Shared movement, counted
For every dot, the calculation asks whether x and y sit on the same side of their averages. Same side adds positive evidence. Opposite sides add negative evidence.
Correlation, made visible.
Math turns a cloud of paired observations into one comparable score. Change the data below and watch exactly what that score notices.
Paired observations
6 pairsXY
The number earns its keep when your eyes disagree.
Zero is not “nothing”
A result near zero says a straight line is a poor summary. A strong curve can still be hiding in plain sight.
Direction
The sign tells you whether the variables usually rise together or move in opposite directions.
Strength
The distance from zero tells you how tightly the dots follow a straight-line pattern.
Comparison
Scaling makes very different units comparable: inches and pounds can produce the same r as centimeters and kilograms.
Three moves. One score.
Pearson's r is not magic. It is a repeatable compression of the picture you just made.
Find each average. Every point is now described by how far it sits above or below the middle.
Pair the deviations. Matching directions produce positive products; opposite directions produce negative ones.
Divide by the total spread. That keeps the answer in a shared language from −1 to +1.
Where correlation can fool you.
A curve can score near zero
Pearson's r listens for a straight-line relationship. A U-shape has a real pattern, but its rising and falling halves can cancel each other.
One point can steer the line
An extreme observation has leverage. Try the “One outlier” preset, then remove its final pair to see how much one dot can move the coefficient.
A score cannot prove cause
Two variables can travel together because of coincidence, a third variable, or reverse causality. Correlation describes association; study design supports causal claims.
Keep the dots, the score, and the explanation.
Your export includes every x/y pair, the computed Pearson coefficient, its plain-language interpretation, and the calculation note behind it.