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 cant think of a single supposedly Black issue that hasnt wasted the original Black target group and then spread like the measles to outlying white experience.”
—June Jordan (b. 1936)
“...Womens Studies can amount simply to compensatory history; too often they fail to challenge the intellectual and political structures that must be challenged if women as a group are ever to come into collective, nonexclusionary freedom.”
—Adrienne Rich (b. 1929)
“The total collapse of the public opinion polls shows that this country is in good health. A country that developed an airtight system of finding out in advance what was in peoples minds would be uninhabitable.”
—E.B. (Elwyn Brooks)
“The average Southerner has the speech patterns of someone slipping in and out of consciousness. I can change my shoes and socks faster than most people in Mississippi can speak a sentence.”
—Bill Bryson (b. 1951)