# Do I need to check for normality in a one-way test (in R)?

http://www.sthda.com/english/wiki/one-way-anova-test-in-r

Here it says when the LeveneTest has small p-value we can use the alternative one

$oneway.test(...,var.equal=FALSE)$


but it doesn't mention how to check or if I need to check for the normality of the residuals.

Follow up question, regardless of the LeveneTest result (i.e. if the LeveneTest big p-value, and I use ANOVA (lm function) for example), can I use the CLT to assume normality of the residuals if n>>30?

• A quick google search says that Welch's one way ANOVA is robust to normality violation, so I'd say you'll be fine. – LAP Jan 25 '18 at 14:31
• Possible duplicate of Is normality testing 'essentially useless'? – Kodiologist Jan 25 '18 at 20:44
• Not necessarily definitive, but the first line in the documentation for oneway.test is "Test whether two or more samples from normal distributions have the same means." – Sal Mangiafico Jan 26 '18 at 15:16
• As to your followup question, see the answer by Frank Harrell here. – Sal Mangiafico Jan 26 '18 at 15:23
• @LAP, I think with such a broad statement, you'll have to bring some quality citations. I'm rather suspicious of the conclusion. – Sal Mangiafico Jan 26 '18 at 16:18

But the practice you are alluding to, choose which test to apply after seeing the results of some preliminary test of normality, is strongly advised against. If you are not reasonably sure about the normality assumption, choose some test which do not depend on it, at the outset! In R that could be kruskal.test.
You could look at the R package (on CRAN) for package WRS which have modern nonparametric methods.