It says that often, things that look like overall trends can be split into sub-groups, in which the effect is gone. For example, take the "Public Schools perform worse than Private Schools" idea. If you split both school populations into the children from wealthy parents vs children without wealthy parents (ending up with 4 groups), you'll find that the test scores are the same for the "wealthy" kids, whether they go to private or public schools.
In other words, it doesn't matter whether kids are going to private or public schools, what matters is whether they have wealthy parents or not. It just so happens that more kids with wealthy parents go to private schools.
More details about the paradox, and a link to a study on private vs public schools, can be found in the Wikipedia article.
Have you ever heard of "Simpson's Paradox"? http://en.wikipedia.org/wiki/Simpsons_paradox
It says that often, things that look like overall trends can be split into sub-groups, in which the effect is gone. For example, take the "Public Schools perform worse than Private Schools" idea. If you split both school populations into the children from wealthy parents vs children without wealthy parents (ending up with 4 groups), you'll find that the test scores are the same for the "wealthy" kids, whether they go to private or public schools.
In other words, it doesn't matter whether kids are going to private or public schools, what matters is whether they have wealthy parents or not. It just so happens that more kids with wealthy parents go to private schools.
More details about the paradox, and a link to a study on private vs public schools, can be found in the Wikipedia article.