I'm busy with a market research case for school and my team is in doubt on which analysis to use. It's important to note that it's not a statistics class, and we're to limit ourselves to ANOVA or Chi².

The situation: We performed a factor analysis and k-means cluster analysis on our basic variables and ended up with 4 clusters. The point is now to check with the other variables in our questionnaire how the 4 clusters differ in terms of different types of behaviour.

The questions are like this:

"I own...

1. Tablet

2. Smartphone

3. etc"

It's clear we use Chi² for this.

Others are like:

"I watch TV...

1. Daily

2. 1x week

3. 1x month

4. Less than 1x month

5. Never".

We thought we had to use ANOVA on those. However, if I remember my old statistics class, we only assume Likert scales are interval when there are 5 options minimum, and n>30 (our n=1600), but with the extra assumption that the difference between 1 and 2 is similar to the difference between 4 and 5.

What should we use on the latter style of questions? One-way ANOVA or Chi²?

Thank you for your input, it's much appreciated.