Anscombe's Quartet
Here is the summary of four data sets. Read them and bet on whether the four sets are the same; afterwards you will see them drawn. At the end you move a single point and watch what happens to the summary.
1. Four summaries
Each set is eleven pairs of values (x, y). For each one, the usual figures have been calculated: the mean and variance of each variable, the correlation between the two, and the line that best fits the eleven points.
Correlation runs from −1 to 1 and measures how far the pairs line up along a straight line: near 1, they rise together; near 0, there is no alignment. In the line, the first number is the starting point and the second is the slope.
2. Move a single point
Now you change a single value out of the eleven and leave the other ten as they are. Choose the set:
Circles: the ten points that don't move. Diamond: the point you move. Hollow circle: where it was. Solid line: the line now. Dashed line: the original line.
With the keyboard, the arrow keys move it in steps of a tenth. You can also drag the diamond.
| Summary | In place | Now | Without that point |
|---|
What you take away
A summary is no substitute for looking at the data: four sets with the same mean, the same variance, the same correlation and the same line can have shapes that look nothing alike. And a single point can drag a statistic along with it.
When someone, a person or an agent, hands you a mean, a correlation or a line, ask for the plot too and check whether any one point rules over the rest.
Data: F. J. Anscombe, "Graphs in Statistical Analysis," The American Statistician, 1973. All the statistics are calculated right here from the eleven pairs of each set; the variance is the sample variance (divided by ten). What you do is not saved.