correlation
In plain wordsA measure of how closely two quantities move together, from −1 (one rises as the other falls) through 0 (no straight-line link) to +1 (they rise together). It does not show that one causes the other.
A measure of the strength and direction of association between two variables. Pearson's correlation coefficient r is the covariancecovariance, n.: A measure of whether two quantities tend to rise and fall together, move in opposite directions, or show no consistent relationship. divided by the product of the standard deviations; it ranges from −1 to +1 and captures only linear relationships. Spearman's and Kendall's rank correlations measure monotonic association and resist outliers. Correlation is symmetric and unit-free, and zero correlation does not imply independence: a perfect U-shaped relation can have r = 0. Models trained on observational data learn statistical associations, which is why they can absorb spurious correlationsspurious correlation, n.: A link in data that fools you: two things move together, yet neither drives the other, because a hidden shared cause, the way the data were collected or luck produced the pattern. AI models readily latch onto such links. and fail under distribution shiftdistribution shift, n.: When the data an AI system meets in real use differs from the data it was trained on — new users, places, times or habits — often making it perform worse than tests suggested.. Correlations are also used to check automatic metrics and LLM-as-a-judgeLLM-as-a-judge, n.: Using one AI language model to grade or compare the answers of another, as a cheaper and faster stand-in for human reviewers. scores against human judgments, to find redundant features and to ask whether different benchmarksbenchmark, n.: A fixed, shared test — a set of questions or tasks with an agreed way of scoring — used to compare AI systems with one another and to track progress over time. measure the same thing. Moving from correlation to causation requires causal inferencecausal inference, n.: Working out whether one thing actually causes another, rather than merely occurring alongside it — for example, whether a new feature made users stay longer or just happened at the same time.: randomized experiments or explicit causal assumptions.
The automatic metric's correlation with human ratings was only 0.41, so we kept human evaluation.
Origin
Francis Galton introduced 'co-relation' and a way to measure it in 1888, building on his work on regression; Karl Pearson gave the product-moment formula its modern form in 1895–1896, after Auguste Bravais's 1846 work. Charles Spearman introduced rank correlation in 1904. The warning that correlation is not causation was a statistical commonplace by the early 20th century.
Related
- covariancecovariance, n.: A measure of whether two quantities tend to rise and fall together, move in opposite directions, or show no consistent relationship.
- spurious correlationspurious correlation, n.: A link in data that fools you: two things move together, yet neither drives the other, because a hidden shared cause, the way the data were collected or luck produced the pattern. AI models readily latch onto such links.
- causal inferencecausal inference, n.: Working out whether one thing actually causes another, rather than merely occurring alongside it — for example, whether a new feature made users stay longer or just happened at the same time.
- confounding variableconfounding variable, n.: A hidden third factor that influences two things at once and makes them look linked. Ice-cream sales and drownings both rise in hot weather; neither causes the other.
- mutual informationmutual information, n.: How much knowing one thing tells you about another — for example, how much a word reveals about the topic of a document. It is zero when the two are unrelated.
- Simpson's paradoxSimpson's paradox, n.: A statistics trap in which combining groups reverses what each group shows: a treatment can do better than another for men and for women separately, yet worse when everyone is counted together.
- causal inferencecausal inference, n.: Working out whether one thing actually causes another, rather than merely occurring alongside it — for example, whether a new feature made users stay longer or just happened at the same time.
Mentioned in
causal inferencecausal inference, n.: Working out whether one thing actually causes another, rather than merely occurring alongside it — for example, whether a new feature made users stay longer or just happened at the same time., coefficient of determinationcoefficient of determination, n.: A score for numerical predictions showing how much of the variation in the true values a model accounts for, compared with always guessing the average: 1 is perfect, 0 is no better than the average., confounding variableconfounding variable, n.: A hidden third factor that influences two things at once and makes them look linked. Ice-cream sales and drownings both rise in hot weather; neither causes the other., cosine similaritycosine similarity, n.: A score from −1 to 1 for how closely two lists of numbers point the same way, ignoring their size. It is the standard test of whether two texts mean similar things., random variablerandom variable, n.: A quantity whose value depends on chance, such as the number rolled on a die or the next word a chatbot will write., spurious correlationspurious correlation, n.: A link in data that fools you: two things move together, yet neither drives the other, because a hidden shared cause, the way the data were collected or luck produced the pattern. AI models readily latch onto such links., covariancecovariance, n.: A measure of whether two quantities tend to rise and fall together, move in opposite directions, or show no consistent relationship., Matthews correlation coefficientMatthews correlation coefficient, n.: A single score from −1 to +1 for a yes-or-no classifier that uses all four kinds of right and wrong answers, so it stays honest even when one answer is far more common than the other., mutual informationmutual information, n.: How much knowing one thing tells you about another — for example, how much a word reveals about the topic of a document. It is zero when the two are unrelated., semantic textual similaritysemantic textual similarity, n.: How close two sentences are in meaning, scored from 'about different things' to 'say exactly the same thing' — and the tests that check whether a computer's scores match people's judgments., Simpson's paradoxSimpson's paradox, n.: A statistics trap in which combining groups reverses what each group shows: a treatment can do better than another for men and for women separately, yet worse when everyone is counted together.