Group and Total Average
Ecological fallacy also happens when the average for a group is approximated by the average in the total population divided by the group size. Suppose one knows the number of Protestants and the suicide rate in the USA, but one does not have data linking religion and suicide at the individual level. If one is interested in the suicide rate of Protestants, it is a mistake to consider as an unbiased estimate the total suicide rate divided by the number of Protestants. This estimate implicitly assumes that the suicidal rate of the other religions is zero.
Formally, denote the variable of interest and the mean of the group, we generally have:
However, the law of total expectation gives
This equation must be used to compute a more congent estimate. In this equation, the only things we don't know how to estimate are in blue. We know that, as a probability of suicide, is between 0 and 1. We can plug in this bound and our total estimate in the equation above to obtain an estimate of .
Read more about this topic: Ecological Fallacy
Famous quotes containing the words group and, group, total and/or average:
“I can’t think of a single supposedly Black issue that hasn’t wasted the original Black target group and then spread like the measles to outlying white experience.”
—June Jordan (b. 1936)
“We begin with friendships, and all our youth is a reconnoitering and recruiting of the holy fraternity they shall combine for the salvation of men. But so the remoter stars seem a nebula of united light, yet there is no group which a telescope will not resolve; and the dearest friends are separated by impassable gulfs.”
—Ralph Waldo Emerson (1803–1882)
“Both the man of science and the man of art live always at the edge of mystery, surrounded by it. Both, as a measure of their creation, have always had to do with the harmonization of what is new with what is familiar, with the balance between novelty and synthesis, with the struggle to make partial order in total chaos.... This cannot be an easy life.”
—J. Robert Oppenheimer (1904–1967)
“The allurement that women hold out to men is precisely the allurement that Cape Hatteras holds out to sailors: they are enormously dangerous and hence enormously fascinating. To the average man, doomed to some banal drudgery all his life long, they offer the only grand hazard that he ever encounters. Take them away, and his existence would be as flat and secure as that of a moo-cow.”
—H.L. (Henry Lewis)