Possibly a simple / daft question so apologies in advance...
Suppose I have several independent observations of a continuous variable, like height. The observations are grouped, and I would like to test whether the groups have significantly different distributions. If the groups are nominal I would use a one-way ANOVA, if continuous I would use a mixed-model, but what should I use if the groups are ordinal but not at regular intervals?
For example, for the continuous variable "height", nominal groups might be English people vs Swedish people vs French people --> ANOVA, if the 'groups' are Age --> Mixed model, but if the groups are, say, "Self-reported weekly exercise", or "eating your greens", where ordinal categories might be: not at all, mild, moderate, lots, what would people suggest?