Archive for category Uncategorized
Bonferroni of Bergamo
Posted by mark in Basic stats & math, history, Uncategorized on June 6, 2010
Bonferroni corrected
Uncorrected (random results)
I enjoyed a fine afternoon in the old Citta Alta of Bergamo in northern Italy – a city in the sky that the Venetians, at the height of their power as the “most serene republic,” walled off as their western-most outpost in the 17 century.
In statistical circles this town is most notable for being the birthplace of Carlo Emilio Bonferroni. You may have heard of the “Bonferroni Correction” – a method that addresses the problem of multiple comparisons.
For example, when I worked for General Mills the head of quality control in Minneapolis would mix up a barrel of flour and split it into 10 samples, carefully sealed in air-tight containers, for each of the mills to test in triplicate for moisture. At this time I had just learned how to do the t-test for comparing two means. Fortunately for the various QC supervisors, no one asked me to analyze the results, because I would have simply taken the highest moisture value and compared it to the lowest one. Given that there are 45 possible pair-wise comparisons (10*9/2), this biased selection (high versus low) is likely to produce a result that tests significant at the 0.05 level (1 out of 20).
This is a sadistical statistical scheme for a Machiavellian manager because of the intimidating false positives (Type I error). In the simulation pictured, using the random number generator in Design-Expert® software (based on a nominal value of 100), you can see how, with the significance threshold set at 0.05 for the least-significant-difference (LSD) bars (derived from t-testing), the supervisors of Mills 4 and 7 appear to be definitely discrepant. (Click on the graphic to expand the view.) Shame on them! Chances are that the next month’s inter-laboratory collaborative testing would cause others to be blamed for random variation.
In the second graph I used a 0.005 significance level – 1/10th as much per the Bonferroni Correction. That produces a more sensible picture — all the LSD bars overlap, so no one can be fingered for being out of line.
By the way, the overall F-test on this data set produces a p value of 0.63 – not significant.
Since Bonferroni’s death a half-century ago in 1960, much more sophisticated procedures have been developed to correct for multiple comparisons. Nevertheless, by any measure of comparative value, Bergamo can consider this native son as one of those who significantly stood above most others in terms of his contributions to the world.
PB&J please, but hold the jelly (and margarine) and put it on toast – a mixture design combined with a categorical factor
Posted by mark in design of experiments, Uncategorized, Wellness on May 27, 2010
My colleague Pat Whitcomb just completed the first teach of Advanced Formulations: Combining Mixture & Process Variables. It inspired me to develop a virtual experiment for optimizing my perfect peanut butter and jelly (PB&J) sandwich. This was a staple for me and my six siblings when we were growing up. Unfortunately, so far as I was concerned, my mother generously slathered margarine on the bread (always white in those days – no whole grains) and then thick layers of peanut butter and jelly (always grape). As you see* in the response surfaces for overall liking [ 🙁 1-9 🙂 ], I prefer that none of the mixture ingredients (A: Peanut butter, B: Margarine, C: Jelly) be mixed, and I like the bread toasted. This analysis was produced using the Combined design tab from Design-Expert® software version 8 released by Stat-Ease earlier this year. I’d be happy to provide the data set, especially for anyone that may be hosting me for a PB&J dinner party. 😉
*Click to enlarge the plots so you can see the legend, etc.
Stat-Ease Corporation celebrates 25 years in business
Posted by mark in history, Uncategorized on May 16, 2010
My business partner Pat Whitcomb started up Stat-Ease as a business entity in 1982,* but he did not incorporate it until June of 1985. So that brings us to 25 years as a Corporation this coming month. This is quite an achievement for a software publisher – not many remain since 1985, I’ll wager, especially ones so specialized as us. That’s our saving grace, I figure – sticking to a niche like a clam in a wave-beaten hollow.
According to this report on U.S. Small Business Administration Office of Advocacy statistics from September 2009, only half of all startups survive five years. This correlates with a decay curve posted by Scott Shanem Professor of Entrepreneurial Studies at Case Western Reserve University, which shows that only about a quarter of companies remain alive after ten years.
I’d say we’ve done very well to make it this far. Having weathered the recent economic downturn in good shape, I feel positive about continuing on for at least a few years more. 😉
PS. If you’re interested to learn more about us, check out this history of Stat-Ease.
*The year the word “internet” was used for the first time according to this timeline. Check out these photos from the 1980’s by the Computer History Museum, especially the Osborne “portable” (24 pounds!) PC with a screen that looks about the size of today’s internet-enabled smart phones.
Two-level factorial experimentation might make music for my ears
Posted by mark in design of experiments, Uncategorized, Wellness on May 9, 2010
I am a fan of classical music – it soothes my mind and lifts my spirits. Maybe I’m deluded, but I swear there’s a Mozart effect* on my brain. However, a big monkey wrench comes flying in on my blissful state when my stereo speaker (always only one of the two) suddenly goes into a hissy fit. I’ve tried a number of things on a hit-or-miss basis and failed to find the culprit. At this point I think it’s most likely the receiver itself – a Yamaha RX496. However, before spending the money to replace it, I’d like to rule out a number of other factors:
- Speaker set: A vs B
- Speaker wire: Thin vs Thick.
- Source: CD vs FM-Radio
- Speaker: Left vs Right.
It’s very possible that an interaction of two or more factors may be causing the problem, so to cover all bases I need to do all 16 possible combinations (2^4). But, aside from the work this involves for all the switching around of parts and settings, I am stymied by the failure being so sporadic.
Anyways, I feel better now having vented this to my blog while listening to some soothing Sunday choir music by the Dale Warland Singers on the local classical radio station. I’m taking no chances: It’s playing on my backup Panasonic SA-EN25 bookshelf system.
*Vastly over-rated according to this report by the Skeptic’s Dictionary.
Kindergarteners pointing fingers for good (math) or bad (gunning for teacher)
Posted by mark in Uncategorized on May 2, 2010
On the one hand, I see this report of a kindergartner suspended for making a gun with his pointer-finger. That’s discouraging. But on the other hand, I come across this news from New York Times writer Benedict Carey of a program called “Building Blocks,” developed by the School of Education at the University of Buffalo, that teaches preschoolers fundamental math skills, so when they point a finger, it’s a one, not a gun. 😉
My wife teaches preschool. She tells me that her kids learn how to count to 100, recognize numbers up to 20, and enumerate physical objects. In his article on “Building Blocks” Carey refers to this as the “numeric trinity” – crucial to “fuse” kindergarteners for learning math.
Previously educators viewed training on math as being developmentally inappropriate for young children. This created an inertia that many kids could never overcome.
“ ‘I’m not a math person,’ they say – and pretty soon the school agrees.”
– Doug Clements, Distinguished Professor of Learning and Instruction at State University of New York (SUNY) at Buffalo
But now “research has demonstrated that virtually all young children have the capability to learn and become competent in mathematics.”* One can only hope that in future kids coming into kindergarten will be pre-charged for math and school in general, so there will be less finger-pointing (gunning) at teachers.
*Source: Description for Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity a report published in July, 2009 by the National Academies Press, which calls for a national initiative to improve mathematics education for preschoolers. See this press release leading to the full report.
Over-reacting to month-to-month economic statistics
Posted by mark in politics, Uncategorized on April 18, 2010
In his column this weekend the Numbers Guy at Wall Street Journal, Carl Bialik, notes* how uncertain the monthly statistics for unemployment and the like can be. For example, the Census Bureau reported that sales of new single-family homes fell to record low last month. However, if anyone (other than Bialik) read the fine print, they’d see that the upper end of 90 percent confidence interval estimates an increase in sales!
“Most of the month-to-month changes are not only nonsignificant in a statistical way, but they are often straddling zero, so you can’t even infer the direction of the change has been accurately represented.”
– Patrick O’Keefe, economic researcher
The uncertainty stems for the use of sampling as a cost-saving measure for government agencies and ultimately us taxpayers. For example, field representatives covering 19,000 geographical units throughout the U.S. only sample 1 out of 50 houses to see whether they’ve been sold.
The trouble with all this uncertainty in statistics is that it ruins all the drama of simply reporting the point estimate. ; )
*(See “It Is 90% Certain That Unemployment Rose. Or Fell.” and a related blog on “What We Don’t Know About the Economy” )
Misuse of statistics calls into question the credibility of science
Posted by mark in science, Uncategorized on March 28, 2010
The current issue of Science News features an indictment of statistics by writer Tom Siegfried. He pulls no punches with statements like this:
“…a mutant form of math has deflected science’s heart..”
“Science was seduced by statistics…”
“…widespread misuse of statistical methods makes science more like a crapshoot.”
“It’s science’s dirtiest secret: …testing hypotheses by statistical analysis stands on a flimsy foundation.”
“Even when performed correctly, statistical tests are widely misunderstood and frequently misinterpreted. As a result, countless conclusions in the scientific literature are erroneous…”
Draw your own conclusions on whether science fails to face the shortcomings of statistics by reading Siegried’s article Odds Are, It’s Wrong.
My take on all this is that the misleading results boil down to several primary mistakes:
- Confusing correlation with causation
- Extrapolating from the region of experimentation to unstudied areas
- Touting statistically significant results that have no practical importance
- Reporting insignificant results from studies that lack power to see differences that could be very important as a practical matter.
I do not think statistics itself should be blamed. A poor workman blames his tools.
Test and evaluation of the Great Panjandrum – a spectacular failure for weaponry
Posted by mark in history, science, Uncategorized on March 23, 2010
When time becomes available – mainly while I do cardio-exercise on my home elliptical, I’ve been watching a classic 26-episode BBC series on The World at War that my oldest son gave me. It’s extremely compelling – rated 9.7 out of 10 by over two thousand voters at the Internet Movie Database (IMDb).
This morning I watched the chronicle of D-Day. Being that I just returned from the Annual National Test & Evaluation Conference by the National Defense Industry Association (NDIA), it was interesting to see what the boffins of Britain invented to defeat the defenses put up along the Normandy beaches. Perhaps the most amazing device was the Great Panjandrum, a rocket-propelled cart, which according to this write-up for Wikipedia was developed by the Admiralty’s Directorate of Miscellaneous Weapons Development. (One wonders about the “miscellaneous” bit.) The clip I viewed on the spectacular failure of the Great Panjandrum can be seen (along with other incredibly-inept military devices for D-Day) in a video on British Secret Wartime Follies posted in this article by UK’s Daily Mail. Check it out!
PS. The Brits continue to come up with the most audacious inventions, such as this flame-throwing moped developed as a deterrent against derelict drivers competing for motorway lanes.
Evolutionary operation
Posted by mark in design of experiments, Uncategorized on March 7, 2010
Last December, after an outing by the Florida sea, I put out an alert about monster lobsters. This reminded me of an illustration by statistical gurus Box and Draper* of a manufacturing improvement method called evolutionary operation (EVOP), which calls for an ongoing series of two-level factorial designs that illuminate a path to more desirable conditions.
With the aid of Design-Expert® software, I reproduced in color the contour plot in Figure 1.3 from the book on EVOP by Box and Draper (see figure at the right). To illustrate the basic principle of evolution, Box and Draper supposed that a series of mutations induced variation in length of lobster claws as well as the pressure the creatures could apply. The contours display the percentage of lobsters at any given combination of length and pressure who survive long enough to reproduce. Naturally this species then evolves toward the optimum of these two attributes as I’ve shown in the middle graph (black and white contours with lobsters crawling all over them).
In this way, Box and Draper present the two key components of natural selection:
- Variation
- An environment that favors select variants.
The strategy of EVOP mimics this process for improvement, but in a controlled fashion. As illustrated here in the left-most plot, a two-level factorial,** with ranges restricted so as not to upset manufacturing, is run repeatedly – often enough to detect a significant improvement. In this case, three cycles suffices to power up the signal-to-noise ratio. This case illustrates a big manufacturing-yield improvement over the course of an EVOP. However, any number of system attributes can be accounted for via multiple-response optimization tools provided by Design-Expert or the like. This ensures that an EVOP will produce more desirable operating conditions overall for process efficiency and product quality.
It pays to pay attention to nature!
*Box, G. E. P. and N. R. Draper, Evolutionary Operation, Wiley New York, 1969. (Wiley Classics Library, paperback edition, 1998.)
**(We show designs with center points as a check for curvature.)
Beware of bugs bearing backpacks
Posted by mark in science, Uncategorized on March 3, 2010
I am attending a conference sponsored by the National Defense Industry Association (NDIA). They provided all of us participants a copy of the latest issue (March) of their publication National Defense. While wiling away the time listening to some long-winded higher-ups I paged through the magazine and admired the weaponry developed to keep our war-fighters supported to the max. However, on page 17 a very odd picture caught my eye – a cockroach carrying a radiation sensor on its back! A researcher at Texas A&M reports that these bugs are ideal for sweeping potentially contaminated areas, ideally in teams of twenty. They can be operated remotely via devices that stimulate their leg muscles.
There is one problem though: Cockroaches cannot crawl backward. One had better hope that none of the bad guys wear pointy-toed cowboy boots, because they will be ideal for killing the sensor-bearing bugs that become stuck in the corners.