How can I answer this question:
Is there any relationship between teachers’ personality and their perceptions of principles of critical pedagogy?
Teacher personality consists of five type of personality critical pedagogy consists of a Likert-scale (1-5).
I would consider an ordered probit or logit model with dummy variables for each personality type. Here's another example of this type of model. This would allow you to express the probability that a teacher's perception of critical pedagogy is 1,2,3, 4, or 5 for each personality type and any additional characteristics.
If the personality measure is ordered, say from least authoritative to dictator, then methods that are simpler and more correlation-like can be used that take advantage of this.
Citation for Ordered Probit:
"A Graphical Exposition of the Ordered Probit" by William E. Becker and Peter E. Kennedy, Econometric Theory, Vol. 8, No. 1 (Mar., 1992), pp. 127-131
