# Spearman Rho or ANOVA when examining effect of ordinal IV on continuous DV?

I have an ordinal independent variable (<1hr, 1hr, 1-3hrs, 3-5hrs, >5hrs) and an interval dependent variable (test scores). Apparently I am expected to examine the relationship between the two by conducting Spearman Rho correlations. However, would it not be more useful to perform a one-way ANOVA and post hoc test? Especially since the mean scores increase across ranks of the IV until the highest rank, at which point they drop. Or will reporting results from both tests be useful in data analysis?

• "would it not be more useful to perform a one-way ANOVA" -- that kind of depends on what you're interested in knowing. I'd think that "examining the relationship" would most usefully be achieved by choosing appropriate displays and perhaps via some form of estimation. It would seem prudent to consider the possibility that the relationship is not monotonic, and your suggestion is one way to look at that. Commented Apr 24, 2013 at 1:24
• Consider using Jonckheere-Terpstra analysis. It is like Kruskal-Wallis "nonparametric ANOVA" but tailored for IV ordered rather then nominal. Commented Apr 24, 2013 at 14:58

The question may be "is the independent ordinal variable meaningful". In other words, do each of the steps in the ordinal variable efficiently separate the interval measure. If you plotted the interval measure as comparative boxplots with notches, you could visualize whether the 95% confidence intervals of the median overlap from one step of the ordinal variable to the next. If the steps are meaningful (significantly different) than the adjacent steps, then the median estimates should increase with each step and the confidence intervals should not overlap. If the steps do overlap, then you cannot really tell the difference from one step to the next as far as the interval measure and the steps should be combined and the number of steps reduced.

Try plotting the data first,it will give you some idea as to distribution of scores and where you want to go with your analysis.

• Differences can be significant even when the confidence intervals overlap. Commented Feb 5, 2017 at 19:28

## Overview

• ANOVA will test the null hypothesis of no group mean differences
• Spearman's rho will look at the rank order correlation.

## General strategy

The most common strategy that I've seen in this context where the IV is ordinal in nature and has been experimentally manipulated is to (a) perform a test of the overall ANOVA and then (b) examine polynomial contrasts focusing first on the linear contrast, and where relevant the quadratic contrast.

• I agree, except I would not necessarily recommend the overall ANOVA. There is a question of what a linear contrast means for an ordinal variable but, as a practical matter, I don't think there is a problem. Some measurement purists may disagree. Commented Feb 5, 2017 at 19:26