ANOVA for Factors With Ordered Levels

In its simplest case, ANOVA can be seen as a generalization of the t-test for comparing the means of a continuous variable in more than two groups defined by the levels of a discrete covariate, a so-called factor. Testing is then typically done by using the standard F-test. Here, we consider the special but frequent case of factor levels that are ordered. We propose an alternative test using mixed models methodology. The new test often outperforms the standard F-test when factor levels are ordered. We illustrate the proposed testing procedure in simulation studies and three typical applications: nonparametric dose response analysis in agriculture, associations between rating scales and a continuous outcome, and testing differentially expressed genes with ordinal phenotypes.