Look before you test

In 1973 the statistician Francis Anscombe published four small datasets. They have almost the same summary numbers: the same average x, the same average y, the same spread, the same correlation (about 0.82) and the same best-fit line.

But when you plot them, they look completely different:

1. A loose, normal-looking cloud around a straight line.
2. A smooth curve, not a line at all.
3. A perfect line with one outlier pulling it off.
4. All points at one x value, except one point far away that creates the whole "correlation".

The lesson

Summary numbers can hide almost everything. The same mean, spread and correlation can come from very different data. A test run on the numbers alone would treat all four the same.

What to do first

• Plot it. A histogram for one variable, a scatter plot for two.
• Look for odd points, gaps, curves and clusters.
• Count: how many data points, how many missing?
• Only then choose a summary and a test.

RememberAlways plot your data before you summarise or test it. Numbers describe data; pictures show it.