Statistics establish a correlation with the stated degree of probability.

They do not of themselves (please note those two words) establish cause and effect.

Popper appears to overlook the methodology of scientific observation. One posits a theory, then formulates what it will predict, then tests those predictions.

Thus, in fact, observation roots speculation which may then be tested.

Ever studied stats, Peedee? It was the only one of my subsidiaries in which I got first.