p values

If a coin is tossed four times and turns up three tails and one head, should we infer that the coin is loaded? Probably not. For a fair coin, there’s a one in four chance that the tosses would come out this way. It could just be a coincidence. If a coin is tossed forty times and turns up thirty tails and ten heads, should we infer that the coin is loaded? Probably. For a fair coin, the chance it could have come up ten or fewer heads randomly is only about one in a thousand. It is really not hard to explain p-values to the man on the street. If I perform an experiment whose outcome is partly due to chance and partly not, the more trials I run, the more certain I can be that the result was not entirely due to chance. That’s the beauty of statistics.