Shapiro-Wilk - apparent discrepancy

coledavis

Correlations.csv

Using the two variables, CapPun and LifeIsLife (comparing attitudes to capital punishment and the notion of full life sentences), the Shapiro-Wilk within the Descriptives section gives the result I was expecting (a high p value, indicating normality of distribution). However, the Shapiro-Wilk test in the Correlation section, 'assumption checks', using the same data, gives a p value which is < .001 (completely unexpected). I had a look at paired t tests, and the results in terms of W were somewhat different again.

patc3

The test is descriptives is univariate (i.e., does each variable follow a normal distribution indiviodually?), while the test in the correlation analysis is either bivariate (do both of my variables taken together follow a bivariate normal distribution?) or multivariate (do all of the variables that I've included together follow a multivariate normal distribution?), depending on whether you checked pairwise or multivariate normality (respectively)

It's quite a bit harder to "achieve" bivariate/multivariate normality than univariate normality