How do I use inferential statistics on Likert scale data?

Question

I'm doing research for a class, and I'm collecting the following data:

The background questions are my independent variables and the survey questions are my dependent variables. For the latter, I'm using a 5-point Likert scale (strongly disagree, disagree, etc.)

The purpose is to observe if there's a difference in preference for food in different demographic groups. E.g. People with higher education have a high preference for Italian food, older people prefer Chinese food than younger people, etc.

Some of my hypotheses:

1. There is a difference in preference across age, income, education, etc.
2. People with higher education have a higher preference for Japanese food than those less educated.
3. People with middle income have a higher preference for Italian food than for other cuisines.

I'm struggling a bit, because the only hypothesis testing we've learned is t-test and ANOVA, and I don't think I can use those on ordinal data. I've googled a bit, and I've come across two potential tests I can use:

• Ordinal regression
• Chi-squared test

Do you think these can be used to test my hypotheses? Hope you can point me to the right direction.

Answer 1

When you have only ordinal Y then ordinal regression can be ideal. If you have only a single X that is possibly ordinal then rank regression may be what you need, with careful attention to how ties are handled. Some choices include Somers' $D_{xy}$, Goodman-Kruskal $\gamma$, and various versions of Kendall's $\tau$. When you have more than one X and want to respect the ordinal nature of one or more of the Xs then you may need to use a Bayesian model that is tailored to ordinal X such as what the R brms package does by default for ordered factors.