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I have 4 independent variables and 1 dependent variable. In my questionnaire (a likert scale), each of the factors consists of 5 questions (items). How do you do the normality test in this situation? Do you test the items one by one, for all 5 items per factor, or compute their mean first to test the factor as a whole? (I am using SPSS.)

gung - Reinstate Monica
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It makes no sense to test either the items or the factor as a whole. Neither could possibly be normally distributed. Consider that the normal distribution goes to infinity in both directions. Is it possible for the ratings to your questions, or the mean of those ratings to go to infinity? A typical likert item is paired with a rating scale that goes from 1 to 7, note that $7\ll\infty$. Even if your data could do that, it still isn't very likely to be normal. For these reasons (and more), I thing testing your data for normality is a waste of your time. (It may help you to read this excellent CV thread: Is normality testing 'essentially useless'?)

Of course, depending on what your purposes are and why you are worried about normality, it may be that your data are close enough to normally distributed for your purposes. To assess that, you could look at a qq-plot or check some descriptive statistics like the amount of skewness or excess kurtosis in your sample.

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gung - Reinstate Monica
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  • Thank you very much for the explanation. I am still new with SPSS and I am learning based on books. That is why I need clarification whether I need to do normality test on every data or not. Thank you again! :D –  Jun 08 '15 at 01:58
  • You're welcome, @amy. To supplement your learning, you may find it helpful to read some of the threads on CV (& ask when you're stuck & can't find an answer among the existing threads). – gung - Reinstate Monica Jun 08 '15 at 02:05