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I have a questionnaire data that consist of composite Likert scale and discrete Likert items.

Likert scales or variables are the sum of few Likert items while the one-item variables are represented by one Likert questions.

Could I run normal distribution tests on both composite and individual Likert variables in order to determine if i have to use parametric or non parametric tests?

Thanks

Wael Ashi
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  • Any individual variable (which typically is scored in no more than seven or ten categories) obviously cannot be even remotely "Normal," so what's the point? – whuber Aug 29 '17 at 20:36
  • Sums of discrete variables are discrete. They *can't* be normal. Given we know before we start that such scales will *not* actually be normal, what is it you're really trying to find out? Note that normality tests are not tests for "approximate normality" -- at large sample sizes a suitable test (e.g. a Shapiro-Wilk) will almost certainly reject. What would rejection tell us that we didn't already know? What would non-rejection tell us other than our sample size was too small? – Glen_b Aug 30 '17 at 01:39
  • I expect a more interesting question than "is it non-normal" would be something like "is it reasonable to use this particular procedure that assumes normality" ... a question which is [not answered by normality tests](https://stats.stackexchange.com/questions/2492/is-normality-testing-essentially-useless). Note also that testing assumptions and choosing a procedure based on the outcome impacts the properties (type I error rates, power) of the subsequent procedures. – Glen_b Aug 30 '17 at 01:41
  • possible duplicate https://stats.stackexchange.com/questions/88071/5-likert-scale-and-normal-distribution-prior-to-parametric-testing ... and https://stats.stackexchange.com/questions/23593/checking-normality-of-a-likert-scaling-question and https://stats.stackexchange.com/questions/126788/how-to-judge-if-5-point-likert-scale-data-are-normally-distributed – Glen_b Aug 30 '17 at 01:44

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Likert variables cannot be normal. Just think yourself, how many levels in that likert you need to approximate the normal distribution?

Now, whether the distribution of the parameters of the model can be approximated by normal distribution is a different question. Here, if you have a large enough sample you have a good chance to get the normal distribution.

Aksakal
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