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I know that to assess the relationship between two categorical variables, you would use a chi square test, but what would you do if you wanted to see the association between a) a ordinal and categorical variable and b) an ordinal and ordinal variable.

I have seen ideas about using gamma, Lambda and taking the linear-by-linear significance, but does anyone have any concrete answers (as this is for my dissertation so I need to make sure I am doing it right).

My data is not normally distributed.

Thank you

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a) ordinal and categorical variable

Strictly speaking Chi-square test is still a possibility. It tests if the proportion of the attributes in the categorical variables are the same across each rank of the ordinal variable; and it tests if the distribution of the ranks are the same across different attributes in the categorical variables.

However, other tests are available as well. For example, the non-parametric version of ANOVA, called Kruskal-Wallis can let you actually compare the mean ranks of the ordinal variable across attributes of the categorical variable.

b) ordinal and ordinal variable.

A conventional method is Spearman's correlation.

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