I have a questionnaire which contains 8 questions on a 4-point Likert scale. This questionnaire is repeated after 8 weeks and a training course about the subject. There are approximately 30 - 35 people answering the questionnaire. I want to determine whether the training had any effect - but a t-test seems very inappropriate, as the data is clearly ordinal and not even closely a normal distribution. Simultaneously, I cannot pair them, as the answers have to be completely anonymous. And additionally, I would like to determine which of three added questions - education level, work experience, and work place - have the most influence on the answers. Any and all suggestions will be taken under consideration. Thank you!
You can use ordinal logistic or probit regression with the scores on the pre- and post-tests as the outcome and time and your other variables as the predictors. Ordinal regression implicitly models a latent logistic or normally distributed variable, which is discretized into the ordinal variable you observe. The coefficients can be interpreted as the linear effect of the covariates on the latent variable.
To examine whether the covariates modify the effect of time, you can include interactions between the covariates and the time variable.