Correlation & Relationships

Correlation measures how strongly two variables move together — but a strong correlation never, by itself, proves that one of them causes the other.

Reading a correlation coefficient

Correlation is usually reported as a number between -1 and 1. A value near 1 means two variables tend to rise together; near -1 means one tends to rise as the other falls; near 0 means there's no clear straight-line relationship between them at all. A correlation of 0.85 between "hours studied" and "test score" says those two tend to move together closely — nothing more specific than that yet.

>>> two variables that move together
hours_studied = [1, 2, 3, 4, 5, 6]
test_scores  =  [52, 58, 63, 70, 75, 82]

# Simple visual check: do both lists rise together?
for h, s in zip(hours_studied, test_scores):
    print(f"{h} hrs -> {s} points")
Output
1 hrs -> 52 points
2 hrs -> 58 points
3 hrs -> 63 points
4 hrs -> 70 points
5 hrs -> 75 points
6 hrs -> 82 points

Every increase in hours studied here comes with an increase in score — a strong positive correlation. It's tempting to immediately conclude "studying causes higher scores," and in this particular example that's probably a reasonable real-world guess, but the correlation number alone doesn't establish that. It just confirms the two variables move together.

Correlation is not causation

The classic example: ice cream sales and drowning deaths are strongly correlated across the year. Ice cream doesn't cause drowning, and drowning doesn't cause ice cream sales — a third factor, hot weather, drives both up at the same time. Whenever two things are correlated, there are always at least three possibilities: A causes B, B causes A, or something else causes both. The statistics alone can't tell you which one it is.

How you actually get closer to causation

Establishing real causation usually needs something beyond a correlation number — a controlled experiment (an A/B test, for instance), a plausible mechanism explaining why A would cause B, and ideally ruling out obvious third factors that might be driving both. This is a large part of what separates a rigorous data science claim from someone excitedly pointing at two lines on a chart that happen to move together.

A habit worth building: whenever you see a compelling correlation, the very next question should be "what else could be driving both of these?" — not "what's the mechanism by which A causes B?" Assuming causation is the single most common statistical mistake made in casual data analysis, and it's an easy one to fall into because a strong correlation genuinely feels like proof.
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