Simpson's Paradox
A striking ecological fallacy is Simpson's paradox. Simpson's paradox refers to the fact, when comparing two populations divided in groups of different sizes, the average of some variable in the first population can be higher in every group and yet lower in the total population. Formally, when each value of Z refers to a different group and X refers to some treatment, it can happen that
When does not depend on, the Simpson's paradox is exactly the omitted variable bias for the regression of on where the regressor is a dummy variable and the omitted variable is a categorical variable defining groups for each value it takes. The application is striking because the bias is high enough that parameters have opposite opposite signs.
Read more about this topic: Ecological Fallacy
Famous quotes containing the words simpson and/or paradox:
“The sun is shining.
The shadows of the lovers have disappeared.
They are all eyes; they have some demand on me—
They want me to be more serious than I want to be.”
—Louis Simpson (b. 1923)
“The paradox of education is precisely this—that as one begins to become conscious one begins to examine the society in which he is being educated.”
—James Baldwin (1924–1987)