probabilities are compared to the expected probabilities, which are calculated by the product of the marginal probabilities. This product indicates the expected probability, if both variables are independent. So, if the observed values differ greatly from the implied/expected, it is evidence that both variables are not independent.
But with the chi-square you have no measure for the strength of association, since chi-square values are not bounded. For that, in case of categorical data, Cramer's V or in special case of a 2x2 table, phi-coefficient can be calculated, similar to other correlation coefficients.
But if you have more "information" at hand, i.e. ordinal or metric variables, you should use it for your estimations. Therefore, Ette Etuk is right, better use Spearman's rho.
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