Post-Hoc Ergo Propter Hoc

I prayed that God would heal Grandma's cancer, and she got better. Therefore:

• There is a God
  
• He answers prayer
  
• He heals the sick

Post hoc, ergo propter hoc is Latin for "after this, therefore because of this." This is also known as "correlation equals causation." One event precedes another, therefore the first event caused the second event. It's like the old joke:

Q: Why do you wear that funny hat?

A: Because it repels lions and tigers.

Q: But there are no lions or tigers around here for a thousand miles!

A: See? It works

You see post hoc reasoning all the time in quack medicine (did you all notice the little ad hominem attack I slipped in there?).  "I had disease X, I took this homeopathic remedy, and disease X went away. See, homeopathy really works!"

Pos hoc reasoning assumes a relationship between events because of their temporal order. I saw a shooting star, and Uncle Harry passed away the next night. So shooting stars can presage the death of someone close.

The problem is that sometimes there IS a causal relationship between two events. Most scientific studies are actually predicated upon this fact. But the error comes when you isolate events and assume causation where it need not exist. Often, one must selectively ignore other, disconfirming data, like the number of times one sees a shooting star and nobody dies. Or the times when I didn't wear the funny hat and still no lions and tigers appeared.

As the Wikipedia article on this logical error so neatly puts its, "The fallacy lies in coming to a conclusion based solely on the order of events, rather than taking into account other factors that might rule out the connection. Most familiarly, many superstitious beliefs and magical thinking arise from this fallacy."