My height is average.
I think height is one of the most important factors of success in sports, namely Basketball
I don't play sports, so it's not an issue.
I wonder if height has any impact in causing schizophrenia?
Definitely not. Schizophrenia has nothing to do with height.
How do you know for certain? There have been studies across 20 countries that show a strong association between schizophrenia and smoking, so you never know
Schizophrenics smoke because it reduces dopamine levels. It helps them cope. Your example is a logical fallacy.
Dopamine
Dopamine (DA, a contraction of 3,4-dihydroxyphenethylamine) is an organic chemical of the catecholamine and phenethylamine families. It functions both as a hormone and a neurotransmitter, and plays several important roles in the brain and body. It is an amine synthesized by removing a carboxyl group from a molecule of its precursor chemical L-DOPA, which is synthesized in the brain and kidneys. Dopamine is also synthesized in plants and most animals. In the brain, dopamine functions as a neurotransmitter—a chemical released by neurons (nerve
nothing, this is the height of emptiness. When it has no commerce with things, this is the height of limpidity. When it rebels against nothing, this is the height of purity. (15, tr. Watson 1968:168-9) 
The Yellow Emperor said, "Do-Nothing-Say‑Nothing — he's the one who is truly right. Wild-and-Witless appears to be so. But you and I in the end are nowhere near it. Those who know do not speak; those who