Hardeep Hira There is no special threshold or point at which a distribution (residuals) becomes "normal". Most parametric tests can handle data that are not perfectly normal, so long as they approximate a normal curve (unimodal, not severely skewed). Recall that the normal distribution is a theoretical distribution, not an observed distribution. The nay-sayer here seems to be under the impression that there is a strict threshold for normality that can be proven/disproven. There is not.

If you're really unsure, there's no rule against conducting both parametric and nonparametric tests with the data and comparing the results. Are they pretty consistent?

the mean more accurately represents the center of the distribution of your data, and your sample size is large enough, use a parametric test. If the median more accurately represents the center of the distribution of your data, use a nonparametric test even if you have a large sample size

Blaine Tomkins Thanks for clarifying! I wasn’t sure which results to include in my write up. Yes, they’re consistent. The conclusions would be the same and the P values are only slightly different.

Hardeep Hira In that case, I think a parametric test is ok.

Do you want to estimate parameters? If so, yes. If not, no.

If you mean a test that makes different assumptions, it will depend what those assumptions are and the amount of deviation from the assumptions. But given you said about parametric, it depends if you want to estimate parameters.

It is suggested that the sample size should be a minimum of 30 to do parametric test. Because sample size of 30 or more is needed to have central limit theorem to be valid. Once the sample size increases the sample means distribution tend to be normal (central limit theorem)