Probability, Events, and People

I ran across this remark in a dark corner of the Internet to which I will not leave a link:

What (my critics) do is attempt to apply GENERAL statistics derived from a population of millions to their own individual situation despite the fact that such statistics are totally meaningless when applied to ONE SPECIFIC individual.

So close, and yet so far.

Probabilities apply to events, and it is individual events to which we cannot apply probabilities. A horse-race is a one-time event in terms of course, condition of the ground, horses and jockeys. It won’t be repeated. Probability needs repetition. The odds a bookie gives at a racetrack are not probabilities, since the bookie needs to make a Dutch book in his favour in order to make a living. But that’s an aside.

A individual person is not an individual event. A person is the site of many thousands of different events, from heartbeats and muscle twitches to things like crossing roads, dealing with customers, and eating food.

The statistics on food poisoning apply to a person because they eat many meals, each one of which is an event that might involve eating something that disagrees with them.

The statistics on divorce apply to an individual man because he has many opportunities to displease or disappoint his wife.

The twist is that most people will look at socio-economic variables to judge their probability of divorce, missing the point that nobody gets divorced because they are a prospering accountant, or a struggling session musician. They get divorced against because they do something that upsets their partner, and nobody ever records or measures those things. I suspect the correlation between social class, occupation and other such macro-variables, and actual divorce-causing behaviours, is actually fairly weak.

Statistics is difficult. The mathematics is surely horrible, but the conceptual difficulty is right at the start, in understanding how to model something, and how to apply the ideas.