Statistical method selection tool

Step 3. You want to know if there is a relationship between an ordinal and an interval/ratio variable. Does the ordinal variable consist of two levels, or more than two levels?



Advice: two sample $t$ test

You want to know if there is a relationship between an ordinal and an interval/ratio variable. The ordinal variable consists of two levels. The two sample $t$ test assuming equal population standard deviations, or the two sample $t$ test not assuming equal population standard deviations seem to be good options! The ordinal variable would be the independent variable or grouping factor, and the interval/ratio variable would be the dependent or test variable. Can't decide between the two types of $t$ tests? A rule of thumb is that if the larger sample standard deviation is less than twice as large as the smaller sample standard deviation, we can assume that the two population standard deviations are equal. Alternatively, Levene's test is sometimes used to test whether the population standard deviations are different.

If the normality assumption of the $t$ test is violated, you could use the non-parametric Mann-Whitney-Wilcoxon test. Again, the ordinal variable would be the independent variable or grouping factor, and the interval/ratio variable would be the dependent or test variable. The Mann-Whitney-Wilcoxon test is also known as the Wilcoxon rank sum test. Click on the links to learn more about these tests.

Advice

You want to know if there is a relationship between an ordinal and an interval/ratio variable. The ordinal variable consists of more than two levels. We can give you two relatively easy options. One option is to perform a one way ANOVA, with the ordinal variable as independent variable or grouping factor and the interval/ratio variable as dependent variable or test variable. The disadvantage of this option is that the ANOVA will not take the ranked nature of the ordinal variable into account. That is, it will treat the ordinal variable as a nominal variable. Another option is to compute Spearman's rho , which is a measure for the relationship between two ordinal variables. The disadvantage of this option is that it treats the interval/ratio variable as an ordinal variable, rather than an interval/ratio variable. Click on the links to learn more about these methods.

A more complicated option is to perform an ordinal logistic regression analysis, with the ordinal variable as dependent variable and the interval/ratio variable as independent variabe. The advantage of this method over the two less complicated methods is that it treats the ordinal variable as ordinal and the interval/ratio variable as numeric, therefore not throwing away information in the data.