Together is not because

Picture a seaside town across one summer. In July, ice cream sales go up. In July, more people get into trouble in the water. In September both fall. Month after month the two lines rise and fall together. Somebody writes a headline: ice cream linked to drowning.

When two things rise together, there are four stories, not one. The first causes the second. The second causes the first. A third thing causes both. Or the count is small and it is chance. Rising together is the fact; the story is a guess until something tests it.

Ice cream sales and sea rescues rise together every July. Does eating ice cream cause people to get into trouble in the water?

• No. A hot day sends people to buy ice cream and to swim, so both rise together.
• Yes. They rise and fall together every month, which is what cause looks like.
• No. The rescues cause the ice cream sales.

The third thing has a name: a common cause. It is one thing that pushes two others, so the two move together without touching. Hot days push ice cream and swimming. Age pushes shoe size and reading. A rich country has more Nobel prizes and more chocolate.

Set the hours of sun and the price of an ice cream. The numbers are made up and round: sales follow the sun and the price; swimmers follow the sun only, and one swimmer in a hundred needs rescuing.

Move both controls.

That move is what a test is. If ice cream causes rescues, changing ice cream on its own changes rescues. If a hot day causes both, changing ice cream alone leaves rescues where they were. Rising together cannot tell the two apart. Changing one thing yourself can.

Put the test in order.

Tap them in the order they happen, first to last. Each tap gets a number.

• Change only that thing, and leave everything else alone
• Compare it with what happened when you changed nothing
• Pick the one thing you think is the cause
• Watch what the other thing does

Each is a pair that goes together. Does one cause the other, or does a third thing push both?

One card at a time. Tap the pile it belongs to.

Scientists have a way to do the test on people. Split a big group in two at random, change one thing for one half only, and compare. The random split matters: it spreads every third thing, age, wealth, habits, evenly across both halves, so none of them can be the hidden cause.

A study finds teenagers who sleep with a phone in the bedroom get lower grades. By this lesson, what can you say so far?

• The phone causes the lower grades. That is what the study found.
• They go together. The phone might cause it, or a third thing might push both. Nobody has changed one thing yet.
• Low grades cause teenagers to take phones to bed.