Correlation isn't causation

Correlation isn't causation.

Probably the most quoted sentence in statistics, and a true one. The thinking often stops there, and the conclusion drawn is that correlations are worthless. That is wrong too. A correlation is not proof of cause, but it is evidence. This article covers what a correlation in personal data can indicate, what it cannot, and how science judges the difference.

Four possible explanations

Suppose the data show that mood tends to be higher on days with exercise. That single pattern is consistent with four quite different explanations:

1. Exercise improves mood, the hoped-for reading.
2. Good mood prompts exercise, which is reverse causation: the run happens because the good mood is already there.
3. A third factor drives both, a confounder: on well-rested days both mood and the urge to exercise rise, and sleep is doing the real work.
4. Coincidence: with enough variables, some pairs align by chance, a problem covered separately.

A raw correlation cannot, on its own, distinguish between the four. It shows that two things move together and says nothing yet about why. That ambiguity is what the phrase means.

Confounders

The textbook illustration: across a year, ice-cream sales correlate with drownings. Ice cream does not drown anyone; summer heat drives both. The confounder, hot weather, produces an association between two variables that have no direct link.

Daily life is full of the same structure. A correlation between coffee and productive days might reflect demanding workdays that raise both the coffee intake and the focus. "Alcohol correlates with poor sleep" is probably real, while "social evenings correlate with poor sleep" may be the same nights under a different name. A confounder is not visible in the pair being compared. It sits behind both variables and moves both, and one of them gets the credit.

The Spurious Correlations project shows how readily numbers align by accident, pairing series such as cheese consumption and deaths by bedsheet entanglement: tight correlations, no meaning.¹

The Bradford Hill viewpoints

If a correlation is ambiguous, the question becomes how any field, such as medicine establishing that smoking causes cancer, ever moves from association to cause. In 1965 the epidemiologist Austin Bradford Hill set out the framework still in use: nine viewpoints for weighing whether an association is likely to be causal.² They are meant to be weighed together rather than ticked off one by one. Several are directly useful for personal data:

• Temporality: the cause has to precede the effect. This is the only strictly necessary viewpoint, and it is why pairing next-day mood with last night's sleep carries more weight than a same-day correlation. It fixes the direction and helps exclude reverse causation.
• Strength: a larger, clearer association is harder to dismiss as chance than a faint one.
• Biological gradient: a dose-response relationship, where more of the cause brings more of the effect, is strong evidence. Two coffees disrupting sleep more than one is more convincing than a yes-or-no association.
• Consistency: a pattern that recurs across time is more credible than one confined to a single month.
• Plausibility: a sensible mechanism strengthens the case, and its absence weakens it.

No single viewpoint is sufficient. Together they turn "these two numbers move together" into "this is probably real, and probably in this direction."

What a personal correlation is good for

A correlation is useful in several ways, as long as it is treated as a question and not as an answer. It can:

• Generate hypotheses worth taking seriously, by pointing at a pattern in the data instead of a hunch.
• Justify a deliberate test. A suspected link between coffee and poor sleep can be checked with a small personal experiment, an n-of-1 trial that varies the coffee on purpose and observes the result. That is the route from correlation toward cause.
• Rule things out. A flat correlation over hundreds of days is informative in its own right: the feared or hoped-for link is not strong.

What a correlation cannot do is support a confident "X causes Y" from observation alone, which is why a tracker should not present one as an established cause.

How Daynostic handles the ambiguity

Daynostic reports associations, attaches confidence tiers and a directional, next-day framing, and does not present a correlation as a proven cause. A flagged result marks a strong, consistent, next-day link between two variables. It is a starting point for deliberate testing and stops short of any claim about what causes what.