comparing likert data scores

Hi...I don't know why this question is so hard to find an answer on. I have a simple situation. I created a questionnaire with 6 point likert answers with a scale going from strongly disagree to strongly agree. There are 8 items within a section. One section is on, for example, "what about distance learning do you find difficult for your learning?..for example one item is, "it is difficult to understand how to do assignments in my distance courses" , another item is "I feel shy to communicate with other students", I want to find out which of these two difficulties is more a problem for my students.

Mean likert values seem to be a good way to display data...along a line, but to compare means...8 of them in a section sounds like anova,

but as this is interval data would I use chi square?

If I use chi square do I even bother to report means?

Does anyone have any good references for statistical analysis of survey data?


TS Contributor
There's a huge debate ongoing in the social / behavioral sciences over whether Likert scales should be treated as ordinal or interval.

Count me as one who thinks it's OK to treat them as interval.

I would analyze the data both ways - with chi-square and with ANOVA, and see how it turns out - if the outcomes are the same, you're all set. If you get something different with each method, then you have something interesting...

Overall, you can treat the scales as interval and run methods that compare means, such as ANOVA. The scales are close enough to interval so that these methods shouldn't lead you astray.
Thanks plu

Many Thanks for the reply...I can imagine the situation with 8 items in a section resulting in 8 means and then doing an ANOVA with these 8 means. Then if significant I need to do a post hoc with..maybe Tukey's test?

In regards to chi square, I can imagine two items being compared by chi square with frequencies of response in each box of the 6 categories of likert answers..chi square test of independent means.

But I can not imagine how to compare frequency of likert scores for 8 items.

Also post hoc for chi square, I am not sure of...

Do I need a tutor? I'm a Phd student submitting a proposal for dissertation today, and distributing quesionnaires in August if all goes well. Finished advanced stats last month, but a few gaps reside...


TS Contributor
Yes, Tukey would be fine for a post-hoc test. It's "middle-of-the-road" in terms of liberal/conservative (Fisher's LSD is liberal, Bonferroni is conservative).

In terms of how you would use chi-square, you could set up a comparison between the groups you want to contrast, and do the analysis on the frequency of each choice, between the groups (i.e., did one group choose "agree" more often than another group). Yes, it would be a chi-square test of independence. The contingency table could be set up with groups as rows, and scale items as 8 columns. The cells of the table would contain the response frequencies.

For chi-square post-hoc, use a simple comparison of two independent proportions with a z test.

You wouldn't necessarily report means with a chi-square analysis, since your interest is in comparing frequencies, but that's not to say you wouldn't do some sort of basic descriptive statistics comparison (means, medians, std dev, etc.)

If you feel you need a tutor, I can help - see my link at the bottom of the post. In your situation, either the "project" or "explanation of concepts" may apply.