Bias illustrated with target analogy

A biased estimator.  The points are not centered on the target.

Adding a circle, equal in size to the innermost target circle and centered on the mean of the yellow points, to show how little they vary.

Adding estimates from an unbiased estimator with a larger variance. The white points are centered on the target, but it takes a much bigger circle to encompass them. Which is better, the unbiased white or the biased yellow?  It depends on the scores you get for hits in different circles.

Copyright © 1991, 2000 Samuel L. Baker
The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of South Carolina.
January 24, 2000