I recommend you to do the mahalanobis distance (you can do it in spss or AMOS, there are tutorials in youtube) and correct the atypical values of the multivariate normality to fit your parameters. Otherwise you can apply globally the Shapiro-Wilk test when some indicator does not meet the normality distribution.

thank you so much. i check the tutorials.

you said Shapiro wilk.! there is a problem. My two variables have skewness and kurtosis near 0. they are in recommended range but there shapiro wilk test is significant.! how can I interpret this issue. can I just depend on skewness and kurtosis and leave shapiro wilk?

Hello Afaque,

Depending on the type of analysis you intend to run, you may be better off checking multivariate normality rather than just univariate (while univariate normality is a necessary condition for multivariate normality, it isn't a sufficient condition).

As well, please note that the normality assumption for parametric tests applies to the "errors" (observed - estimated/predicted/fitted value), and not the raw scores. Hence, if you're running a regression analysis, check the fit of the residuals to a normal distribution. If you're running t-test, anova, etc., then either check normality separately for each cell or compute errors from the structural model and check those for normality.

A final note: Goodness of fit tests (like Shapiro-Wilk, Anderson-Darling, Kolmogorov-Smirnov) are effectively testing fit of all the moments of a distribution to the target distribution (in your cass, a normal distribution), whereas the test of skewness or of kurtosis just looks at one moment, each.

Good luck with your work.

Thank you so much dear sir