Stats Made Easy

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Monday, June 30, 2008

Inverse transformation puts mileage comparisons on track

Tomorrow the IRS adds 8 cents per mile to their allowable rate for deductions on automobile use for business purposes. Precipitated by the rapid rise in fuel prices, this is an unprecedented mid-year boost of over 15 percent from the previous rate of 50.5 cents per mile.

When the price of gas went over 4 dollars a gallon, I started paying attention to which of my three cars went where. For example, my wife and her sister traveled 100 miles the other day to do some work at the home of their elderly parents. They had our old minivan loaded up, but, after thinking about it getting only about 15 miles per gallon (mpg), I moved all the stuff over to my newer Mazda 6 Sport Wagon, which gets 25 mpg. That meant no zoom-zoom for me that day going to work, but it was worth enduring the looks of scorn from the other road warriors.

A few weeks ago, National Public Radio’s All Things Considered led off with this quiz: “Which saves more gas: trading in a 16-mile-a-gallon gas guzzler for a slightly more efficient car that gets 20 mpg? Or going from a gas-sipping sedan of 34-mpg to a hybrid that gets 50 mpg?” Of course the counter-intuitive answer is the one that’s correct – the first choice.

This is a "math illusion" studied by Richard Larrick, a management professor at Duke University. According to a recent article in the journal Science, Larrick found it easy to fool college students into making the wrong choice in puzzlers like that posed by NPR. He suggest that it makes far more sense to report fuel efficiency in terms of gallons per 10,000 miles -- an average distance driven per year by the typical USA car owner. Most of you who are likely to read this blog can easily apply this inverse transformation on mpg, but to check your math see this table posted by Duke University's Fuqua School of Business.

According to this report by Reuter’s Professor Larrick was inspired to promote “gpm” (vs mpg) after realizing in the end that he’d be better off trading in the family minivan and only gaining 10 miles per gallon with a station wagon; rather than swapping his second car, a small sedan, for a highly efficient hybrid. This must be the basis for the NPR’s quiz.

This is definitely an issue where all things should be considered, but most importantly, just how much gas money might be saved one way or the other. Do the math!

PS. News flash: You can rest easy tonight – there will be no leap second, positive or negative, according to this post by the Time & Frequency Division of the National Institute of Standards and Technology (NIST).


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