Two things rise and fall together, so surely one drives the other? That leap is the most common — and most expensive — mistake in data analysis. A correlation says two variables move in step. It says nothing about why.
Note
What a Correlation Coefficient Says
The correlation coefficient (r) runs from −1 to +1 and captures the strength and direction of a linear relationship — how tightly the points hug a straight line, like the scatter above.
| r | Meaning |
|---|---|
| +1 | Perfect positive — up together, exactly |
| 0 | No linear relationship |
| −1 | Perfect negative — one up, one down |
| 0.8 | Strong positive, but still just a pattern |
Watch out
Three Reasons Two Things Correlate
When A and B move together, causation is only one of several explanations — and rarely the safest bet.
| Explanation | Example |
|---|---|
| A causes B | More exercise → lower resting heart rate |
| B causes A (reverse) | Assumed 'ads → sales' when high sales fund more ads |
| A third thing causes both (confounder) | Heat drives both ice cream and drownings |
| Pure coincidence | Two unrelated trends that happen to line up |
The confounder is the sneakiest. A hidden common cause makes two effects rise together with no direct link at all — the classic ice-cream-and-drownings trap.
Reverse Causation and Coincidence
- Reverse causation: you have the arrow backwards — successful companies buy more software, not the other way around
- Coincidence: with enough variables, some will correlate by pure chance — dredge a big dataset and spurious pairs appear
- Selection effects: the way data was collected can manufacture a correlation that isn't real in the population
Tip
What It Takes to Claim Cause
Establishing causation needs more than a coefficient. The gold standard is a randomized controlled experiment; short of that, careful designs can build a strong case.
- 1A randomized experiment — randomly assign the treatment so confounders are balanced out.
- 2A plausible mechanism — a reason A would cause B, not just a pattern.
- 3Correct time order — the cause must precede the effect.
- 4Ruling out confounders — control for the obvious common causes, or match on them.
Studying Relationships in the SKARI Statistical Lab
SKARI's Statistical Lab measures relationships honestly — correlation for association, regression to control for other variables, and matching designs to strengthen a causal argument.
- Correlation analysis with the coefficient and significance
- Multiple regression to hold confounders constant while estimating an effect
- Propensity Score Matching (PSM) and Regression Discontinuity (RDD) for stronger causal designs
- Assumption checks so a linear coefficient isn't read past what it supports
Takeaway
Frequently Asked Questions
Does a strong correlation ever imply cause?
Not by itself. It can motivate a causal hypothesis, but proof requires experimental design or careful control of confounders.
How do I spot a confounder?
Ask what could plausibly cause both variables. If a common driver exists, control for it in a regression or design around it.
Can regression prove causation?
Not on its own — but controlling for known confounders makes a causal story far more credible than a raw correlation.
Key Takeaways
r shows
Pattern
linear, −1 to 1
Not
Cause
just movement
Beware
Confound
hidden driver
Proof
Design
experiment/control
A correlation is a starting point, not a conclusion. Before acting on 'these move together,' rule out reverse causation and confounders — and remember that only a good design, not a big coefficient, earns the word 'cause.'
Takeaway
Hypothesis Testing Basics
Is the relationship even real?
Regression Analysis
Control for confounders
A/B Testing
The experiment that shows cause