How Do I Determine if My Data Is Not Normally Distributed (Non-Normal)?

In the Analysis Properties function , the output tab has a function called “Test for nor- mality and outliers”. After selecting this function, run the analysis. In the output, there is a link called “Assessment of normality”.This output will give the minimum and maximum values for each variable along with the skewness and kurtosis of the data.

Figure 5.41 Assessment of Normality Result

Skew—is the tilt in the distribution. The more common type is right skew, where the smaller tail points to the right. Less common is left skew, where the smaller tail points left. Negative skew is left-leaning, positive skew right-leaning.

Kurtosis—is the peakedness of a distri- bution. Negative kurtosis indicates too many cases in the tails of the distribution. Positive kurtosis indicates too few cases in the tails.

Figure 5.42 Examples of Skew and Kurtosis

Your data is still considered to be normal if your skew values range between −2 and +2. For kurtosis, the range is −10 to +10 to still be considered normally distributed. Based on our results, we can see that both the skew and kurtosis are in an acceptable range to be considered “normal”.

If your data is non-normal, you can use another estimation method (GLM instead of maxi- mum likelihood), which does not assume multivariate normality. A more common technique to address non-normality is to run your model with the bootstrap technique. Bootstrapping is a resampling procedure of the original data to determine if your estimated relationships fall within a confidence interval. For a detailed explanation on how to use bootstrapping to assess a model that has non-normal data, see page 287 in Chapter 10.

Source: Thakkar, J.J. (2020). “Procedural Steps in Structural Equation Modelling”. In: Structural Equation Modelling. Studies in Systems, Decision and Control, vol 285. Springer, Singapore.