You are useless at statistics. Yup. Useless. Intuitively, I mean. You may well be able to sit down and work out the actual objective chances that something will happen, but that is not how the brain naturally works. Your brain works in stories and pictures, not complicated mathematics.
If you watch somebody tossing a coin repeatedly you expect a random sequence of heads and tails. If they get several heads in a row, you feel the next one is more likely to be tails. Of course, the next one is still just as likely to be heads as tails, but that isn’t how it feels. And as the run of heads grows longer, your feeling that the next has to be tails grows stronger. But it is still 50/50.
You know, intellectually, that it is still a 50/50 proposition, but that doesn’t stop your brain crying out that the next one simply has to be tails.
Similarly, consider the following statement: among stockbrokers almost half of all sick days taken are on either a Friday or a Monday.
You may jump to the conclusion that some stockbrokers are trying to extend their weekends. You might come up with some justification that less trading is done on a Friday as the working week winds down, or on a Monday as people are slow to get going after the weekend. Or they want to go away for a long weekend sometimes, and can’t get the leave.
Actually, I made the statement up. I have no idea of the break down of sick days among stockbrokers, or any other occupation. However, I would expect almost half of stockbrokers’ sick days to be either a Friday or a Monday. Not because of anything to do with stockbrokers or the weekend. I would expect it simply because Friday and Monday together make up two fifths of the working week, which is nearly half.
Our brains though, when hearing a statement like that one, don’t automatically think of statistics. Our brains love stories, so we try to come up with reasons to explain the apparent anomaly.
Those examples were easy to explain with very simple statistics and just a little thought, but how many times are we shocked by some similar claim in the news? It is very possible that much of what we are surprised by is simply because of the way we heard the information, and that statistics would show that it is nothing that should be unexpected.