# Does p value below 0.05 in mvShapiro.Test mean multivariate normality or not?

I am performing mvShapiro.Test from mvShapiroTest package. I get MVW = 0.9578, p = 0.0007656. I want to know whether the variable is normally distributed or not. One person in his thesis has showed that p-value below 0.05 do not violate normality. Is he correct? When p is below 0.05 in a univariate Shapiro test, that means it is not normal. Moreover, if it is non normal, what is best way to normalize it?

• A comment below in reply to an answer implies that you have Likert scale data. That being so, you cannot even in principle achieve normal distributions! – Nick Cox Jul 1 '15 at 19:21
• In addition to @NickCox's comments & the answer below, be aware that 'normalization' refers to transforming a variable to lie within [0,1], not with transforming it to be normally distributed. – gung Jul 1 '15 at 19:23