The Art of Statistics: Learning from Data

by David Spiegelhalter

George Gallup, who essentially invented the idea of the opinion poll in the 1930s, came up with a fine analogy for the value of random sampling. He said that if you have cooked a large pan of soup, you do not need to eat it all to find out if it needs more seasoning. You can just taste a spoonful, provided you have given it a good stir.

population can be thought of as a group of individuals, but also as providing the probability distribution for a random observation drawn from that population.

But I will never know if this daily ritual does me any good in the long run; it depends on which of my many possible future lives actually occurs. If I never have a heart attack or a stroke, I will have no idea whether I would have never had one even if I had not taken the tablets, and all this pill-popping for years was a waste of time. If I do have a heart attack or a stroke, I will not know if this event was delayed by taking the statin. All I can ever know is that, on average, it benefits a large group of people like me, and this knowledge is based on large clinical trials.