Scatter plots & correlation

So far you have looked at single data series: a mean, a range, a distribution. But often something else is interesting: do two quantities move together? Do students who study longer do better? Does electricity use rise as it gets colder? For questions like these there is a picture of their own and a term of their own.

The scatter plot

For each person or each day you have two numbers. One is plotted to the right, the other upwards, and you get a point. All the points together form a cloud. Its shape is the real answer: if the points lie roughly along a rising line, both quantities grow together. If they fall, they move in opposite directions. If they form a shapeless cloud, there is no relationship.

Strength and direction

Two things describe a correlation. The direction is positive or negative, depending on whether the cloud rises or falls. The strength says how tightly the points hug a line. It is measured with a number between $-1$ and $+1$, the correlation coefficient. At $+1$ all the points sit exactly on a rising line, at 0 there is no linear relationship, at $-1$ they all sit exactly on a falling one.

A relationship is not a cause

Now comes the most important sentence of this topic. A correlation only says that two quantities occur together. It does not say that one causes the other. For every observed correlation there are four possible explanations, and only one of them is the obvious one.

First: A really does cause B. Second: B causes A, so the direction is reversed. Third: a third quantity causes both. Fourth: pure coincidence. The classic example is ice cream sales and the number of swimming accidents. Both rise together, but ice cream does not cause accidents. The third quantity is warm weather, and it drives both.