Stats Made Easy

The title of this blog comes from French philosopher Marcel Proust who continued on to say of these cheerful friends that “they are the charming gardeners who make our souls blossom.” For good companionship I’d pick Proust over his cynical countryman Camus, whom I quoted in my previous blog on happiness on 4/2/07 seen here along with the related one from the day before. My return to the contemplation of happiness was precipitated by my pleasure over recently released research showing that happiness is infectious. Evidently good news travels fast! 🙂

As reported by Karen Kaplan of the Los Angeles Times, scientists from Harvard and University of California at San Diego tapped into participants of the famous Framingham heart study to assess how happiness spreads. What I found most interesting was the one exception to the general rule that the best way to be happy is to surround yourself with happy people — it does not work at work. Could that be true? I hope not. But I suppose that’s why they call it “work” and not “fun.”

PS. The photo of me comes from my recent work/vacation trip in Puerto Rico. The toothy statue is a pre-Columbian figure on display at the Historical Park of the Arecibo Lighthouse. My work was in Ponce for a medical device company that had the happiest employees that I’ve ever seen. I cannot describe the delight for a cold Minnesotan like me to be welcomed into such a warm environment as was nurtured by this Puerto Rican manufacturer. Perhaps this is the exception that proves the rule of no happiness spreading in the workplace. However, my intention is keep on smiling and being positive as much as I can wherever I am — it makes me happier, that is for sure.

I am enjoying a week of teaching class in pleasantly warm Puerto Rico (consider what it’s like in Minnesota this time of year!) and their servings of thick coffee with real cream and sugar. Normally I drink it black, but here I’ve been asking for el café con leche y con azúcar. One of my students, Jorge Nieves, gave me the heads up on some good PR coffee brands. He should know from growing up on a coffee plantation. Here are Jorge’s recommendations: Garrido Expresso, Alto Grande and Yauco select. The Yauco website says that the “University of Puerto Rico scientists studying the proximity of our farms to the Caribbean Sea theorize that micro nutrients are brought from the sea to the farm by the Alisian winds.” I cannot find anything on “Alisian” winds, but they feel good wafting in on my beachfront balcony!

Jorge explains that one must pay more for Puerto Rican coffee due to the relatively high cost to harvest the beans. The cherries (like the ones I pictured at a botanical garden outside Tampa) must be hand picked. November is the peak of production in Puerto Rico.

It seems to me that for this luxury of life the premium cost may actually add to its luster. However, Puerto Rican tourism officials may be overdosing on caffeine to think that their recent initiative for promoting coffee tourism will lure visitors inland from the lovely Caribbean beaches. On the other hand, how about a “surf and turf” vacation? That sounds good. After soaking up enough sun on the sand, then head for the hills and hit the haciendas. Now you’re talking! (I really should call it quits for the day on drinking coffee.)

PS. Here are some interesting stats on coffee that I read in my airline magazine* while en route to San Juan from Minneapolis:
— Coffee is known as “Joe” due to the US Secretary of Navy who in 1914 banned wine from officer’s mess – leaving only this hot, stimulating drink as an option.
— It’s estimated that 1.6 billion cups of coffee are drunk worldwide every day. However, because the volume of a “cup” varies, no one can say how much coffee this really is!
— The name Coffee is derived from “Kaffa” – a region in Ethiopia where in AD 800 a goatherd noticed his flock frolicking more than usual after eating certain berries. Fill in your joke here.
— From Ethiopia “Kaffa” became the drink of choice for Arabians and then Europeans. A Dutchman established a plantation in Java in 1696 – hence that became a nickname for this stimulating drink.
— Brazil is the leading country for coffee production — 36 million 60 kg bags per year.
— The manufacturer of Barcalounger claims they introduced coffee to the American workplace about a century ago in Buffalo. Didn’t they also invent spicy chicken wings?
— Coffee seems destined to continually rise in popularity for the USA as evidenced by an increase in consumption by 18 to 24 year olds from 2.5 cups in 2005 to 3.1 in 2007 and 3.2 for 2008. ** (Americans measure a cup as 8 ounces – that’s nothing!)
— The average American consumes 300 milligrams of caffeine per day.
— Does drinking coffee help you stay awake behind the wheel? A French study measured the number of times coffee-drinking drivers crossed the center line. Those who took it decaffeinated crossed the line 159 times versus only 29 by the ones who kept the jolt in their Joe. Viva la difference!

*Source: “The Power of Joe” by Nancy Oakley, Delta’s Sky magazine, November 2008 .

** To counteract this assertion, I offer this anecdotal evidence: In the population of my 5 offspring and 2 in-laws – all younger than 30 years old – only one drinks coffee. The others go for caffeinated soft drinks (300 mg at least every day, I am sure!).

Several years ago I gave a talk on design of experiments at a national conference of microbiologists in California. One of the other speakers in my session was an enologist (a scientist that deals with wine and wine making) from UC Davis – Associate Professor David Block. He helped me settle a debate in my family on how long one should keep wine stored after opening. Opinions ranged from indefinitely (years!) to less than 3 days as a guideline. My guess was 10 days at the max.

Naturally I thought of ways to put this to the test. My idea was to try a triangle tasting over time. Each taster is given three wines, two of which are the same. I saw this in a book I am reading called The Drunkard’s Walk, How Randomness Rules Our Lives. (By the way, the author thinks professional wine ratings are nonsensical for the most part — purely random.)

However, after hearing from Prof Block, who like me is a U of Minnesota chemical engineer, I may not bother to experiment on aging wine because his answer fits my preconceptions (warning: technical details ahead!):

“The aging of wine is mainly related to the amount of oxygen in the bottle after it is opened, the amount of SO2 used by the winemaker for that particular wine, the wine pH, the amount of phenolics (more in red than white wines), and the amount of previous oxidation. So, for instance, if you only drink a small amount and put the bottle in the refrigerator, you are likely to see less oxidation than if you drink almost the entire bottle and leave lots of head space in the refrigerator.

My experience is that with sweet, dessert wines, I can leave them for months and they are still OK. This may be due to the winemaker adding more SO2 to decrease the chances of growth on the residual sugar. The SO2 can protect the wine somewhat from oxidation and production of aldehydes (typically associated with off-flavors or aromas).

Something like a sherry can be kept for a very long period of time at room temperature, typically because it is already oxidized during long barrel storage necessary to get the sherry-like characteristics (e.g. butterscotch, carmel, dried fruit aromas).

The effects of phenolics are a little more difficult to describe as they can be oxidized themselves, liberate H2O2 in reaction when they react with O2 (that eventually produces aldehydes), etc. However, it is generally felt that red wines with higher phenolics will last longer than white wines with lower phenolics. And…of course, all of these reactions are sensitive to pH and temperature.

That’s kind of a complicated answer to your straightforward question…but it is a pretty complicated system. I keep off-dry white wines in the refrigerator for months. Dry reds and whites…probably less than a week. Sherries and ports and brandies…more or less indefinitely at room temperature.

Remember, that different people have different abilities to taste and smell various aromas and flavors, so one person’s acceptable period may be different than a second person’s period.”

So for the dry red wines I enjoy (tonight it is a boutique Syrah from Paso Robles California), I drink up the bottle within one week. That’s my theory (with support from Prof Block) and I am sticking to it!

PS. Wine is fine for sipping and entertaining at the fancier soirees, but for an old-fashioned backyard barbecue it’s hard to beat a can of cold beer. The trick is keeping your brew cool on a steamy summer evening. Check out the results of this very enterprising and creative beer drinker who experimented on can cozies . The one made of rice krispies is unusual but I’d bet on a Thermos brand can insulator like this one that claims to keep your beverage cold ten times longer and 3 times longer than foam cozies.

Last week I heard interviews of top pollsters by a public radio host who could not accept that their results could vary so much – from a margin of 14 percent for Obama to only a 1 percent edge over his opponent McCain. Clearly these predictions differed significantly. Given the power of statistics, how could that be?

The main reason from what I gathered was the variation in pollster’s models on who will actually vote. For example, as I reported in my blog of 12/31/05 (“Surveys produce precisely inaccurate findings”), about 60 percent of self-stated voters did not cast their ballot in the previous election. This attrition rate historically varies by party (Democrats tending to slack off more than Republicans, perhaps) and demographics. Furthermore, people are more and more resistant to being polled – two out of three now refuse according to an article by Rick Montgomery of McClatchy Newspapers (11/2/08). Furthermore, the demise of landline phones in favor of mobiles makes it ever harder to even contact prospective voters. Who wants to burn up precious cell time on a poll?

Amazingly enough, despite all these difficulties in coming up with accurate predictions based on pre-election surveys, the political snapshots proved sharp according to Ken Dilanian of USA Today (11/6/08). Despite dire warnings by analysts such as political scientist Steven Schier of Carlton College (Northfield, Minnesota), I suppose that since all of the polls correctly forecast a win by Obama (his margin was 6 percent – in the middle of the pre-election range of predictions), the statisticians will get by with the usual excuse of “random variation – the old bell curve,” as Scott Rasmussen of Rasmussen Reports put it. Hopefully they learned some things that will lead to better models next time on who will actually vote, how unreachable cell phone users vary from readily-accessible ‘land-liners,’ and the behavior of the silent majority who refuse to answer any questions. Good luck and please take me off your call list.

PS. One of the more interesting statistics I heard about voting is that for every 1 inch of rain in any voting precinct the Republicans gain a 2.5 percent edge! Maybe McCain’s supporters should have invested in fire trucks to hose down voters waiting in line to vote.

While cruising the massive Medical Device & Manufacturing show last week in Minneapolis, I noticed many exhibitors trying to entice visitors with a bowl of candy.* It failed to work on me because invariably a salesperson was perched nearby watching for potential prey to be snared by their sweet trap.

Meanwhile, my morning newspaper featured news that, if you want to “bias the situation in your favor,” a cup of fresh coffee may be just the trick. So advises University of Colorado psychologist Lawrence E. Williams, who co-authored a study reported in the recent Science journal. This press release by Yale University provides details on the experiments done there to support the theory that “people are more likely to give something to others if they had just held something warm.” A more entertaining write-up on this “sneaky study” is provided by AP Medical Writer Lauran Neergaard. She reveals that Williams is now a marketing professor (enough said).

I suggest you become beware of strangers offering you hot drinks – a twist on the warning I remember hearing as a child about unknown people offering me candy. Gratuitous coffee, tea or hot cider will be hard for me to resist, especially now that the cold is pouring in (it’s snowing as I write this). Maybe if I keep one hand securely on the billfold my other hand can be free to enjoy the warmth.

*This is an aside, but I must say that I am intrigued by Hershey’s new Take 5 bar, which “provides a unique taste experience by combining five favorite ingredients in one candy bar,” including pretzels! Years ago I taught Mixture Design for Optimal Formulations to their food scientists in Pennsylvania. However, although these methods are great for finding the sweet spot, I never would have thought to add something salty.

Ok, I went off track a bit on this title (a hypothetical crossword clue), but I really like the name of Arithma’s handy old mechanical Addiator. I came across this particular one at a church rummage sale.

As detailed at John Wolff’s Web Museum “Addiator,” originally the brand name of the German manufacturer Arithma, became the generic term for a host of similar devices used primarily for addition and subtraction. The Addiator I bought (25 cents!) came with no instructions. However, I quickly surmised that I ought to insert the stylus (clipped to its right side) into the slots next to the numbers and move them around somehow. Clearly the top set of numbers would be used for addition, and the bottom for subtraction. However, rather than puzzle it out any further, I prevailed upon my son Hank, a professional programmer, to figure out how it works. He explains:

“The trick is knowing this simple operating rule for both sections of the Addiator: Move gray numbers towards the middle of the machine, but if it becomes red, you must move it outwards and around the bend. For example, let’s say you want to calculate the following sequence of additions and subtraction: 0 + 98 + 54 – 77. Before doing anything else check the display of numbers in the middle circles. If they are not all at 0, pull up the reset bar at the top of the Addiator.

Step 1, (0 + 98), top half: Insert the stylus into the gray slot next to the 8 in the first column, push toward the middle (down). An 8 is now appears as the first digit. The display should show 08. Do the same for 9 in the second digit column. You now have 98.

Step 2, (98 + 54), top half: Insert the stylus into the red slot next to the 4 in the first column. Since it is red it gets pushed toward the top. The top is rounded, you should push the stylus around the bend and back down. This has the effect of “carrying” the one into the next digit. The display now has an up arrow for the second digit and a 2 for the first digit. Do the same with the 5 in the next column, which pushes the third digit to 1. You should now have 152.

Step 3 (152 – 77), bottom half: Insert the stylus in the red slot next to the 7 in the first column. It is red, so it gets pushed down and around the bend. The display should now read 145. Do the same with the 7 in the second column. You should end with 75.”

I tried this and it worked! Now I have no excuse for adding up my deposits incorrectly, which I do on an embarrassingly frequent basis, considering I am an engineer and all.

PS. Contrast the Addiator – based on an 1889 invention – to 2008 technology in the form of the similarly-sized (amazingly small!) Samsung Instinct demonstrated in this video by Sascha Segan, Lead Analyst for Mobile Devices with PC Magazine. This PDA phone offers a readily accessible calculator via the initial touch screen. I’ll bet it even does multiplication and division!

Tom Murphy and Peter Fortini recently published a great answer to the question of how many significant digits to use when reporting test results relative to manufacturing specifications.* All engineers (such as me) know not to round the intermediate results of a multistage calculation. Nevertheless, it’s good to be reminded of this. However, I was unaware that, when rounding a test result for reporting purposes, the interval should be between 0.05 and 0.5 sigma. Murphy and Fortini offer the example of a test result of 1.45729 with a standard deviation of 0.00052, which leads to a rounding of 1.457 (the nearest thousandth). That’s good to know!

I guess that I’ve been slacking off on this rounding deal because I was also ignorant of the “five-even” rule that these two authors note as being de rigueur for “most standards for science and technology.” For example, this rule causes 98.5 to be rounded down to 98, whereas 99.5 gets round up to 100.

My informal survey of math-literate acquaintances revealed that most had learned only to round 5 and higher up (and 4 and lower down). However, my son Hank, a programmer by profession, was familiar with the five even rule, which this Wikipedia entry on rounding says is also known as “statistician’s rounding.” That makes sense because when dealing with large sets of scientific data, where trends are important, traditional “five-up” biases the data upwards.

When I worked in R&D, I noticed that my fellow engineers seemed to be scared to death of rounding – even when reporting their results to non-technical management – marketing folks and the like. Reporting data to a dozen decimal places generally blunted their spear, whereas rounding their numbers to no more than three significant digits would have made their point a lot sharper. Isn’t that ironic?

* “Reporting Test Results, Determining Significant Digits and Rounding Properly,” ASTM Standardization News, September/October 2008 (link for article content may require subscription )

Yesterday, which happened to be Talk Like a Pirate Day, I did a pro bono webinar for a crew of food scientist students assembled by their teacher Tyre at North Carolina State University . They are located in Raleigh – not far from where the notorious Blackbeard hung out in his hay days. Evidently he hosted some very wild parties with his bloodthirsty cohorts, as detailed at this Pirates Realm . (Their webmaster warns that copyright “thieves shall be gullied and fed to the sharks!”)

Tyre and his NC State crew concocted a punch that purportedly imitated an orange drink similar to Kool Aid® — a brand of artificially-flavored drink mix now owned by the Kraft Foods Company but originally invented by Edwin and Kitty Perkins of Hastings, Nebraska.

Now I know that no Carolinian would touch such a tame Midwestern beverage. Thus I strongly suspect that NCSU keeps at least a firkin of rum handy for their apprentice galley slaves – oops, I meant to say food scientists. I am thinking that rum may be the principal component in the mysteriously unidentified “flavor” in the recipe sent to me by Tyre. Given that the a proper rum-laced pirate grog often included lime juice to help to stave off scurvy and a measure of cane sugar to help kill the bitterness of the water, it stands to reason that this NCSU “orange drink” also contains citric acid and sucrose. However, being as I was without a spyglass for this webinar, who knows what this piratical Carolinians were up to.

The treasure these tasters seek is 5 on a 0 to 10 intensity scale. Notice on the graph how they favor this so-called “flavor.” As a statistician turned pirate I say ahRrrrggg-Squared to that. They’d best send me a hogshead of this so-called “kool-aid” or I will be forced to send Tyre the Black Spot in lieu of my usual report.