For Becker this is literally true: what we regard as normality is our collective, protective madness, in which we repress the grim truth about the human condition.

With large sample sizes, both tests are very sensitive to slightest violations and will usually have p-values below .05, although the data/residuals are sufficiently normally distributed.

Underlying Assumptions: Normality

However, platykurtosis can have a profound effect when your group sizes are small. This leaves you with two options: (1) transform your data using various algorithms so that the shape of your distributions become normally distributed or (2) choose the nonparametric Kruskal-Wallis H Test which does not require the assumption of normality.

Testing for Normality using SPSS Statistics