# Can I use a one way ANOVA with multiple categoricals as a response variable?

I do not know a lot about stats so forgive me. I have a dataset which has $N$ number of participants and their choice between 1, 2, and 3 at any given point. I want to analyze the distribution of the choices between 1, 2, and 3 by participants' age and sex. How would I set up a test to look for significant interactions between these variables? I thought I needed a one way ANOVA but I am not sure.

Thank you

• One-way ANOVA is used to detect differences in location of a quantitative outcome based on categorical predictors. In your case, you have a categorical outcome and either two categorical predictors or one categorical and one quantitative predictor (depending on how you code age). You could use multinomial logistic regression. – Max Jul 24 '12 at 16:50
• Hi, @Max, that seems to be exactly the answer to this question. Would you mind making it an official answer (possibly elaborated a little more, I gather the OP won't be familiar w/ that)? – gung Jul 24 '12 at 17:34
• One quick question... does the order of 1, 2, 3 count? For example, is it a rating like, sort of like, don't like? Or, is it really categorical. It's rare people make choices that are truly categorical like that. – John Jul 24 '12 at 18:24
• @John Hello, yes I believe it is categorical. The choice was "left", "middle", or "right". Was I wrong to use 1,2,3 as an example? – Mike Stumpf Jul 25 '12 at 13:21

Given your comments I believe it might be better to treat your dependent variable as ordinal rather than nominal. Consider Maybe even recode it to 0, 1, 2 and make it distance from the left. Now it's easy to see that it's ordinal. There's a good package for this in R called, appropriately if not redundantly, 'ordinal'. If you have multiple judgments / subject then you want multi-level ordinal regression, which this package can do as well.

Why ordinal? It's much easier to discuss (and the regression is much nicer). You can talk about the probability of a response shifting more rightward and think of response distributions moving in directions, which don't exist in nominal space.

To analyze it graphically you want to look at distributions of the scores separated by sex, and age. Line plots are best for this with the ordinal variable on the x-axis and counts on the y. The ordinal regression can treat age continuous but for convenience of visualization you need to bin it into 2 or 3 groups separately for your two sexes... which would each be in separate plots. You can also plot the predicted counts from the regression on the graph as lines and leave the empirical as points.