topic Re: Association between nominal variable and ordinal variable in Statistical Procedures

Association between nominal variable and ordinal variable

palolix — Thu, 08 Jan 2026 21:48:53 GMT

Dear SAS Community,

I would like to know if there is an association between a nominal variable 'Ethnicity' (8 unordered levels) and an ordinal variable 'Overall1 ' (9 ordered levels) which means overall acceptance. In other words, if there is an influence of the Ethnicity of the consumer in the overall acceptance of the fruit that is presented to the consumer.

If I try proc freq with the chisq option I get the following table:

proc freq data=one;
tables Ethnicity*Overall1 /chisq;
run;

Statistic	DF	Value	Prob
Chi-Square	40	48.3949	0.1702
Likelihood Ratio Chi-Square	40	50.1632	0.1302
Mantel-Haenszel Chi-Square	1	0.4461	0.5042
Phi Coefficient		0.1349
Contingency Coefficient		0.1337
Cramer's V		0.0603
WARNING: 37% of the cells have expected counts less than 5. Chi-Square may not be a valid test.

Which statistic test should I use to see if there is an association between these two variables?

I would greatly appreciate your response!

Re: Association between nominal variable and ordinal variable

StatDave — Thu, 08 Jan 2026 22:00:19 GMT

If the association you want to assess is, as you say, the effect of ethnicity, then a nonmodel-based approach would the 2nd CMH statistic from FREQ:

proc freq; table ethnicity*overall1 / cmh; run;

Or you could use a model-based approach - see the Type3 test of ethnicity:

proc logistic; class ethnicity / param=glm; model overall1=ethnicity; run;

Re: Association between nominal variable and ordinal variable

WarrenKuhfeld — Thu, 08 Jan 2026 22:00:28 GMT

You can run PROC TRANSREG with a model statement like this:

MODEL MONOTONE(substitute your ordinal variable) = CLASS(substitute your nominal variable) / TEST;

Re: Association between nominal variable and ordinal variable

palolix — Thu, 08 Jan 2026 22:55:13 GMT

That was super helpful, thank you so much!

So with the second statistic you mean I should use the Row mean scores differ (0.7198)? I thought I should use the general association (0.1707).

Cochran-Mantel-Haenszel Statistics (Based on Table Scores)
Statistic	Alternative Hypothesis	DF	Value	Prob
1	Nonzero Correlation	1	0.4461	0.5042
2	Row Mean Scores Differ	5	2.8717	0.7198
3	General Association	40	48.3767	0.1707

Re: Association between nominal variable and ordinal variable

StatDave — Thu, 08 Jan 2026 22:59:30 GMT

If you want to assess the influence of ethnicity on overall1, then you are essentially asking if the row (ethnicity) means differ. A similar approach is taken by the logistic model I showed. The general association statistic would be more appropriate if both variables were nominal.

Re: Association between nominal variable and ordinal variable

palolix — Thu, 08 Jan 2026 23:30:40 GMT

ok, thank you! Good to know that in the case of two nominal variables (general association).

What about two ordinal variables? Should I use plcorr?

proc freq data=one;
tables Freq*Score/plcorr;
run;

And if I want to see if there is an effect of a continuous variable in an ordinal variable should I use kendall?

Re: Association between nominal variable and ordinal variable

StatDave — Thu, 08 Jan 2026 23:39:06 GMT

You could, but that assumes that the ordinal variables are crudely measured normally-distributed variables. If both are ordinal, you could use the first CMH statistic, or several of the statistics from the MEASURES option, or again, the logistic model. For an ordinal response and continuous predictor, use the logistic model.

Re: Association between nominal variable and ordinal variable

palolix — Fri, 09 Jan 2026 00:18:19 GMT

Good to know, thank you StatDave!

If I try this proc logistic code to test the association between the continuous predictor and the ordinal response then I don't get the type 3 effect table. Am I missing something?

proc logistic data=one;
model Overall1=DM;
run;

Re: Association between nominal variable and ordinal variable

StatDave — Fri, 09 Jan 2026 01:46:32 GMT

If your predictor is continuous and so don't have the CLASS statement, then you don't get a Type3 table - you just need the test of the variable in Maximum Likelihood Estimates table.

Re: Association between nominal variable and ordinal variable

Ksharp — Fri, 09 Jan 2026 08:33:37 GMT

https://blogs.sas.com/content/iml/2023/12/11/polychoric-correlation.html

And macro %magree might give you a hand.

https://support.sas.com/kb/25/006.html

Re: Association between nominal variable and ordinal variable

palolix — Fri, 09 Jan 2026 22:58:46 GMT

Oh ok. Thank you so much StatDave for your great help on this!

Re: Association between nominal variable and ordinal variable

palolix — Fri, 09 Jan 2026 22:59:11 GMT

Very useful, thank you very much!

Re: Association between nominal variable and ordinal variable

palolix — Fri, 09 Jan 2026 22:59:51 GMT

Thanks for the info!