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:
“I don’t want to stay on the line. He’s going to beat the s— out of me.”
—Nicole Brown Simpson (1957–1994)
“The conclusion suggested by these arguments might be called the paradox of theorizing. It asserts that if the terms and the general principles of a scientific theory serve their purpose, i. e., if they establish the definite connections among observable phenomena, then they can be dispensed with since any chain of laws and interpretive statements establishing such a connection should then be replaceable by a law which directly links observational antecedents to observational consequents.”
—C.G. (Carl Gustav)