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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?

kjetil b halvorsen
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Tim
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  • Please look here: https://stats.stackexchange.com/questions/105681/likert-item-as-independent-variable-for-anova, here: https://www3.nd.edu/~rwilliam/stats3/OrdinalIndependent.pdf and here: https://link.springer.com/article/10.1007/s13253-014-0170-5 – Federico Tedeschi Oct 02 '18 at 12:47

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Your ordinal variable seems to be the covariable, so, you could use ANOVA as the case with nominal covariable. The difference might be in the post-analysis (that is, after calculating the ANOVA-table, where the nature of the groups might suggests some natural contrast to test.

To get a more complete response I need more details, about your setup and goals.

kjetil b halvorsen
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  • Hi Kjetil, Thanks for this. As you say, the ordinal variable is the covariate in my data. My goal is to ask whether group membership is associated with a significant change in dependent variable (here: height). For setup, what information would help? I have an ordinal scale, five groups, and about 100 members per group. My concern is that ANOVA is less sensitive to changes in the dependent variable between groups, since it takes no account of the order of the groups. I wondered if a "non-parametric" mixed-model exists, or similar? Happy to supply more details. Thanks, Tim – Tim Jan 30 '15 at 11:42
  • Can you give full detail of the construction of your ordinal co-variable? – kjetil b halvorsen Jan 30 '15 at 13:46
  • Sure. It's an assessment of the amount of exercise that people get, taken by survey, with answers fitted into a Likert scale from 1-5 - 1 is very little, 5 is several hours' exercise a day. Does that help? Thanks, Tim – Tim Jan 31 '15 at 15:12