I have two scales measuring the same construct, and I would like to know which scale is distributed more closely to a normal distribution. There are various possibilities for comparing a distribution with a normal distribution (e.g., kolmogorov-smirnov test, etc.), but is there any possibility to compare the deviance from normality between two scales directly?
The R package
nortest contains 5 normality tests that you can conduct to test the normality of your samples. The question "which scale is distributed more closely to a normal distribution?" is wrongly formulated in my opinion, unless you can come up with a satisfactory distance in your context.
Please, find a simulated example below:
library(nortest) set.seed(123) data = rnorm(100) ad.test(data) cvm.test(data) lillie.test(data) pearson.test(data) sf.test(data)