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July 30, 2013 12:04 PM Don’t Get Snookered by Statistics with Arbitrary Ranges

By Keith Humphreys

I was watching a baseball game with a mathematician friend, during which the announcer said of a batter “He’s been on a hot streak, with 6 hits in his last 19 at bats”.

My friend said “Which means he has 6 hits in his last 20 or more at bats”.

Of course this was true, because if the batter’s hot streak went back farther than his last 19 at bats, the announcer would have extended the range of his statistic accordingly. The announcer was trying to make a point, and a 7-for-20 or 8-for-21 run of hitting sounds hotter than a mere 6-for-19.

Pundits often use this trick to make ominous sounding pronouncements that are in fact content-light, for example when forecasting who will or will not get elected president. Hillary Clinton will never be in the Oval Office, by the way, because no candidate whose first name starts with an H has been elected President in the past 64.5 years.

Arbitrary ranges can also be used to make the case for a historical trend that may not actually be substantive. At the end of the 1980s, some Republicans crowed that Democrats had lost “5 of the past 6″ presidential elections. Today, some Democrats brag that Republicans have failed to win the popular vote in precisely the same arbitrary timespan.

Politicians also snooker voters with arbitrary ranges. If Mayor Jones says that crime is down for 5 straight months, s/he may well be covering over the fact that crime was up in the months before that. Be particularly skeptical when a politician’s long-ago launched pet initiative is said to have “not really gotten off the ground” until the precise moment that the referenced time range of an upbeat statistic begins.

Obviously, range-based statistics have to have some starting point, and that’s fine as long as they are meaningful: A new person comes into office, a new law is passed, the fiscal year’s budget comes into force, a war begins or ends etc. If there isn’t a qualitative demarcation point like that at the start of a referenced time range, the person quoting the statistic is probably either fooling himself or trying to fool you.

[Cross-posted at The Reality-Based Community]

Keith Humphreys is a professor of psychiatry and behavioral medicine at the Stanford University School of Medicine.