Paulos: Statistical Ties and Coin Flips

ByABC News
November 30, 2000, 1:00 PM

Dec. 1 -- The Florida election is essentially a statistical tie.

As Ive written in a previous column, the number of votes in dispute in this election is many times greater than the difference in vote totals between the candidates and so the election might reasonably be settled by a coin flip.

Since such a decisive coin flip is unlikely to occur, we should ideally avoid the appearance of dredging for votes in Democratic counties (although they are the source of almost all the reported irregularities) and hand-count all the counties.

Still, given the closeness of the election and the margins of error and interpretation involved, any recount, even a careful manual one, of the entire state would be more or less tantamount to flipping a coin anyway.

The Buchanan Factor

To illustrate the iffy nature of the outcome, let me examine after a short statistical detour one of the continuing points of contention in the post-election campaign: the Buchanan vote in Palm Beach County.

There is a standard approach that statisticians use to understand the relationship between two variables. Take, for example, the heights and weights of people in one group or other. For each person in the group one plots a point on a graph indicating his or her weight (on the vertical axis, say) and height (on the horizontal axis).

Using mathematical techniques that go by the name of regression analysis, one can find and drawthe best-fitting straight line through these points. As common sense suggests, we would note that there is a positive relationship between the weight and height of people: the taller someone is, the heavier he or she generally is. There will, of course, be some outliers, very tall, light people or short, heavy ones, but these exceptions are unlikely to be extreme.

How is this relevant to the election? Since the vote totals for the candidates in each of states 67 counties are readily available, we can examine the relationship between the number of votes Reform Party candidate Patrick Buchanan received in a county and the number that Gov. George W. Bush received in that county by following the same procedure.