Thank you very much, Glenn. What you said that I will get is kind of what I want. I just would like to have a statistical analysis to justify these patterns. If I get these three divisions, I would be able to separate teachers as overall weak, some strengths and some weaknesses and overall strong, for example. But at least it would not be arbitrary. However, I am still at the beginning of the development of the questions. Basically, I have a classroom situation, and I ask the teacher what would be the best thing to do. I then provide 4 options, in which, one of them is the best option (based on the situation proposed). However, in any option, the teacher shows some knowledge about what is being assessed. I would be glad if you could give me some advice about that.

Why not perform factor analysis or item response theory (IRT) on the data to generate a scoring algorithm for the entire survey. That will allow you to then rank your teachers according to their overall score. You could also consider 

Melise, 

If your audience is highly technical, IRT is a good solution; but I have found that audiences trained in classical test theory don't intuitively understand it. Something that the lay audience and educated/non-technical audience understands is conduct a discriminant function analysis. Mahalanobis distances will tell you how likely a teacher is to belong to a group and the data indicate how many groups you actually have within your data.

As far as I know, neither Factor analysis nor IRT will group the participants according to similarities in their response patterns.

One way to accomplish this is to transpose your data matrix so that the respondents become the columns and the variables the rows. You can then use that as the basis for a distance matrix that can be input to a cluster analysis. In effect, you will be generating measures of similarity between the participants, according to how similarly they responded to the items.

This also allows you to use factor analysis, where each factor groups together participants according to how highly correlated their responses are. In factor analysis, this is known as Q factoring (where the usual approach is then called  R factoring).

What is known as Q-analysis relies on this kind of factoring, although it usually involves a number of other techniques and assumptions that you don't need to get into if all you want to do is cluster your participants.

FYI how you do the transposing will depend on what analysis package you are using. The simplest thing to do might be to export the subset of variables you want to use to Excel, and transpose that before you reimport it. In any case, a little internet searching will help you find the relevant commands.

Hi

Maybe yo need to try more tan one method. Remember that the use of a technique is conditioned by the number of subjects in the study. In my opinion, it is important to have a theory for an initial approach; so you can get an idea of what might be found in the data.

If you have enough cases, you might try some tools in the context of the IRT. For example, you could build a "Wrigh Map" which orders in the same scale, items and examinandos', you could use factor analysis, cluster analysis, etcetera.

The use of more than one technique may help you discover patterns that can not identify with others; then you could build a "theory" of what the data show him. Thus, in a second round, a model could be built with tools or more specific techniques.

If you provide details of their study, maybe I could try to suggest more specific tolos.

I did a little further searching, and it appears that SPSS has an option in CLUSTER where you simply specify whether you are clustering cases or variables. If you are indeed using SPSS, this link should be especially helpful:

http://www.norusis.com/pdf/SPC_v13.pdf

Thank you all. I'll have a look at all suggestions and I'll tell you afterwards.