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 Shapiro Wilk Test gives different output depending on how many variables I add

John Travolta's profile image
John Travolta posted Sun December 08, 2024 08:37 AM

Hello there,

I am no big statistic mind, but I am trying to analyse whether my variables are distributed normally or not. I am using the explorative data analysis. But when I enter only one of my variables, I get a different result compared to entering all of them.

Could you explain why and which ones I can trust?

Best regards

Jon Peck's profile image
Jon Peck

First, I suggest that you install the STATS NORMALITY ANALYSIS extension command via Extensions > Extension Hub if your SPSS version qualifies.  It will appear in the menus under Analyze > Descriptive Statistics.

As for  your question, you probably have some missing values that are leading to more cases being excluded when you use more variables.

Bruce Weaver's profile image
Bruce Weaver

Why do you want to test for normality?  If you are doing so to justify the use of t-tests, ANOVA, or some other OLS method, I would not bother.  Here is why.

  • A sufficient normality assumption for OLS models (including t-tests, ANOVA, linear regression) is that the errors (i.e., the deviations of the observed values of Y from the true, population regression expression) are sampled from a normal distribution with mean = 0 and variance = sigma2.
  • As n increases, those sampling distributions approach the normal distribution, even if the errors are not normally distributed. 

Putting it all together:

  • The smaller n is, the more important it is that the errors are sampled from a normal population; but with small n, tests of normality have low power, and are probably unable to detect important deviations from normality. 
  • As n increases, normality of the errors becomes less important, but tests of normality have increasing power, and therefore, throw up the red flag of non-normality when there is no important violation (because the sampling distributions of the parameter estimates are approximately normal). 

For those reasons, I once gave a short conference presentation in which I described testing for normality as a precursor to t-tests as silly and pointless.  YMMV.

I hope this helps.