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

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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? – Wrigley242 Jul 25 '12 at 13:21