Stats Made Easy

Practical Tools for Effective Experimentation

Sunday, July 29, 2007

One of the all-time achievements for engineering: Brunelleschi’s Dome

I just completed a wonderful book by Ross King about Brunelleschi’s Dome -- an engineering marvel that dominates the skyline of Florence, Italy. The dome crowns the cathedral of Santa Maria del Fiore, the foundation of which began in 1296. It took 140 years for the church to be considered complete enough to be consecrated. The 140 foot diameter of the dome exceeds that of Saint Paul’s in London and Saint Peter’s in Rome. It was masterminded by Filippo Brunelleschi who dared to span it without a centering arch for support. He also came up with ingenious devices to lift some seventy million pounds of rock hundreds of feet up to their final resting places. For pictures and detail on Brunelleschi’s feat, see this site by Maria Patricia Farfan of McGill University.

Aside from the lasting fame he earned from the marvelous dome of Santa Maria del Fiore, Filippo should be venerated for something much more important for all inventive engineers and scientists – being the holder of the world’s first patent issued in 1421. Ironically it was for an invention that did not work out – an ungainly vessel dubbed Il Badalone – “The Monster.” It failed miserably at carrying the marble from Carrara needed for the final stages of construction to provide a beautiful façade. However, the advent of patent law provided protection against the rampant plagiarism of engineering innovations. It should be considered one of the milestones that separate the Middle Ages* from Renaissance times.

“Many are ready, when listening to the inventor, to belittle and deny his achievements…but after some months…they use the inventor’s…design…[and]…boldly call themselves the inventors of the things they first condemned…”
-- Filippo Brunelleschi

*(I went to the Monty Python play Spamalot today. One of the characters, King Arthur perhaps, ponders how anyone would have known it to be the Middle Ages. The play poses many imponderables of this sort as well as non-stop implausible and improbable happenings – all in great fun. I give it two thumbs up, but as a native son of Hormel’s hometown of Austin, Minnesota, I must confess to liking anything concocted of Spam (excepting email).)

Thursday, July 19, 2007

Blowing up film takes on a whole new meaning (Part 2 – Statistical analysis)

The results of my mixture design on Alka Seltzer rockets are shown in the graph, which reveals that the flight time in centiseconds (hundredths) lengthened as the proportion of air-to-water increased (p<0.01 for linear mixture model with no significant lack of fit). The predictive equation in terms of real components (fraction of actual space within the film canister) is:

Flight time (seconds) = 1.24Water+1.95Air

For example, a container filled half way with water before dropping in the Alka Seltzer can be expected to propel the lid for 1.59 seconds (159 centiseconds) of flight time (= 1.24x0.5 + 1.95x0.5).

Give this a try and tell me how close you come to this outcome. I guarantee that you will flip your lid. However, be careful -- you'd best wear goggles. I can imagine my mother catching wind of me doing something like this and yelling "that thing will poke your eye out!"

Blowing up film takes on a whole new meaning (Part 1 -- Design of experiment)

To illustrate design of experiments on mixtures at its simplest level, I blew up a plastic film canister Tuesday evening – not just once, but at least a dozen times. It was really nerve-wracking, but I was prepared to have a headache because the explosive power came from Alka Seltzer® -- an amalgam of citric acid, sodium bicarbonate (baking soda) and aspirin.

You can see the apparatus for my experiment pictured: launching tube, container with water, the tablets, plastic film canister (Fuji’s works best), a scale and stop-watch. Research via the Internet produced many write-ups on making Alka Seltzer “rockets.” They generally recommend using only a quarter of one tablet and advocate experimentation on the amount of water, starting by filling the canister half way. I quickly discovered that the tablets break apart very easily, so it was most convenient and least variable to simply put in a whole tablet. Unfortunately, my assistant Katie is a troublesome teenager who discovered that the canister would blow up a second time when I went over to record the first shot’s results in Design-Expert. That’s what frazzled my nerves.

However, I must say that Katie was incredibly cool under the pressure of the plop, plop, fizz, fizz. It took a steady hand to quickly snap on the top of the canister, over which I then placed the launching tube and prepared to press my stop watch. After some seconds the explosion occurred – propelling the lid nearly to the roof of our two-story house. See (and hear!) a launch video from Mad Physics Dot Com (“…where knowledge becomes dangerous”). They flipped the film canister over, whereas I left it upright, thus shooting off the lighter lid.

Before designing my experiment, I did some range finding to discover that only 4 cc of water in the 34 cc canister would produce a very satisfactory explosion. However, it would not do to fill the container because the Alka Seltzer effervesced too quickly and prevented placement of the lid. After some further fiddling, I found that a reasonable maximum of water would be 20 cc’s – more than half full. I then set up a user-defined mixture design with Design-Expert that provided the extreme vertices (4 to 20 cc of water), the centroid (12 cc) and axial check blends at 8 and 16 cc’s. I replicated the vertices and centroid to provide measures of pure error for testing lack of fit.

Sunday, July 15, 2007

Drowning in statistics

Here’s another cartoon contributed by Nadeem Irfan Bukhari (previous one published in the blog of Friday, April 27, 2007). It reminded me of a couple of old jokes. Did you hear about the statistician who almost drowned in a lake averaging only 2 inches in depth? (Normally this joke leaves no chance of survival, but I wanted to be nice and leave some probability of this.) Perhaps this is the reason for the more positive outcome: How do you save a drowning statistician? Take your foot off his (or her) head.

Sunday, July 01, 2007

Smart thinking to be born first

I am the oldest of seven siblings, so naturally I agree with new evidence reported by Benedict Carey of the New York Times that eldest children develop higher IQs. Aside from getting a big head over this news, what I find intriguing is the assertion by Robert Zajonc, a psychologist at Stanford University, that the main source for intellectual stimulation comes from tutoring — a natural role for the oldest.

“Explaining something … solidifies your knowledge and allows you to grow more extensively.” -- Professor Robert Zajonc

That’s why when I teach workshops for Stat-Ease on-site I suggest that students work in teams of two, with the more advanced ones paired up with those that may be just beginning. Both partners learn more as a result of this tactic to encourage tutoring. Also, this purposeful pairing reduces the odds of two slow learners dragging back the class relative to a more dynamic duo. If students are allowed to select their own partners, it seems inevitable that the range between teams of two will be maximized, making it very difficult to achieve just the right pace for presentation.

An editorial cartoon by Steve Sack of the Minneapolis Star and Tribune (pointed out to me by Pat Whitcomb) provides an alternative explanation for why younger siblings end up a bit slower mentally: They get regularly rapped on the head by their elders! If you are the oldest, like me, you will get a kick out of emailing Sack’s cartoon to your family.