# What statistical test to use for ordinal independent variable

I think this is a rather basic question, but it has been a rabbit hole for the last couple hours and I still haven't found an obvious answer.

I'm trying to perform a statistical analysis for an ordinal independent variable (educational attainment with four levels) and a quantitative/ratio dependent variable (monthly spending on electricity). The sample size is large so I assume each ordinal level is normally distributed, though not necessary normally distributed across the four levels as a whole -- I'm not sure if this matters.

It seems I could do 6 separate t-tests to test the difference in means between all 6 pairings of ordinal levels, or a one way ANOVA test to test the strength of difference between at least two groups. Ideally, I want to be able to test the relationship across all ordinal levels, i.e. if higher educational attainment shows a measurable increase in monthly electricity spending, but I can't figure out if there's a statistical test appropriate for that given the nature of the variables. Any advice is greatly appreciated.

• Why do you say that the large sample size make it so that the dependent variable is normally distributed within each ordinal level? Central limit theorem? – Dave Dec 13 '20 at 16:43
• ANOVAs are a good place to start. This will produce an ombudsman F-test that at least one of the ordinal levels is nonzero. This overall test can be followed by invoking an option available in most stat packages to produce parameter estimates for each level. If you include an intercept, then three parameters can be estimated and compared for significant differences from the fourth level. Excluding the intercept will enable simultaneous estimates for all four levels, a test that the levels are significantly different from zero. Finally, a multiple group comparison test would give even more info – user234562 Dec 13 '20 at 17:37
• What I posted earlier about the central limit theorem alludes to a common misconception: stats.stackexchange.com/questions/473455/…. – Dave Dec 13 '20 at 18:31
• @Dave because of precisely that misunderstanding. Thank you for clarifying! Though, separately from my misconception, I do think it's normally distributed, I'll now look into how to test for normality to make sure I can use parametric tests. – Tyler P. Dec 13 '20 at 20:45
• I had a hunch it was that misconception—glad to help! // Formal testing for normality is basically worthless. We have a post on here with a title along those lines that explains why. The gist is that your data are a little bit non-normal, and your test will catch that, so it becomes a judgment call about how non-normal the data are. – Dave Dec 13 '20 at 21:15