One-way ANOVA or Chi².

Hey guys,

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.


Omega Contributor
Yeah, not sure that scale really fits Likert format, and not sure if an assumption of interval data means that each group is suppose to be equal distance from each other this would work under that definition.

This may fall under chi square, where did you get the scale from and how do others traditionally analyze data from this scale?

FYI, for non-normally distributed data, Kruskal Wallis is usually used in lieu of ANOVA.
Thank you for your reply hlsmith.

I'm also not sure whether the scale fits Likert format, especially since there seems to be no 'room' between different options.

I'm aware of the Kruskal Wallis test, but our professor explicitly told us to limit ourselves to either Chi² for the nominal dependent variables and ANOVA for the interval variables.

I suppose these types of questions would be Chi² then.

However, what about the following:

Q22 | Frequency TV (V22)
On average, how often have you watched TV in the past 6 months?

1  Systematically every day of the week, i.e. 7days /7
2  Almost every day of the week, i.e. 5 or 6 days/7
3  Often, i.e. 3 or 4days / 7
4  Now and then, i.e. 1 or 2 days/ 7
5  Rarely , i.e. less than 1 dag/7
6  Never
7  Don’t know

When I look at the wording of the options, I would think this could be done via ANOVA. However, looking at the specifications next to it, I would exclude ANOVA again.

The problem is that we haven't seen this type of data in exercises. Either it's been clearly chi², or clearly an interval variable. But these types of questions have us fumbling in the dark a bit.


TS Contributor
The items you cite are ordinal scaled. Why don't you just use tests for ranked
data? E.g. hlsmith mentioned the Kruskal-Wallis H test as an alternative to oneway

With kind regards