To test normality for a likert scale, you need to sum the tiems to get the total score for each participants. The you can run skewness test {from  descriptive option in SPSS}. If the skewness value less then .20, this will be excellent for normality. The maximum accepted level for narmality in many textbooks is not to exceed 1.0

Dear Muayyad,

Thank you for your quick response.

I just want to clarify weather it is reasonable to sum the items in this case. Question is formulated in the following manner: Please evaluate to what extent do you like each of 5 brands (0= strongly dislike and 10=strongly like). So I have in my data 5 variables for each brand  with separate scores. So, I have to sum this scores and calculate scale score (one variable) and then use skewness and kurtosis option, right? You are absolutely, right that different acceptance level is considered in different sources. Which one to consider ? Rule of thump is the following

If skewness is less than −1 or greater than +1, the distribution is highly skewed.

If skewness is between −1 and −½ or between +½ and +1, the distribution is moderately skewed.

If skewness is between −½ and +½, the distribution is approximately symmetric.

What about kolmogorv smironov  and Shapiro wilks tests? 

If i find it is not normal and skewed, then which test would you suggest for understanding to what extent my variable deviates from normality? 

Best regards, 

Davit 

Dear/ Dr. Muayyad

How are you wish you are doing well. I need verification about test normality for a likert scale you mentioned that we should sum the items to get the total score for each participants "

so what do you mean by each participants     do you mean after entering the whole data for all participants? 

OR.... Do you mean I should use an example of one participant & then I'll have the normality value?

Thanks