Teaching examples for the design of experiments: geographical sensitivity and the self-fulfilling prophecy.

Many scientists believe that small experiments, guided by scientific intuition, are simpler and more efficient than design of experiments. This belief is strong and persists even in the face of data demonstrating that it is clearly wrong. In this paper, we present two powerful teaching examples illustrating the dangers of small experiments guided by scientific intuition. We describe two, simple, two-dimensional spaces. These two spaces give rise to, and at the same time appear to generate supporting data for, scientific intuitions that are deeply flawed or wholly incorrect. We find these spaces useful in unfreezing scientific thinking and challenging the misplaced confidence in scientific intuition.