Hi, I would first recommend you to make sure that you followed all the assumptions required on conducting your data and then do the normative test like you're saying that you did on it. And then you can use the SPS data results that come out, but they say non-normal. Hope that helps, thank you Marina Khan.

The values for asymmetry and kurtosis between -2 and +2 are considered acceptable in order to prove normal univariate distribution (George & Mallery, 2010). Hair et al. (2010) and Bryne (2010) argued that data is considered to be normal if skewness is between ‐2 to +2 and kurtosis is between ‐7 to +7

When maximum likelihood (ML) estimation is used in covariance-based structural equation modeling (CB-SEM), multivariate normality is assumed. However, violations of normality are not necessarily problematic. Robust ML estimation methods (e.g., Satorra-Bentler correction) or bootstrapping (Bollen-Stine) can be used to adjust the model fit statistics and standard errors when variables are not normally distributed.

Thank you for your inputs Marina Khan , Kaspul Anwar and Christian Geiser

Commonly, when you are working with big enough samples non-normality is not important. For example, using Student t test 40 cases or more samples non- normality is irrelevant. Similar when a variance analysis is done.

Your sample size is large enough to offset the effects or relevance of non-normality as in Z-tests and tests of variance. So I think that you will be in order to use your data to conduct analysis in SPSS and CB SEM.

Thank you José Luis Palacios and Chinelo Duze . That is very encouraging.

Smita, you asked "Can I work in SPSS and CB SEM using non-normal data?".

First, not all methods require data to be normally distributed, and indeed you may expect non-normality. For example, if you were trying to describe the distribution of income in a country you would make a prediction that it would be skewed to the right and you could use tests of normality to check if your data did indeed deviate from a normal distribution. You can do this in SPSS, so to some degree the answer is 'Yes'. Can you do all analyses appropriately in SPSS if your data are non-normal?, then the answer is probably 'No'. Indeed, the "Can I work in ..... CB SEM using non-normal data?" part of the question could be restated as "Is there any better why to handle non-normal data than CB SEM?" then the answer would probably be 'No'. Indeed when you are testing measurements and complex patterns of relationships then there is probably no other option that SEM. Nowadays, what we used to call SEM is a much broader statistical framework that can accommodate both continuous and categorial variables very easily and, as Christian said, we have methods of estimation that are very forgiving about departures from normality.

Mark

Thanks a lot for a very comprehensive answer Mark Shevlin