First of all, sorry for catchy title, my question is not that broad as it suggests.
I just came to conclusion that I don't need parametric tests. Instead, I need some feedback if my reasoning makes sense. Here it is:
To use some parametric test (like t-test or ANOVA), we have to check assumptions of it (normality, heterogeneity of vaiance). But all the tests for assumptions (Shapiro-Wilk, Kolmogorov-Smirnov, Anderson-Darling, Bartlett, Snedecor's F and so on) test null hypothesis of assumption being met against alternative that it is violated.
So I can only reject null (conclude that assumption is violated) or say that I don't have enough evidence to do that. Typically, in later situation, I use parametric tests. This means that I use it when I do not actually know if assumptions are met.
My conclusion: I should use nonparametric test anyway.
My conclusion 2: I can use parametric test only when I have some "external" knowlegde about assumptions being met (like I somehow know exact distributions of my data).
That's all. I'll be greatful for any suggestions if above makes sense.
Edit: I know that parametric tests are more powerful when their assumptions are met. My concern is that we can never know that this is the case (unless we have "external" knowlegde). So, I think, using parametric tests is pointless since we don't know if we have data appropriate for them.
Analogy that comes to my mind: Imagine two stain removers: Parametric Remover is perfect for cherry juice stains and Nonparametric Remover is OK, but not perferct, for all the stains. Since I can never confirm that my stain is cherry juice, I should always use Nonparameric Remover.