Designing an experiment is like gambling with the devil: only a random strategy can defeat all his betting systems.

– R.A. Fisher

Along those lines, I watched with interest when weather forecasts put Tampa at the bulls-eye of the projected track for Hurricane Isaac.  My perverse thought was this might the best place to be, at least early on when the cone of uncertainty is widest.

In any case, one does best by expecting the unexpected.  That gets me back to the topic of randomization, which turns out to be surprisingly hard to do considering the natural capriciousness of weather and life in general.  When I first got going on DOE, I pulled numbered slips of paper out of my hard hat.  Then a statistician suggested I go to a phone book and cull numbers from the last 4 digits from whatever page opened up haphazardly.  Later I graduated to a table of random numbers (an oxymoron?).  Nowadays I let my DOE software lay out the run order.

Check out how Conjuring Truly Random Numbers Just Got Easier, including the background by Keats on pioneering work in this field by British (1927) and American (1947) statisticians.  Now the Australians have leap-frogged (kangarooed?) everyone, evidently, with a method that produces 5.7 billion “truly random” (how do they know?) values per second.  Rad mon!

“Some time during the past couple of years, statistics became data sciences older, more boring sibling that always played by the rules.”

– Nathan Yau*

I tend to agree—being suspicious of changes in titles as a cover for shenanigans.  It seems to me that “data science” provides a smoke screen to take unwarranted leaps from shaky numbers.  As the shirt sold at JSM by American Statistical Association (ASA) says, “friends don’t let friends extrapolate.”

*Incorrectly attributed initially (my mistake) to Carnegie Mellon statistics professor Cosma Shalizi, who was credited by Yau for speaking up on this subject.

For more background on decimal styles over time and place see this Science Editor article by Amelia Williamson.  It credits Scottish mathematician John Napier* for being the first to use a period.  However, it seems that he wavered later by using a comma, thus setting the stage for this being an alternative.  Given the use of commas to separate thousands from millions and millions from billions and so on, numbers can be misinterpreted by several orders of magnitude very easily if you do not keep a sharp eye on the source.

So, all you math & stats boffins—watch it!

*As detailed in this 2009 blog I first learned of this fellow from seeing his bones on display at IBM’s Watson Research Center in New York.

“Many bits of straw look like needles.”

- Trevor Hastie, Professor of Statistics, Stanford University, co-author of The Elements of Statistical Learning (2nd edition).

I take issue with extremely tortuous paths to complicated models based on happenstance data.  This can be every bit as bad as oversimplifications such as relying on linear trend lines (re Why you should be very leery of forecasts). As I once heard DOE guru George Box say (in regard to overly complex Taguchi methodologies): Obscurity does not equal profundity.

For example, Lohr touts the replacement of earned run average (ERA) with the “Siera”—Skill-Interactive Earned Run Average. Get all the deadly details here from the inventors of this new pitching performance metric. In my opinion, baseball itself is already complicated enough (try explaining it to someone who only follows soccer) without going to such statistical extremes for assessing players.

The movie “Moneyball” being up for Academy Awards is stoking the fever for “big data.” I am afraid that in the end the call may be for “money back” after all is said and done.

When working on the committee that developed the ASTM 1169-07 Standard Practice for Conducting Ruggedness Tests, I introduced the half-normal plot for selecting effects from two-level factorial experiments.  Most of the committee favored this, but one individual – a professor emeritus from a top school of statistics – resisted the introduction of this graphical tool.  He believed that only numerical methods, specifically analysis of variance (ANOVA) tables, could support objective decisions for model selection.  My comeback was to dodge the issue by simply using graphs and tables – this need not be an either/or choice.  Why not do both, or merge them by putting number on to graphs – the best of both worlds?

“A heavy bank of figures is grievously wearisome to the eye, and the popular mind is as incapable of drawing any useful lessons from it as of extracting sunbeams from cucumbers.”

– Economists (brothers) Farquhar and Farquhar (1891)

In their article which can be seen here Feinberg and Wainer take a different tack (path of least resistance?): Make tables look more like graphs.  Here are some of their suggestions for doing so:

• Round data to 3 digits or less.
• Line up comparable numbers by column, not row.
• Provide summary statistics, in particular medians.
• Don’t default to alphabetical or some other arbitrary order: Stratify by size or some other meaningful attribute.
• Call out data that demands attention by making it bold and/or bigger and/or boxing it.
• Insert extra space between rows or columns of data where they change greatly (gap).

Check out the remodeled table on arms transfers which makes it clear that, unlike the uptight USA, the laissez faire French will sell to anyone.  It would be hard to dig that nugget out of the original data compilation.

Certainly many great minds, particularly authors, abhor math and stats, even though they many not suffer from dyscalculia (only numerophobia).  The renowned essayist Hillaire Belloc said*

Statistics are the triumph of the quantitative method, and the quantitative method is the victory of sterility and death.

I wonder how he liked balancing his checkbook.

Meanwhile, public figures such as television newscasters and politicians, who appear to be intelligent otherwise (debatable!) say the silliest things when it comes to math and stats.  For example a U.S. governor, speaking on his state’s pension fund said that “when they were set up, life expectancy was only 58, so hardly anyone lived long enough to get any money.”**  One finds this figure of 58, the life expectancy of men in 1930 when Social Security began, cited often by pundits discussing the problems of retirement funds.  Of course this was the life expectancy at birth, in times when infant mortality remained a much higher levels than today.  According to this fact sheet by the Social Security Administration (SSA), 6.7 million Americans were aged 65 or older in 1930.  This number exhibits an alarming increase.  The SSA also provides interesting statistics on Average Remaining Life Expectancy for Those Surviving to Age 65, which show surprisingly slow gains over the decades.  I leave it to those of you who are not numerophobic (nor a sufferer of dyscalculia) to reconcile these seemingly contradictory statistical tables.

*From “On Statistics”, The Silence of the Sea, Glendalough Press, 2008 (originally published 1941).

**From “Real world Economics / Errors in economics coverage spread misunderstandings” by Edward Lotterman.

After the presentation a number of educators brainstormed on interactive stats.  David Lane of Rice U (author of many stat applets) suggested the use of “interactive clickers” – see this short (< 2 min.) newscast, for example.  I wonder what happen when a majority vote for the wrong answer?  For some teachers it might be easiest just to declare the most popular response as the correct answer.  That would be consistent with the way things seem to be going in politics nowadays. ; )

*Just for fun try the Investigating the Central Limit Theorem (CLT) applet (click the link from the page referenced above or simply click here).  This would be a good applet to provide when illustrating CLT using dice (such as is done in this in-class exercise developed by two professors from De Anza College). In this case, pick the uniform Population and sample size 2.  Then Draw a Sample repeatedly, and, finally, just Draw 100 samples.  Repeat this exercise with sample size 5 a la the game of Yahtzee (a favorite in my youth). Notice how as n goes up the distribution of averages becomes more normal and narrower. That’s the power of averaging.

Now imagine grade schoolers being lectured like this at home and then spending their time in class following up one-on-one or in small group sessions with the teacher. See this report from a 7th grade math teacher in California who takes advantage of this “blended learning” approach. As face-to-face time with educators becomes ever-more expensive, expect more-and-more use of asynchronous web-based training like this. That’s what I foresee. Don’t you?

Seeing this CBS News about Maine legalizing switchblades for one-armed people reminded me of a riddle about limbs that’s posed by some statisticians for educational purposes.  Here it is: “The great majority of people in [fill in your country here] have more than the average number of [choose either arms or legs here].”

For an answer {UK, legs}, see this posting on averages by Kevin McConway, Professor of Applied Statistics in the Department of Mathematics and Statistics at The Open University.  I heard this riddle also from Hans Rosling in his BBC TV program on “The Joy of Statistics.”*  He spoke of his home country of Sweden, whose inhabitants on average have 1.999 legs.

I’m quitting while I’m ahead.  Oops, this makes me wonder if I have an average number of heads – a scary thought, my hunch being that I’m below average for this.  I never imagined that averages could be so creepy!

*See this StatsMadeEasy blog on Rosling

I spoke today to a resident of Busan with a daughter in high school.  She said the school runs from 8 in the morning to 8 at night Monday through Friday and a half day every other Saturday.  No wonder South Korean teenagers test so highly relative to the USA!