I'm making a code in R that contains some parametric and non-parametric tests, like ANOVA and Kruskal-Wallis.
To know if I should use one or another I check the "normality" of the test sample. My question is the following: my sample has thousands of values (let's say, around 10000) so I checked the histogram, boxplot and used the ad.test to check if can be accepted the normality assumption. Since is a large sample ($n\ge30$) we should consider that the sample could be normal, even if the p-value is below the significance level (0.05), but if the outliers have a lot effect, we should reject the normality assumption, right? Is there any percentage of outliers that must exist to reject the normality hypothesis?
Sorry if this question is confusing. I'm not used to work on statistics so I'm a little confused with this topic.