Stats Made Easy

I forget how I first heard about the Ebbinghaus Forgetting Curve (it escapes me!) but it describes very well what I’ve observed when teaching statistics – a very rapid loss of knowledge – possibly as fast as 50 percent per day. However, it’s been found that by repeated review and practice, details can be remembered for a much longer period of time. That’s why hands-on workshops can be so effective, as opposed to an academic lecture.

For example, I doubt that by noon I’d have been capable of recalling half of what I learned from an 8 AM organic chemistry lecture back in college. Ebbinghaus’s original forgetting curve probably fit my inability to remember chemical formulas. To make matters worse, my notes trailed off every few lines as I nodded off from all the boring details. That was not good, because the chem prof worked completely by lecture – no reference text. There was no chance of getting a ‘re-do’ on any of the presentations – no re-course so to speak (pun intended). Thus my performance on the final exam left much to be desired (at least I passed).

The lesson here is that reviews can be vital for remembering – repetition is the key to recall. Based on recall experiments (for example, the little know fact that Rudyard Kipling invented snow golf), researchers recently discovered the optimal intervals for repeating study sessions. This depends on how long a person wants to remember things. College students hoping to remember information just long enough for the semester-ending final should space study sessions every week apart may be ideal. However, to recall the details a year later a spacing of some months may be far better.

“To put it simply, if you want to know the optimal distribution of your study time, you need to decide how long you wish to remember something.”
— From Spacing Effects in Learning by Nicholas J. Cepeda, Edward Vul, Doug Rohrer, John T. Wixted, and Harold Pashler

If you are determined to remember stuff, consider investing $35 in a flash-card program called FullRecall that promises to “help you memorize the knowledge for lifelong periods with the minimum time investment.” Its neural network converges on the user’s forgetting curve to schedule reviews just in time –i.e., when one gets close to forgetting a detail they hoped to remember.

PS. When I mentioned this blog on memory to my son, he recalled that a fellow named Pimsleur developed a graduated-interval recall system that’s now used for learning languages. In a 1967 publication titled A Memory Schedule, this Ohio State University professor observed that “the process of forgetting begins at once and proceeds very rapidly. If the student is reminded of the word before he has completely forgotten it, his chances of remembering will increase. After each such recall, it will take him longer and longer to forget the word again. Thus, a small number of recalls, if properly spaced, can bring about retention over a long period.”

PPS. By reading the PS above, you just added some length to your recall of how repetition enhances memory. Good for you!

In July of 2007 The New York Times reported an amazing study on obesity by Harvard Medical School. Based on a statistical analysis of a large social network – over twelve thousand people followed for over thirty years, it concluded that a person’s chances of becoming obese nearly tripled when a close friend got fat (or to put it more nicely: “gravity challenged”). Apparently this effect works at a distance, thus a parent like me who just sent a child off to college can anticipate a pile of pounds from the dreaded “freshman fifteen.” Hey – that’s just not fair for one who’s already fighting a battle of the bulge! Also, I worry about getting connected up to wide-bodied people via LinkedIn and Facebook. I’ve noticed that whenever I start surfing these nets I start munching on Twinkies and other bad foodstuffs. This is not good!

Meanwhile, this bulletin from Yale University (might there be a rivalry between this school and Harvard?) counters with a Study [that] Contradicts Earlier Reports That Some Health Issues Are ‘Contagious’ Among Friends. Using similar statistical techniques as the one done on obesity in social networks the Yale researchers discovered that an individual’s height increased by 20 percent of a close friend’s tallness. Therefore I conclude that by spending equal time emailing my beanpole friend and another buddy who inherited a more roomy body type then things will balance out weight-wise on a per height basis.

Now that’s how you can put stats to work with just a little creativity.

I presented a world-wide webinar Wednesday on “An Introduction to Mixture Design for Optimal Formulations” (posted with prior Stat-Ease webinars). As an ice breaker I described the view from my desk of downtown Minneapolis cloaked in a fog of frozen water crystals. One of the participants, our new value-added reseller Peter Trogos of Boston Software Group, expressed curiosity as to how Minnesotans can stand living in our Nation’s icebox. It is hard to explain, but here’s an example of what works for me — embracing the elements.

I dressed up for a walk yesterday and my wife Karen got very alarmed. She misread our outdoor digital thermometer as -13 degrees, but I could see it was only -1.3 degrees. The placement of a decimal makes all the difference!

For my fortitude in walking no matter what the elements (like the proverbial postman) I was rewarded with this vista of the soccer field adjoining a nearby preschool. It was fun to think of upcoming days in Spring when it will be filled with energetic kids!

However, I enjoy the solitude of this frozen season, when only the conifers and hardy birds (and manic Minnesotans) remain active.

“It was January and cold in Minnesota, which was redundant.”

— Garrison Keillor as Guy Noir in the 1/24/09 radio broadcast of A Prairie Home Companion

I’ve just completed my first year of high-deductible medical insurance coupled with a health savings account (HSA). I like this relatively new option very much. However, it requires yet another form to be submitted to the Internal Revenue Service (IRS 8889). I printed this out yesterday. It seemed complete, but then one last page spit out with only this paperwork reduction notice — nothing else on either side. Have you ever felt like crying and laughing at the same time? Anyways, I feel better now after processing this piece of paper with the IRS paperwork reduction notice. You can see where I put stuff like this — a machine that makes a very satisfactory grinding noise, which saves me gnashing my teeth.

International (aka “Frostbite”) Falls reported a record low of 42 below Fahrenheit the other day. Would statisticians deem this an outlier? I think not – just another notch on the low end of the normal curve of temperature in this northern Minnesota city.

On the other hand, this morning I came across this pictured vehicle from Florida. That is much more unusual in the dead of Minnesota winter. You may not resolve the license plate in the photo, but here are a couple of clues that the driver is not a Minnesotan:
— They did not brush off the snow from the rear window – only ran the wipers.
— They are tailgating on the exit ramp to Interstate 694 on a day of extreme cold when black ice* makes the roads extremely slippery.

Given these unsafe practices, I predict that this outlying Floridian car will soon be off the roads and we will be back to our normal distribution of Minnesotan and Wisconsites (don’t get me going on them!).

PS. Here’s a little poem that just came through in an email circulating around these parts (author unknown):

The weather here is wonderful
So I guess I’ll hang around
I could never leave Minnesota
‘Cause I’m frozen to the ground!

*If you do not know about black ice, consider yourself fortunate. It’s a phenomenon that occurs only in below-zero cold: The water resulting from the internal combustion engine freezes when the exhaust hits the road. This ice cannot be seen – hence the designation of it being “black.”

Today’s Wall Street Journal article on Doing Math to Find the Good Jobs reports that the top three professions are mathematician, actuary and statistician! The perpetrator of this outrageous claim is Les Krantz, author of the “Jobs Rated Almanac.” You can infer what floats his boat by comparing these three ivory tower jobs to the down and dirty ones he rated as the absolute worst: lumberjack, dairy farmer and taxi driver.

So it seems that this caps the revenge of the nerds. However, I am not sure what to conclude from a school chum who went on to become an actuary, made a mint in investments on the side and then retired early to become a dairy farmer. I suspect that many math mavens secretly desire being outdoors chopping trees rather than crunching numbers in an office.

Nevertheless, maybe it’s best for those of us that can do the calculations to resist acting upon our daydreaming during the deadly dull parts. For example, when I rev up my little chain saw things often get quickly out of control, such as the time I took it up a ladder to cut off a branch and while leaning at a particularly dangerous angle got stung viciously by a wickedly large wasp. At times like this one must be thankful for a job involving numbers that can be done despite being temporarily incapacitated.

Sorry, I must have been napping because I just now got around to the May issue of Scientific American which reported that even a six-minute snooze boosts recall. The benefits of sleep for enhancing memory are well known, but how quickly doe s it occur? Olaf Lahl, a psychology professor at the University of Dusselfdorf, gave subjects at his sleep lab two minutes to memorize 30 words. An hour later, after playing solitaire the whole time, the average subject recalled under 7 words. A short nap raised this above 8, while a longer, deeper sleep increased the average recall to more than 9 words. This article by the London Telegraph relays a theory by another sleep researcher Dr Robert Stickgold, from Harvard University. He thinks that “just before sleep, the brain ‘replays’ recent events, producing dreamlike sensations and ‘crazy’ thoughts.” Stickgold speculates that the brain sifts through newly entered material in a period of “thought marshalling” which may be crucial for recall.

I’ve always been a great believer in napping for as short a time as possible – just long enough to actually fall asleep, which takes me about 10 minutes. Then I drink a cup of coffee, and off I go again for many hours. I always thought of this as a “power nap.” The Wikipedia details a number of variations on this: cat-nap (same as power nap, but for slackers!), caffeine nap (drink coffee before laying down!) and NASA nap (good if you are an astronaut!).

The NASA findings favoring short sleeps for thier workers gained the notice of some employers, according to this ABC News report. As co-Director of Stat-Ease, I don’t like this idea very much. Once I literally stumbled across one of our summer programmers laid out on the office floor taking a snooze. Maybe I should be more open-minded about such behavior, but my name goes on the pay checks and I hate to think of getting no work per hour. That is not a good productivity statistic!

Last month I enjoyed a visit to the Arecibo Observatory in Puerto Rico (pictured). I found the view as astounding as I’d thought from seeing it featured in the movies GoldenEye (James Bond) and Contact. In this latter film Jodie Foster starred as a character that author Carl based on Jill Tartar. Tarter is director of the center for research at SETI (Search for Extraterrestrial Intelligence) Institute in Mountain View. Evidently the future of SETI lies in arrays of telescopes, not a big dish like Arecibo, which will be closed down in few years according to their visitor center information.

After my visit to Arecibo I saw this CNN television feature on Tartar. She touted SETI’s new array of 350 steerable dish antennas built with the help of a $25 million endowment from Microsoft co-founder Paul Allen. See this fact sheet for details on progress so far and the goal for the Allen Telescope.

Do intelligent beings live outside our planetary system? Many people imagine so, for example in the movie The Day the Earth Stood Still that premiered this week (a remake of the 1950’s classic). The brilliant physicist Enrico Fermi also felt sure ET must be out there, but if so, why hadn’t we seen them yet? This became know as the Fermi paradox. Later Frank Drake formulated an equation, which Sagan used for an optimistic view on the possibility of ETI. Author Michael Crichton (Jurassic Park, etc), recently departed, did not consider this calculation very scientific as noted in this blog by statistician William Briggs, which delves deeply into the whole controversy whether it’s even worth speculating about extraterrestial intelligence.

I think it’s not worth arguing about, but I am in favor of listening for signals, especially with the awesome ‘ears’ of Arecibo and the newer arrays such as the Very Large Array in New Mexico (where I am pictured from a visit in December, 2006).

“Absence of evidence is not evidence of absence.”
— Carl Sagan