1. Regression Fallacy

2. Pre-test, post-test
A preschool program attempts to boost children’s IQs.
The children are tested when they enter the program (pre-test) and again when they leave (post-test)
On both occasions, the scores average out to 100 with a SD of about 15.
The program seems to have no effect.

3. Program effects
On a closer look, the children who were below average on the pre-test had an average gain of about 5 IQ points.
Conversely, those children who were above average on the pre-test had an average loss of about 5 IO points.
Does the pre-school program equalize intelligence?

4. The regression effect
We cannot expect the children to score the same on both tests. There will be differences. These differences will make the scatter diagram for the test scores into a football-shaped cloud. The spread along the SD line makes the bottom group come up, and the top group come down. This is the regression effect.

5. The regression fallacy
The regression effect is the fact that in virtually all test, re-test situations, the bottom group on the first test will on average show some improvement on the second test, and the top group will on average fall back.
The regression fallacy is thinking that this regression effect must be due to something important, rather than just spread around the SD line.