I have used a questionnaire to collect data from 200 people.
This questionnaire was obtained from a published research paper in which researchers had used it in a specific population. It involves 34 items that are nominal multiple choice questions with one possible answer.
For example: Which factor do you consider?
- X
- Y
- Z
Questions do not have all the same number of possible answers. For example, question1 has 3 possible answers, question2 4 and so on.
According to the paper, Cronbach's $\alpha$ was 0.62.
I wanted to use the questionnaire in a different population. I carried out a pilot study in 20 people and made some changes. My colleague in charge of the statistics calculated Cronbach's $\alpha$. It was 0.65. When I finished the study, gathering data from 200 people, the calculated Cronbach's $\alpha$ was 0.57.
However, I myself think that Cronbach's $\alpha$ is not suitable in this case, as my questionnaire is not Likert, nor scaling. I believe that neither was it suitable in the original published paper. Unfortunately, time has passed and test-retest cannot be performed.
So, do you think that Cronbach's $\alpha$ can be applied in this questionnaire? Which is the correct way of coding these data (different coding results in a different Cronbach's $\alpha$)? What other reliability tests can be performed in this case?