Why correlation does not guarantee causation?

Answer 1

Correlation shows a possible relationship between two random variables. It does not say one variable causes a result in another. It further is wrong to conclude if event B occurs after event A, then A caused B. An example from Darrell Huff's book, "How to Lie with Statistics": A correlation is found between smoking and low grades. Does that mean that smoking causes low grades, or low grades cause people to smoke? It seems a good deal more probable that neither of these things produced the other, but that both are a product of some third factor. The inches of rain in Spain may correlate with the temperatures in Mexico, only because there is similarity of seasons. Small or improperly taken sample may show excellent correlations. The cumulative sum of births in China in one year (each day the total is the sum of all other previous days) will show an excellent correlation with the cumulative sum of rainfall in Germany. This correlation is because the the same values are repeated in the cumulative sums.