Random Sampler

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Statistical Ties

by Charles L. McClenahan 

As we once again enter the election season we will undoubtedly hear the pundits refer to any poll where the difference is within the margin of error as a "statistical tie." This is, of course, just another example of the modern American education system—the math is wrong, but nobody's self-esteem is injured.  

While this fallacy is somewhat reminiscent of the story of the two actuaries hunting rabbit, it has some appeal to us Cub fans (Red Sox too, I suppose). I mean, given a seven-game sample….

But before we gloat too much over this obvious lack of understanding of the mathematical world's basic nature, let us look at how we, as supposedly learned practitioners, apply what we know (ASOP No. 36): 

Determination of Reasonable Provision—When the stated reserve amount is within the actuary's range of reasonable reserve estimates, the actuary should issue a statement of actuarial opinion that the stated reserve amount makes a reasonable provision for the liabilities associated with the specified reserves.

Range of Reasonable Reserve Estimates—The actuary may determine a range of reasonable reserve estimates that reflects the uncertainties associated with analyzing the reserves. A range of reasonable estimates is a range of estimates that could be produced by appropriate actuarial methods or alternative sets of assumptions that the actuary judges to be reasonable.

Aaron Levenstein said, "Statistics are like bikinis. What they reveal is suggestive, but what they conceal is vital." Yet the statistics themselves are neither modest nor immodest. Any concealment that exists is the result of ignorance, misinterpretation, or both. A four percent difference with a four percent margin of error means there could be a tie, not that there is a tie. A reserve at the low end of the range of reasonable estimates means the reserve could be reasonable, not that it is reasonable. When the pundit reports the result as a "statistical tie," or the appointed actuary opines that the low-end reserve is "reasonable," it is not the statistical process that is hiding the truth.