Why a correlation of one variable with time explains nothing

Plot mobile phone ownership against any quantity that has grown steadily since the nineteen-nineties and the correlation will be high. The pairing can be reversed to produce the opposite headline, using the same arithmetic, because the number being computed is not about the two subjects at all.

What everyone sees

A strong correlation coefficient is treated as a finding, and its size is reported as the strength of the relationship. The coefficient is honestly computed. What it measures, in a pair of trending series, is that both moved in the same direction over the same period — which was already known before either was measured.

What is actually happening

Time-series data commonly contain trends, and two independently trending series will show high correlation regardless of any connection. Yule described this as spurious correlation between time series in 1926, and Granger and Newbold demonstrated that regressions on non-stationary series produce apparently significant results routinely. Detrending or differencing the series usually removes the association entirely, which is the diagnostic.

Why it stays hidden

The artefact hides because the coefficient looks like a measurement of the relationship rather than of the trend. Charts also encourage it: two rising lines on shared axes read as a mechanism. Trended series are the most available data in the world, so the pairing is easy to produce, and the failure mode is a property of the method rather than of any dishonesty in the analyst.