Stats Made Easy

Practical Tools for Effective Experimentation

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).

Saturday, June 21, 2008

Origin of 3.2% alcohol beer – an antidote for those dispirited by the Great Experiment

"Our country has deliberately undertaken a great social and economic experiment, noble in motive and far-reaching in purpose." -- Herbert Hoover

75 years ago, legal beer – albeit only 3.2% alcohol, returned to the U.S. and provided a spark of hope for a country in a depression – this is the subtitle of a recent story by the LA Times by Maureen Ogle on “The day the beer flowed again”. This ended a hugely unsuccessful experiment on temperance that lasted over a dozen years beginning in 1920. I still remember a home brew recipe from this era, yellowed and curled, that my grandfather had tacked up above his workbench – it was labeled “Bill’s Beer.” I’ll bet it tasted good on a dry decade!

My interest in 3.2 beer was piqued by the author of Land of Amber Waters, Doug Hoverson, who spoke last weekend at gathering sponsored by our county's historical society. Before Prohibition* the alcohol level in beer was 2.75% but on April 7, 1933 it went back on the market with a higher amount of 3.2% that was considered “chemically necessary to make a better beer.” Hoverson said that two US Congressmen experimented on how much they needed to feel so intoxicated that they could no longer function properly in their work. [Insert your joke here.]

This experiment by Prohibition-busting USA lawmakers may have benefitted from a more scientific "titration" to develop a dose-response curve as illustrated by this white paper from the University of British Columbia. I'd always thought of titration as something a chemist did, for example to precisely determine pH of a solution. However, my colleague Pat Whitcomb showed me how this concept can be applied in a very sophisticated statistical approach for dose response curves. This is presented in a new workshop he developed called Designed Experiments for Life Sciences -- a great introduction to powerful tools of value to scientists, engineers, and technical professionals working in the pharmaceutical, biomedical technology and biomedical device fields, as well as organizations and institutions that devote the majority of their efforts to research, development, technology transfer, or commercialization of life enhancing products.

* According to the USA’s National Institutes of Health (NIH) detailing of 3.2% beer, the 18th Amendment, which outlawed intoxicating liquors, but made no reference to alcohol content. However, the Volstead Act, named after a Representative from Minnesota (land of intemperate emigrated Scandinavians) set the legal alcohol limit at one-half of 1 percent. Thus the only "beer" that could be sold legally in the United States during Prohibition (1920-1933) was "near beer"(now known as “low point beer”) – a “wishy-washy, thin, ill-tasting, discouraging sort of slop that it might have been dreamed up by a Puritan Machiavelli with the intent of disgusting drinkers with genuine beer forever," according to food critic Waverly Root.

Wednesday, June 18, 2008

Brains for beer

Looking over the guide to parents provided by the University of Wisconsin Eau Claire, I came across the obligatory admonitions against student drinking. What caught my eye was a graph showing ever-shrinking GPA as a function of the number of beers or other alcoholic beverages. A shallow search on Internet dredged up this study by Rebecca Nelson of Mary Washington College, who provides this support for this contention:
“Three of the four regressions give a negative coefficient to drinking 13 or more drinks per week. The magnitudes of these signs were greater for freshmen as well. While drinking has a negative affect [sic] on GPA throughout all the students, freshmen’s GPA is hit harder. This indicates that upperclassmen become more efficient in their drinking as well. Upperclassmen learn how and when to drink in moderation. Students may not change the amount they drink as they progress through college, but they do change how they drink.”

I really hate seeing young people drink themselves into oblivion – it’s sad, really. On the other hand, as you will surmise from reading other blogs, I am fond of a brew or two and thus I do not begrudge the same for those of legal age who drink responsibly.

PS. Joke found on the Internet (attributed to Sunita Saini of University of California, Davis):

A stats major was completely hung over the day of her final exam. It was a True/False test, so she decided to flip a coin for the answers. The stats professor watched the student the entire two hours as she was flipping the coin...writing the answer...flipping the coin...writing the answer.

At the end of the two hours, everyone else had left the final except for the one student. The professor walks up to her desk and interrupts the student, saying: "Listen, I have seen that you did not study for this statistics test, you didn't even open the exam. If you are just flipping a coin for your answer, what is taking you so long?"

The student replies bitterly (as she is still flipping the coin): "Shhh! I am checking my answers!"

Friday, June 13, 2008

Sign for physics students still unclear on the concepts

While waiting around for my daughter to register for her first semester of college at the University of Wisconsin at Eau Claire, I read this sign in their physics department. It took me a moment to process the directions at the bottom, but then it hit me.

Sunday, June 01, 2008

GPA mongers lose out to students willing to take on tougher classes

My youngest daughter, now graduated from high school as of last night, concluded her senior-year AP stats class with a study on some factors that may predict performance on ACT testing of her college-bound classmates. She and her study-mate got data from 38 students on their GPA, ACT and the number of AP classes taken. The teacher did not give much direction on what to make of this information, so when my daughter asked me to help, I steered her to a modeling of ACT as a function of the GPA and AP. This is pictured here in an output from Design-Expert® software. What I find interesting is that after accounting for the impact of the number of AP classes (highly significant, p=0.0003), the students' GPA makes essentially no difference (p=0.4596).

It seems to me that this provides an insight on the impact of being motivated to learn. At our high school, those aiming for high GPA do better by NOT taking the relatively difficult college-level AP classes. Those who do load up on APs are willing to chance a lowering of their GPA in return for an enriched curriculum. Is it any wonder that these are the ones who do test better on ACT?