Yule (1926)
G. Udny Yule, "Why Do We Sometimes Get Nonsense-Correlations between Time-Series? A Study in Sampling and the Nature of Time-Series," Journal of the Royal Statistical Society 89, no. 1 (1926): 1–64. doi:10.2307/2341482
What it found
The share of Church of England marriages and the death rate in England and Wales, 1866–1911, correlate at "+ 0·9512" (p. 2), yet "the correlation is simply sheer nonsense; that it has no meaning whatever" (p. 2). Smooth, trending series break the assumption of independent observations that the usual significance test relies on: "Neither series, obviously, in the least resembles a random series" (p. 5).
Why it matters
Two metrics that both trend up over the year, or both peak in Q4, will correlate whether or not one has anything to do with the other.
Note. Yule's term is "nonsense-correlations." His case is two series that trend over time, not a hidden third factor. ("Spurious correlation" is Karl Pearson's term, from 1897.)
Hill (1965)
Austin Bradford Hill, "The Environment and Disease: Association or Causation?" Proceedings of the Royal Society of Medicine 58, no. 5 (1965): 295–300. doi:10.1177/003591576505800503 · free copy (PMC)
What it found
"the decisive question is whether the frequency of the undesirable event B will be influenced by a change in the environmental feature A" (p. 295). Hill offers nine viewpoints (strength, consistency, specificity, temporality, biological gradient, plausibility, coherence, experiment and analogy): "Here then are nine different viewpoints from all of which we should study association before we cry causation" (p. 299). And "None of my nine viewpoints can bring indisputable evidence for or against the cause-and-effect hypothesis" (p. 299).
Why it matters
His decisive question is the lever question. Before pushing on a KPI, ask whether changing it would change revenue.
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Messerli (2012)
Franz H. Messerli, "Chocolate Consumption, Cognitive Function, and Nobel Laureates," New England Journal of Medicine 367, no. 16 (2012): 1562–1564. doi:10.1056/NEJMon1211064
What it found
Across 23 countries, chocolate eaten per person tracked Nobel laureates per 10 million people: "r=0.791, P<0.0001." The note, written deadpan, lists the possibilities: "either X influences Y, Y influences X, or X and Y are influenced by a common underlying mechanism."
Why it matters
A strong, significant correlation between averages says nothing about what pulling one lever will do.
Note. Written tongue in cheek, as an "Occasional Note," not a research article. It compares country averages.
Vigen (2015)
Tyler Vigen, Spurious Correlations (New York: Hachette Books, 2015), and tylervigen.com.
What it found
Comparing thousands of unrelated series against each other turns up matches like US margarine consumption and the divorce rate in Maine, 2000–2009, at r = 0.993 (tylervigen.com, read Oct 26, 2026). In Vigen's words: "any sufficiently large dataset will yield strong correlations completely at random."
Why it matters
Search enough dashboards and you'll always find a "driver." Data dredging finds coincidences.
Note. The site's AI-written "explanations" (added in 2024) aren't research.
Lewis, Rao & Reiley (2011)
Randall A. Lewis, Justin M. Rao and David H. Reiley, "Here, There, and Everywhere: Correlated Online Behaviors Can Lead to Overestimates of the Effects of Advertising," Proceedings of the 20th International Conference on World Wide Web (2011): 157–166. doi:10.1145/1963405.1963431 · free copy
What it found
In a randomized Yahoo! Front Page experiment, the true lift in brand searches was 5.4%. Comparing people who saw the ad with people who didn't suggested 1,198%. They call it "activity bias": "the surprising amount of time-based correlation between the myriad activities that users undertake online." Exposed-versus-unexposed comparisons overstated the lift "on the order of 200 times the correct value."
Why it matters
The people who see your ads are busier online in general, so they search, click and buy more whether or not the ad worked. Only a holdout separates the two.
Note. The ad did work: a 5.4% lift. The finding is how much the usual comparison overstated it.
Shmueli (2010)
Galit Shmueli, "To Explain or to Predict?" Statistical Science 25, no. 3 (2010): 289–310. doi:10.1214/10-STS330 · free copy (arXiv)
What it found
Explaining and predicting are different jobs. She defines "explaining as causal explanation" (§1.1); a predictive model is for "predicting new or future observations" (§1.2), and "the 'wrong' model can sometimes predict better than the correct one" (§1.5).
Why it matters
A lead score can predict value well without anything in it being a lever. Use it to sort; test before you steer.
Note. Quoted by section: the free copy's page numbers differ from the journal's.
Pearl & Mackenzie (2018): the ladder of causation
Judea Pearl and Dana Mackenzie, The Book of Why: The New Science of Cause and Effect (New York: Basic Books, 2018); Judea Pearl, "The Seven Tools of Causal Inference, with Reflections on Machine Learning," Communications of the ACM 62, no. 3 (2019): 54–60. doi:10.1145/3241036 · free copy (Pearl's site)
What it found
Three rungs: association (seeing), intervention (doing) and counterfactuals (imagining). Intervention "ranks higher than Association because it involves not just seeing what is, but changing what we see" (Pearl, 2019). "Questions at level i can only be answered if information from level i or higher is available."
Why it matters
Dashboards live on the first rung. Where to spend is a second-rung question, and first-rung data can't answer it on its own.
Note. The quotes are from Pearl's 2019 article; the book's text isn't quoted here. "Correlation is not causation" is the mantra Pearl argues against, not his slogan.