Boxes and Averages

Public conversation loves categories: men and women, generations, professions, nations, introverts and extroverts. Thinking is impossible without categories, but the average characteristic of a group easily turns into an invented biography of a specific person.

Categories save effort. And immediately create new errors.

Inside one category, differences start to look insignificant. Between neighbouring categories, excessive. A person with a temperature of 37.9 and a person with a temperature of 38.0 may fall under different lines of a protocol, although their conditions are almost identical.

The boundary is convenient for the system, but nature was not notified of it.

Categories of people call for particular caution. Age, profession, country, diagnosis or social group can carry statistical information. But a group average describes a specific person badly, and description easily turns into prescription:

Since he belongs to this category, he ought to behave this way.

A category is a tool for compressing information, not an inner essence of the object. Its usefulness depends on the task.

For prescribing a drug, age can be material. For assessing an argument, usually not. When designing a building, a user’s mobility matters. Their taste in music can probably be left out of the evacuation calculation.

The problem is not that we sort the world into boxes. The problem starts when we forget that we made the boxes ourselves.

Statistical averages are one such box. They are useful for estimating probabilities, but they work badly as a ready-made description of an individual.

A treatment, a course, an experience or a habit may help most people and not help one particular person. That does not refute the general regularity. And the other way round: one person’s good experience does not prove the method works for everyone.

So it makes sense to use both levels of information.

First, the group data:

• how often the result occurs;
• what it was compared with;
• how large the effect is;
• what risks are known;
• how similar the study participants are to us.

Then, the individual check:

• how the person responds;
• whether side effects appear;
• whether the required result is achieved;
• whether conditions have changed;
• whether an adjustment is needed.

Reviews are useful for impressions, but they are a poor substitute for systematic data. A thousand enthusiastic accounts can be collected among those who stayed happy, while the unhappy ones simply stopped using the product. A statistical average, however, is not a personal promise either.

The boundary is especially visible where money is attached to it. A family with an income one rouble above the threshold loses its benefit entirely and ends up poorer than a family one rouble below. There is no natural difference between them; the difference was created by a line in the rules. What follows is predictable: people start managing not their income but how it appears on a form — turning down extra work, asking not to be paid a bonus on the books. A box invented for description begins to change what it describes.

The same happens with averages, only more quietly. An average promises an individual nothing, but it looks like a promise, and so it is used with equal convenience by those selling a method and by those explaining why the method did not work for them.