Normal distribution, likert data, median or mean?

Question

1. Which aspects of my data do I need to check for normal distribution please? If it's Likert scale items; they cannot be normally distributed right? So how can I determine what to check for normal distribution and whether I can use parametric tests at all please?

2. I'm doing a study on two sample groups. I have collected data on a likert scale for 3 different measures; eg. measuring attitudes on a 20 question scale-strongly disagree to strongly agree. I need to run a mediation model between these 3 variables but how do I actually put all of the responses into one variable for running the mediation; so what do I need to do to be able to put 'attitudes' as a variable in my mediation?

Answer 1

To question 1: Data obtained in the real world, be it by measuring or by Likert scales, is never normally distributed in the strict sense. Normal distribution is a mathematical concept. You can think about it, but never realise it (infinitly small and infinitely large and infinit number of decimals,...). The question may be: Is my data close enough to data that is drawn from a normal distribution to accept the small deviance. Usually the question is: Are the residuals "normal enough". There is a lot of margin for personal opportunity, what is "normal enough" for parametric testing and what is not. Often times, it depends on the sample size. Many parametric tests become quite robust against deviations from normality, if the samples are large. So the question usually only has meaning in small sample sizes, where all testing does not work good, anyways.

Question 2, I do not understand but agree with the comment of Antoine, that there should be one question per thread.

Answer 2

Question 2: Likert data is ordinal data, so use some methods for ordinal data, for example ordinal logistic regression for comparing your groups. Search this site for ordinal regression, you can start with Interpretation of ordinal logistic regression