Categorical vs Ordinal data analysis

[MiltonF]

I have a question regarding some data analysis I am conducting. I'm trying to find significance and degree/direction of association between two variables.

I'm using a contingency table to do this. One variable is a categorical variable; yes or no. The other variable is ordinal; ranging from 0-5 ("none" to "a lot")for example.

So far I've used Fisher's Exact Test to find the significance of association (because many of the cells have counts of less than 5). To get a measure and direction of association, I've been using Goodman and Kruskal's Gamma.

But now I may be in trouble because I may have done this all wrong. Fisher's is supposed to be used only when both variables are categorical data? Gamma is supposed to be used only when the variables are ordinal?

Can one be categorical and one be ordinal? Is there a way these definitions can be "fudged" to make this still viable, or do I need to do this in a different way?

What sort of test is usable in such a situation for both significance and degree/direction of association?

Thanks

[CowboyBear]

Dichotomous categorical variables can arguably also be conceptualised as ordinal in some cases - your dichotomous variable represents "more" of some quantity, I imagine? It could be possible to take this argument and justify sticking with gamma, though I don't really know anything about this specific test.

An alternative specifically designed for correlating dichotomous and ordinal data is the rank biserial correlation coefficient.

Hope that helps

[MiltonF]

Dichotomous categorical variables can arguably also be conceptualised as ordinal in some cases - your dichotomous variable represents "more" of some quantity, I imagine? It could be possible to take this argument and justify sticking with gamma

Thats what I was thinking.

However, now that you point out this other test, it says on your link that this may be the same as Somer's D. Somer's D seems to work the same way as Gamma, but when you have a dependent ordinal variable vs a nominal variable.

Am I correct in assuming that Somer's D works just right in this case?

Thanks for your help

[ElroyS]

Using Somer's D (even one of the asymetric versions) is not appropriate for ordinal versus nominal strengths of association. There is a fallacy floating around the web that this is appropriate, and it's not. If you want proof, just create a small dataset in SPSS. Call your first variable the IV, and the second the DV. For the IV, put in about 5 subjects with "1", 5 with "2" and 5 with "3". This will be your nominal IV. Now, put some scattered 1,2,3,4,5 values in for the DV. Produce a Somer's D (through crosstabs). Ok, now, in the IV, change all the subjects with "2" to "3", and all the subjects with "3" to "2". If this is truly a nominal variable, the value for Somer's D shouldn't be affected by this. However, if you reproduce your Somer's D values, you will see that NONE MATCH THE ORIGINAL VALUES. Q.E.D., not appropriate for nominal versus ordinal.

There is not a good nominal versus ordinal strength of association unless you're willing to use ordinal logistic regression, and use one of the pseudo R2 values. Optionally, if your ordinal measure doesn't have too many categories, you can push it to a nominal variable, and use one of the nominal versus nominal strengths of association.