B.F. Skinner did a cool little
experiment that demonstrated Coincidental Correlation. He set up a
food pellet dispenser to dispense food at random intervals. He put a
pigeon in a box with said dispenser.
After a while, the pigeon trained itself to perform unnatural acts like hopping on one leg and tucking its head under its wing in the hopes of getting a treat, because by coincidence, a pellet had been dispensed the last couple of times it had done that.
This is what Skinner called superstition. I think of this experiment every time I hear someone resort to Coincidental Correlation.