Hello Brian,

1. It's the model residuals which need to be checked for distributional assumptions.

2. Checking skew, kurtosis means evaluating just one distibutional moment at a time. S-Wilks test attempts to check multiple moments. Thus, such goodness of fit tests are evaluating different hypotheses and using different methods of defining fit.

So, for G-O-F to a normal distribution, please note than any two tests you select may not agree. The key is, before condemming one or the other, are the p-values close (especially when near your arbitrarily chosen significance threshold) or wildly different? Finally, it makes more sense to settle on the one you're going to pay attention to before the analysis.

3. With small sample sizes, tests for normality may be a bit of an exercise in futility.

4. No, there's nothing wrong with trying variable score transformations, as long as these make sense. (For me, most scales are pretty much arbitrary to begin with.)

5. You can opt for robust regression methods, or for bootstrap methods of estimating model parameters. These allow you to set aside worry about specific distributional shapes.

Good luck with your work.

Hello David,

Thank you so much for your assistance. I will attempt to fit the data to a normal distribution by using the log 10; for the Shapiro-Wilks significance, I may simply add a comment.

I used a p-p plot in regression to determine the value of the residuals, and the 'dots' lie relatively close to the diagonal line; a few are not as close, but the majority are, so I can assume that the residuals are normally distributed.

If I use the data transformation, do I then use the transformed data to include in my descriptions and analysis? i.e. the M, SD and so on? Or continue to use the original data?

Brian.

If you have the possibility of using the Mplus program, you can define your variables as skewed T-distributed or as skewed normal distributed.

Hi Jan,

Thank you for your answer. Unfortunately, I can only use SPSS for this thesis. However, your suggestion is helpful.

Hello again Brian,

Should you opt for transforming one or more variables, I'd suggest reporting summary statistics for both original & transformed values (especially if DV was transformed). Do include correlations (transformed values) as part of summary stats.

However, for interpreting estimated regression coefficients, your discussion needs to make clear that you're talking about predicted score differences in the transformed metric(s), not the original.

Good luck finishing your thesis.

Hello David,

Thank you once again for your assistance. This information is valuable!