Correlation vs Causation: Do Big Feet Read Better?

Full transcript

Word for word what is said in the video — the same text as the subtitles. Times are minutes:seconds into the video.

0:00Do big feet read better? ▶

Sixty children at one primary school, one dot each: foot length against a score on a reading test. Children with bigger feet tend to read better: the correlation, r, is plus zero point seven five. A headline writes itself: bigger feet linked to better reading. Give it one more day, and it turns into: big feet boost reading. The link is real, but that second headline is not. By the end of this video: what is really behind this link.

0:39The slogan, and two ways to get it wrong ▶

Last video ended on a question: when two things move together, did one cause the other? Most people know the slogan: correlation does not imply causation. Yet in one course, two out of three psychology students who had already passed statistics still found a study built on a correlation convincing. The opposite mistake is just as real: deciding that a correlation means nothing at all. But imply here means guarantee, not suggest: a link can't prove a cause, but it can point to one. There is one simple habit for every link you meet.

1:18Three stories for every link ▶

Here is the habit: every link comes with three stories. Story one: feet cause reading, so big feet make children read better. Story two: reading causes feet, so reading makes your feet grow. Story three: something else pushes on both at the same time. Here the first two sound silly, but with most links all three sound possible. So write down all three, and keep them until something rules one out. The third one is the hardest to see, because it is not in the picture.

1:56The third factor ▶

Story three has a name in statistics: a confounder. We will simply call it a third factor. It pushes on both things at once, so they move together even if neither touches the other. In a survey of Harvard freshmen in nineteen eighty-seven, students who had been coached for the entrance test scored lower on average. That does not show that coaching hurt: the students who went looking for help may have been the weaker ones to begin with. Being weaker already would push on both: more coaching and a lower score. So which third factor could push on both feet and reading?

2:40What happens inside one age? ▶

If you thought of age, this school wrote it down: seven, nine or eleven. Before the dots change colour: what happens to the link inside one age group?

2:55Coloured by age: the link is gone ▶

Here they are, coloured by age, and not one dot has moved. Inside each colour, the link is gone: r is close to zero at seven, at nine and at eleven. Older children have bigger feet, and older children are better readers. Age pushed on both, and we know why from outside the data: children grow, and every school year teaches them more. The cloud could only show the two moving together. That is what a third factor can do: build a real link between two things that never touch. But this school happened to write down age. Often, nobody wrote down the third factor. So how does anyone ever show a cause?

3:46Rule 1: hand it out by lottery ▶

The first rule: to show a cause, stop watching who happens to have it, and hand it out yourself. You cannot hand out bigger feet, but you could give a reading programme to half the children by tossing a coin. Then every possible third factor, like age, parents or sleep, lands in both groups about equally. If the programme group now reads better, the programme is the best explanation left. A correlation alone can't show a cause: a lottery like this, an experiment, is the most direct way. Most of us never run one, though: we read the news about a study, and that is where the words slip.

4:32Rule 2: read the verb ▶

The second rule is about words. One study followed science news from the university press release to the newspaper. Claims slide down a ladder: associated with, linked to, might increase, can increase, increases. The top two only describe a link; the bottom three claim a cause. When the press release had already overstated the study, eighty-one percent of the news stories did too. When it had not, only eighteen percent did. So the slide often starts before any journalist touches the story. Read the verb before you believe the claim, but don't throw the link away either.

5:18Rule 3: a link is still a clue ▶

The third rule keeps you from the opposite mistake: a correlation is not nothing. So yes, in this school, children with big feet really do read better. Foot length does help you guess a reading score, because age hides inside it. It just can't tell you what to change. And a surprising link is often where a good experiment starts.

5:46One look back ▶

Back to video ten: in class A, more hours on the phone went with fewer hours of sleep. Which of the three stories is it? All three fit: the phone keeps you awake, lying awake makes you grab the phone, or a stressful week does both. The cloud alone cannot rule any of them out.

6:10In one picture ▶

So, in one picture: every link comes with three stories. One causes the other, it runs the other way round, or a third factor pushes on both. Split the cloud by that third factor, and the link falls apart. A lottery shows a cause most directly, a link is still a clue, and the verb tells you which rung you are on,

6:37Next: how graphs steer you ▶

but headlines are not the only thing that can steer you. Next time: how a graph can make the very same numbers tell a different story. And if you have ever seen a headline slide down that ladder, tell me in the comments. And if you want to keep learning, subscribe, the next video will find you. Until then: happy learning.