Ecological Fallacy - Simpson's Paradox

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


\begin{align} \forall z,	E> E \text{ while } 	E< E
\end{align}


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:

    If you have any information or evidence regarding the O.J. Simpson case, press 2 now. If you are an expert in fields relating to the O.J. Simpson case and would like to offer your services, press 3 now. If you would like the address where you can send a letter of support to O.J. Simpson, press 1 now. If you are seeking legal representation from the law offices of Robert L. Shapiro, press 4 now.
    Advertisement. Aired August 8, 1994 by Tom Snyder on TV station CNBC. Chicago Sun Times, p. 11 (July 24, 1994)

    A good aphorism is too hard for the teeth of time and is not eaten up by all the centuries, even though it serves as food for every age: hence it is the greatest paradox in literature, the imperishable in the midst of change, the nourishment which—like salt—is always prized, but which never loses its savor as salt does.
    Friedrich Nietzsche (1844–1900)