# Correlation between numeric and ordinal variables

What test can I use to test correlation between an ordinal and a numeric variable? I think linear regression (taking numeric variable as outcome) or ordinal regression (taking ordinal variable as outcome) can be done but none of them is really an outcome or dependent variable. Which test can I use here? Will Pearson's, Spearman's or Kendall's correlation work here? Thanks for your insight.

• So the predictor variable can have a series of values, which can be set in order, but it makes no sense to calculate differences (like kindergarten, primary school, high school, college) and the predicted variable is a continuous variable, varying within a range, right? – Dirk Horsten Jul 23 '15 at 13:07
• And all you want to proof is that there is a dependency, you are not trying to model anything? – Dirk Horsten Jul 23 '15 at 13:22
• Yes, I want to determine correlation between class (like kindergarten etc) and age, but dependency and I am not trying to model anything. – rnso Jul 23 '15 at 13:29
• Please visit stats.stackexchange.com/q/103253/3277 which shows some of possible ways. – ttnphns Jul 23 '15 at 13:31
• That is a very useful link on this topic. I am not restricting to non-parametric methods and would like to know if there are any parametric methods also. – rnso Jul 24 '15 at 3:38

## 1 Answer

To find out if the levels of your predictor variable do influence the value of your predicted variable, you need a one way ANalysis Of VAriance ANOVA. The criterion to reject the null hypothesis that there is no dependency is the F-statistic. A typical example in SAS would be

proc glm data=myTable;
class predictor;              /* to indicate it can only have certain variables */
model predicted = predictor;  /* to indicate what you want to predict based on what */
means predictor / hovtest;    /* if you also want to test for Homogenity Of Variance */
run;

• I clarified that I do not want to use predictor and predicted terms, since that is not the relation here. Moreover, the variables are ordinal and not unrelated groups or categories. ANOVA does not take that into account. – rnso Jul 23 '15 at 14:08