Anscombe Quartet Diagnostics

The Anscombe quartet comprises four datasets that have nearly identical simple statistical properties, yet appear very different when graphed. They were constructed in 1973 by the statistician Francis Anscombe to demonstrate both the importance of graphing data before analyzing it and the effect of outliers on statistical properties.

Experiment with the Module

You can interact with the four datasets directly using the Anscombe Quartet Diagnostics module.

1. Set the Dataset control to "I" and observe the scatterplot. Notice how it looks like a typical linear relationship with some variance.
2. Change the Dataset to "II". The summary statistics (mean, variance, slope, intercept, correlation) remain nearly identical, but the plot reveals a perfect nonlinear (quadratic) relationship. A simple linear model is inappropriate here.
3. Change to Dataset "III". This dataset exhibits a perfect linear relationship except for one massive outlier that alters the fitted slope and intercept.
4. Change to Dataset "IV". Here, the x values are constant except for one extreme leverage point. The slope is entirely determined by that single observation.
5. Adjust the Y scale to "0" and note how the correlation and R² become undefined as the variance of y drops to exactly zero.