Statistical analysis plays a major role in biology, be that population genetics or enzyme kinetics.
What this simply means is that numbers can be employed to express relations that describe cause and effect in a system. On the other hand, the knowledge of which characteristics causes the other is not the result of this numerical description. To understand cause and effect, we need to understand the mechanism underlying the observed properties. To answer the question if biology is a statistical science, we have to understand why it is a necessity to know about mechanisms. The latter disciplines are statistical sciences and describe systems at equilibrium, very simple systems at that.