In the past, I used a 20% cut-off as a rule-of-thumb when making decision about use or not to use parametric procedure on a numerical response variables. For example, there would be a 3-factorial experiment with 3 fixed effects arranged in 2x2x3=12 treatment combinations. Each combination would be evaluated for the compliance with assumption of normality of residuals.

a. If all 12 groups are normally distributed, great, I would apply parametric method, such as factorial ANOVA. That does not happen in my practice very often.

b. If all 12 are not normally distributed even after evaluating outliers and applying transformation (the same transformation applied to all observations and groups of the variable), and other distributions like binomial, exponential, Poisson, Gamma, Betta, Log-normal..., also fail, I may use nonparametric Cochran-Mantel-Haenszel test.

c. When 2 of 12 (~17%) are not normally distributed, I would still go with parametric method.

d. When 3/12 (25%) are not normally distributed (like in b.) I look for nonparametric approach.

I learned this during statistics training from my mentors.

I am wondering if other community members use similar approach and if there is a proper citation to this?