One analogy I used to use when talking to non-mathematicians (& to mathematicians too, come to think of it) about the limits of statistical methods is probably already incomprehensible to anyone under pension age. So here it is, just for posterity.
You are listening to an old fashioned AM only radio; through the crackles & hisses you can dimly discern, you are sure you can hear, someone talking.
A delicate hand on the tuning knob, a reorientation of the aerial, maybe just turning the set around, & you may be able to make out the words. One day engineers & scientists will have worked their magic & produced a radio which produces a signal which is crystal clear.
Data sets are like that; a jumble of numbers, a set of points scattered all over the graph. But you are sure there is a pattern in there.
And here comes the clever mathematician to show you how to find it – the perfect straight line.
But, just because you can hear every word that is being broadcast, doesn’t mean it’s true. You might be listening to Lord Haw Haw.
