Question about Normality of 5-point Likert scale I'm really having a hard time trying to normalize my data. My study is about green IT product acceptance. There are eight factors, six are 5-point Likert scale (Str.disagree - Str.agree), one is 2-point Yes/No question, and the other one is 3-point scale (Don't know/Maybe/Know). I have 618 returned questionnaires. 
I add data into SPSS, compute variables, and round them up. I explored skewness and kurtosis of all factors and found that they're not normally distributed. I tried a Two-Step Transformation to Normality and Box-Cox, but the KS and SW Sig. are still .000. However, Q-Q plot change from loosely distributed to perfectly follows the slope.
My questions are:


*

*Is it a crucial problem if my data isn't normally distributed?

*Someone said Likert scales are not normal in their nature, is that true? 

*Do you know any literature to cite and explain why Likert scale isn't normally distributed?

*Do I need to normalize all variables before I do Structural Equation Modeling?

 A: 
  
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*Is it a crucial problem if my data isn't normally distributed?
  

Data are (almost) never normal. Whether that's an issue depends what forms of deviation from normality the procedure you want to use is sensitive to (and how much), how non-normal it is and in what way it's non-normal (strictly we're talking about the distribution the sample was drawn from rather than the sample itself). 
Where there's much doubt about the potential impact, try to avoid assuming things you don't need to.


  
*Someone said Likert scales are not normal in their nature, is that true?
  

They're discrete and bounded, normal distributions are not. 


  
*Do you know any literature to cite and explain why Likert scale isn't normally distributed?
  

"They're discrete and bounded, normal distributions are not." is 100% of the literature you should need ... it's simple mathematical fact, instantly apparent from looking at the definition of the normal density and a Likert scale that anyone could check for themselves. Would you really quote literature to support a plain statement of fact like "3 is not an even number"? 


  
*Do I need to normalize all variables before I do Structural Equation Modeling?
  

What is assumed normal in SEM and does that imply marginal normality of every variable? (My understanding is that the errors might be assumed MVN but that doesn't imply marginal normality of all variables, so it wouldn't automatically suggest transformation of variables that don't look normal on their own.
Note that "normalize" carries a more common particular meaning (or actually a couple) distinct from "transform to normal distributions" (see the tag wiki for normalization for a brief explanation)
