What is a potential outcome in causal inference?
A potential outcome is what would happen to a unit under each possible treatment. A field has one yield if you fertilise it and another if you don’t, and the effect is the difference. But you can farm it only one way at a time, so one outcome always stays hidden: the fundamental problem of causal inference.
Last time's quick check: Lind's comparison was fair because similar sailors got different remedies under the same conditions. It was fragile because there were only two per remedy, and he chose who got what. A year after Lind's comparison, in 1748, the Scottish philosopher David Hume tried to pin down what we mean by a cause.
His first definition: one thing regularly followed by another. In later editions, he added a sharper way of putting it. A cause, Hume wrote, is something where "if the first object had not been, the second never had existed." That sharper phrasing is the heart of causal inference.
To say the oranges cured a sailor is to say: without the oranges, he would not have recovered. A cause is defined by what would have happened without it. Statisticians now call these potential outcomes. Take one field. It has a yield if you fertilise it, and a yield if you don't.
Both are real possibilities, and the effect of fertiliser on that field is the difference between them. But this year you can farm the field only one way. You see one outcome; the other stays a ghost. It's been called the fundamental problem of causal inference: you never see both outcomes for the same field at the same time.
Every method in this series is a way of estimating the ghost: from other fields, other years, or a fair comparison. Then, for much of a century, statistics tried to do without causes. In the 1880s Francis Galton developed correlation: one number for how closely two things move together.
His successor Karl Pearson went further. In The Grammar of Science he argued that causation was only an idealised extreme of correlation, and that science could manage without it. Correlation was a powerful tool. But it can't tell you which way influence runs, or whether something else drives both.
In 1926 the statistician George Udny Yule showed the danger. Between 1866 and 1911, the share of marriages held in the Church of England moved almost in lockstep with the death rate in England and Wales: a correlation of 0.95. Church weddings didn't keep people alive.
Both were simply falling over the same decades, for different reasons. Yule called it a nonsense correlation. Farm data is full of trends like that: yields, inputs, prices and nutrient levels all drifting over the years. Two trends can match without either causing the other. Next: what happened when food itself became the experiment. Rice, chickens and maize.
You never see both potential outcomes for the same unit at the same time. This year a field is either fertilised or not, so the yield it would have had the other way stays a ghost. Every causal method is a way of estimating that missing outcome: from other fields, other years, or a fair comparison.
Yule’s name, in 1926, for two series that move together without either causing the other. Between 1866 and 1911 the share of Church of England weddings tracked the death rate in England and Wales with a correlation of 0.95. Both were simply falling over the same decades. Yields, inputs, prices and nutrient levels drift in the same way.
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