Archive for category Basic stats & math
New math sums digits from left to right: Does this add up as an improvement?
Posted by mark in Basic stats & math on November 22, 2009
A recent article in my local newspaper, the Stillwater Gazette, provided enlightenment on our school district’s new way of adding numbers – from left to right, rather than right to left. I might have to try this – maybe it will help me improve my accuracy when tallying checks on deposit slips. (I always hand-calculate these as a way to maintain my math muscles.)
Supposedly this left-to-right approach makes it easier for children to learn, because it goes in the same direction for processing numbers as for reading words. Here’s how it works. Let’s say that you and your spouse both collect up pennies and the first jar nets 237 cents versus 159 for the second. How much in total can be taken to the bank? The way I learned to add one first adds 7 and 9, recording 6 as the right-most digit (the ones column), and then carrying a 1 to the second column (the tens). This carrying part is where I sometimes get off, mainly due to my poor handwriting, which even I cannot always read. The new left-to-right approach eliminates a lot of carrying, but not all, I figure, as shown in the following case. Start by adding the left-most (hundreds in this case) column of numbers:
247
+159
=300
Do not forget to put in the zeroes to hold the place of what you just added. Now go to the next column to the right and add it:
= 90 (4 + 5)
And so forth until there’s no more columns:
= 16 (7 + 9)
Finally, tally up all the numbers you calculated:
300
+90
+16
406
I have a feeling that the old saying about not trying to teach an old dog new tricks might be operative for me in regard to this new math. I think I will just keep adding the old way, or admit that using a calculator or, better yet, a computerized spreadsheet for doing my deposits would be smarter. Am I shortchanging myself (pun intended)?
PS. This innovation in learning math struck a chord with my son Hank, who programs for Stat-Ease. He made me aware that “endianness” is a major issue in coding. Evidently programmers continually feud over the order in which bytes in multi-byte numbers should be stored – most-significant first (Big-Endian) or least-significant first (Little-Endian).* The “endian” terms come from Jonathan Swift who mocked the pettiness of social customs, such as which end one ought to first attack when shelling an egg.
“…the primitive way of breaking Eggs, before we eat them, was upon the larger End: But his present Majesty’s Grand-father, while he was a Boy, going to eat an Egg, and breaking it according to the ancient Practice, happened to cut one of his Fingers. Whereupon the Emperor his Father published an Edict, commanding all his Subjects, upon great Penaltys, to break the smaller End of their Eggs.”
— Jonathan Swift, Gulliver’s Travels, A Voyage to Lilliput, Chapter IV.
*For more details, see Basic concepts on Endianness.
Gambling with the devil
Posted by mark in Basic stats & math, design of experiments on November 15, 2009
In today’s “AskMarilyn” column by Marilyn vos Savant for Parade magazine she addresses a question about the game of Scrabble: Is it fair at the outset for one player to pick all seven letter-tiles rather than awaiting his turn to take one at a time? The fellow’s mother doesn’t like this. She claims that he might grab the valuable “X” before others have the chance. Follow the link for Marilyn’s answer to this issue of random (or not) sampling.
This week I did my day on DOE (design of experiments) for a biannual workshop on Lean Six Sigma sponsored by Ohio State University’s Fisher College of Business (blended with training by www.MoreSteam.com.) Early on I present a case study* on a training experiment done by a software publisher. The goal is to increase the productivity of programmers by sending them to workshop. The manager asks for volunteers from his staff of 30. Half agree to go. Upon their return from the class his annual performance rating, done subjectively on a ten-point scale, reveals a statistically significant increase due to the training. I ask you (the same as I ask my lean six sigma students): Is this fair?
“Designing an experiment is like gambling with the devil: only a random strategy can defeat all his betting systems.”
— RA Fisher
PS. I put my class to the test of whether they really “get” how to design and analyze a two-level factorial experiment by asking them to develop a long-flying and accurate paper helicopter. They use Design-Ease software, which lays out a randomized plan. However, the student tasked with dropping the ‘copters of one of the teams just grabbed all eight of their designs and jumped up the chair. I asked her if she planned to drop them all at once, or what. She told me that only one at a time would be flown – selected by intuition as the trials progressed. What an interesting sampling strategy!
PPS. Check out this paper “hella copter” developed for another statistics class (not mine).
*(Source: “Design of Experiments, A Powerful Analytical Tool” by Christopher Nachtsheim and Bradley Jones, Six Sigma Forum Magazine, August 2003.)
Digging into numbers to the last vigintillionth of a yoctometer
Posted by mark in Basic stats & math on September 25, 2009
I love esoteric measures, for example when working early in my career for an oil company where barrels ruled, I made it my business to know the number of firkins in a hogshead.* Therefore I was piqued by “Coding the Wheel” blogger James Devlin making a point about precision to level of “the last vigintillionth of a yoctometer” (yes, evidently those are real units of measure!).
Fyi, math whiz Landon Curt Noll made a “heroic attempt to put names on hippopotomonstrosesquipedalian numbers” (quoted from this web page on Naming Large Numbers). He provides this utility for getting the English name of any number you enter. I entered 1,000,000,000 and got “one billion” as the result. But then I changed from the American to the European system and Noll’s number-namer spit out “one milliard”! So then I tried 1,000,000,000,000,000 and came up with “one billiard”!! That sent me back for a draft of brew from my firkin (depicted in this video).
Thus fortified, I kept after these mind-muddling measures and verified that this pool-player’s favorite number (billiard) is considered acceptable under the “long scale” (European) branch of the SI (Système International) of units – the modern metric system.
Who knew? (Please forgive my ignorance of European styles, being that I’m a mid-continent dweller of North America. I am learning!)
*See this picture of a 19th century hogshead barrel and learn how it varies in gallons depending on whether it contains beer, wine or tobacco.
Making random decisions on the basis of a coin flip
Posted by mark in Basic stats & math on August 28, 2009
I watched the movie Leatherheads last night – a comedic tribute to the early days of professional football. It re-created the first coin flip used to determine which team would kick off. The referee allowed the coin to fall to the ground – introducing a bit more randomness into the outcome (as opposed him catching it). That’s one of the findings presented in the Dynamical Bias in the Coin Toss by a trio of mathematics and statistics professors from Stanford and UC Santa Cruz. Surprisingly, they report that for “natural flips” the chance of a coin coming up as started is 51 percent. In other words, this procedure for creating an even probability is biased by the physics.
My “heads up” (ha ha) on this came from a former colleague of mine. He sent me a link that led me to this flippant (pun-intended) summary by blogger James Devlin . Devlin warns against spinning a coin to create a 50/50 outcome – a heavy-headed coin can fall tails-up as much as 80 percent of the time! It seems to me that this approach would also increase the odds of a flipistic singularity – normally very rare (1 in 6000 chance).
Another colleague, who once collected comics about Donald Duck, told me the tale of flipism – a random way to live life. However, I think I will not go down this road, but rather quit this blog while I am still ahead.
“Life is but a gamble! Let Flipism chart your ramble.”
– Slogan in Flip Decision by Carl Barks
PS. A fellow trainer starts off statistics workshops with a fun icebreaker that gets students involved with flipping a coin. He asks the class what they expect for an outcome and then challenges this assumption experimentally. The first student gets heads, which the trainer tallies on a flipchart. Each student in turn gets the same outcome until someone finally gets suspicious and discovers that it’s a two-headed quarter.
Small sample sizes produce yawning results from sleep studies
Posted by mark in Basic stats & math, design of experiments on July 15, 2009
“Too little attention has been paid to the statistical challenges in estimating small effects.”
— Andrew Gelman and David Weakliem, “Of Beauty, Sex and Power,” American Scientist, Volume 97, July-August 2009 .
In last week’s “In the Lab” column of the Wall Street Journal (WSJ)*, Sarah Rubinstein reported an intriguing study by the “light and health” program of the Rensselaer Polytechnic Institute (RPI). The director, Mariana Figueiro, is trying to establish a lighting scheme for older people that will facilitate their natural rhythms of wakefulness and sleep. In one 2002 experiment (according to WSJ), Dr. Figueiro subjected four Alzheimer patients to two hours of blue, red or no light-emitting diodes (LEDs). After then putting the individuals to bed, their nurses made observations every two hours and found that the “blue-light special” out-did the red by 66% versus 54% on how often they caught patients napping.
Over the years we’ve accumulated many electrical devices in our bedroom – television, cable box, clocks, smoke and carbon monoxide monitors, etc., which all feature red lights. They don’t bother me, but they keep my wife awake. So it would be interesting, I think, if blues would promote snooze. Unfortunately the WSJ report does not provide confidence intervals on the two percentages – nor do they detail the sample size so one could determine statistical significance on the difference of 0.12 (0.66 minus 0.54). (I assume that each of the 4 subjects were repeatedly tested some number of times.) According to this simple calculator posted by the Southwest Oncology Group (a national clinical research group), it would take a sample size of 554 to provide 80% power for achieving statistical significance at 0.05 for this difference!
So, although whether blue light really does facilitate sleep remains questionable, I am comforted by the testimonial of one of the study participants (a 100 years old!) – “It’s a beautiful light,” she says.
PS. Fyi, for more sophisticated multifactor experimentation (such as for screening studies), Stat-Ease posted a power calculator for binomial responses and provided explanation in its June 2009 Stat-Teaser newsletter .
* “Seeking a Light Approach to Elderly Sleep Troubles,” p. D2, 7/7/09
Cartoon guides to math & stats
Posted by mark in Basic stats & math on July 5, 2009
In the latest issue of Scientific Computing, Statistician John Wass reviews The Manga Guide to Statistics. He suggests that this simplistic guide may be better suited for middle school than the adult learners it’s aimed at. See for yourself by viewing this excerpt from Chapter 4 of The Manga Guide to Statistics: “Standard Score and Deviation Score” .
I am partial to the Cartoon Guide to Statistics myself. See these sample pages on comparing small sample means . I think this hits the target for those looking for a light refresher on basic stats.
Wass confesses to a “lifelong infatuation” with Walt Disney’s Duck clan, which led me to a movie featurette on Donald in Mathmagic Land, which one can find posted on YouTube and the like. June 25 was the 50th anniversary of its release. Unfortunately, as noted in Wikipedia, a cartoon character states that “Pi is equal to 3.141592653589747, et cetera, et cetera, et cetera.” The last two digits should be 93 – not 47. So the scientist who wrote the script had to eat some humble pi. 😉