# Correlations between groups of Likert-type answers – choice of statistical test

#### ajvar

##### New Member
I'm looking for the optimal way to interpret some data, so any constructive advice will be appreciated.

A questionnaire with 3 groups of 50 questions was distributed to all companies of a certain type (that is, whole population). All in all, there were 40 companies. Each and every company replied to every question that was in the questionnaire. We can assume that they replied truthfully to all questions, although there is a possibility for bias. The answers were collected via Likert type scales:
1. group | 5-point Likert-type | measuring attitude
2. group | 5-point Likert-type | measuring resources
3. group | 6-point Likert-type | measuring effectiveness

I have an assumption that certain correlations between the answers should exist. That is, I believe that if a certain company replied in a certain way on a question in the first group, it is more likely the same company will answer in an expected way to the related question in the third group.
Furthermore, I believe that the population can be divided in 2 groups (10 companies in one group and 30 companies in the other), and that there should be some similarities between their answers.

What statistical tests would you recommend for testing of these hypotheses? Would Kendall test of association be a good match for the first hypothesis? Or would Spearman be more appropriate? And how to approach the problem of determining ranks?
Would Mann Whitney U test be appropriate for testing of the second hypothesis?

Any additional advice will also be welcomed (including where to move my post if this is not the best sub-forum for the subject matter). I’m using “R” for calculation.

#### noetsi

##### Fortran must die
You can create a dummy independent variable with the two groups of companies and run this against the likert scale variables. Depending on how you define this this might involved ordered logistic regression or multinominal regression. If the independent variable is signficant it means the two groups are different from each other on these variables.

You might run factor analysis between the companies and see how the factors that result vary from each other. Or you might try structural equation models that compare groups to the likert scales. The later is pretty complex and requires speciality software.