Archive for June, 2024
Design of experiments (DOE): Secret weapon for model rocketry
Posted by mark in science, Uncategorized on June 27, 2024
Attracted by its focus on model rockets, I took a summer class on physics at Macalester College in my early teens. What a blast—literally! I really enjoyed learning about force, mass, acceleration and all the other aspects underlying aerospace. (Keep in mind this being the height of the 1960s race to the Moon.) But the best part was building a scale model of the Saturn V featuring multiple solid propellant motors and a parachute recovery system. For the grand finale of our class, we successfully launched our rocket. The parachute did deploy. However, our ship drifted over Saint Paul’s magnificent urban forest (soon to be decimated by Dutch elm disease) and got hopelessly hung up 100 feet overhead.
These great memories from my youth came back to me earlier this year when asked for advice on validating the OpenRocket simulator. The question came in from a mentor using Stat-Ease® 360 software on a low-cost educator license to support a high-school rocket club achieve the American Rocketry Challenge goals for altitude and flight duration. I happily deferred this request for stat help to my colleague Joe—a physics PhD who plays a dual role providing statistical advice and programming. Without getting into the details (after all, this is rocket science!), suffice it to say that, yes, our DOE software does provide “the right stuff.”
By the way, just last week a NASA sounding rocket carrying student experiments reached an altitude of 70 miles. See the video for the launch. (I advanced it to the countdown. After the blast off, move on. That is the only exciting bit.)
What I find most amazing is that the nose cone on this rocket can carry up to 80 plastic cubes as payload. These accommodate experiments by 11-18 year old students. Check out this Cubes in Space STEM program. Page down to the BREAKING NEWS about an important discovery made by a group of elementary students from Ottawa. I recommend you watch the CTV video—very impressive to hear from such science-savvy grade-schoolers. They will go far!
Coin-flip hack: How to call it—heads or tails—to improve your odds
Posted by mark in Basic stats & math on June 12, 2024
As I reported in this 2009 StatsMadeEasy blog, math and stats experts Persi Diaconis, Susan Holmes and Richard Montgomery long ago worked out that “vigorously flipped coins tend to come up the same way they started.”* Based on principles of physics, the “DHM” model predicts about a 0.51 chance that a coin will come up as started. That is not a big difference over 0.50 but worth knowing by its cumulative impact over time providing an appreciable winning edge.
Now in a publication revised on June 2nd the DHM model gains support by evidence from 350,757 flips that fair coins tend to land on the same side they started. All but three of the 50 (!) co-authors—researchers at the University of Amsterdam—flipped coins in 46 different currencies and finally settled on 0.508 as the “same-side bias,” thus providing compelling statistical confirmation for the DHM physics model of coin tossing.
This finding creates many potential repercussions, for example on NFL football games going into overtime, particularly under the old rules when a team that won the coin toss could immediately win with a touchdown. The current rules provide one chance for the opposing team to tie under these circumstances. Nevertheless, it seems to me that referees should randomly pull their coin out without knowing which side came up, keep it covered up from sight of the caller and then flip it.
Let’s keep things totally fair at 50/50. (But do sneak a peek at the coin if you can!)
*Dynamical Bias in the Coin Toss, SIAM (Society for Industrial and Applied Mathematics) Review, Vol. 49, No. 2, pp. 211–235, 2007.
Common confusion about probability can be a life or death matter
Posted by mark in Basic stats & math on June 3, 2024
As a certified quality engineer (CQE), I often focused on the defect rates of manufactured products. They either passed or failed—a binary outcome.
I learned quickly that even a small probability of failure would build up quickly when applying a series of operations. For example, I worked as chief CQE on a chemical plant startup that involved several unit operations in the process line—all to a scale never attempted before. It did not go well. By my reckoning afterwards, each of the steps probably had about a 80/20 chance of succeeding. That led to optimism by the engineers in the company who design our plant. Unfortunately, though, multiplying 0.8 repeatedly is not a winning strategy for process improvement (or gambling!).
As we approach the 80th anniversary of D-Day this diabolic nature of binary outcomes takes on a deadly aspect when you consider how many times our warriors were sent into harms way. The odds continually waver as technology ratchets forward on the offense versus defense. This can be assessed statistically with specialized software such a that provided by Stat-Ease with its logistic regression tools. For example, see this harrowing tutorial on surface-to-air missile (SAM) antiaircraft firing.
Thanks to a heads up from statistician Nathan Yau in one of his daily Flowing Data newsletters, I became aware that many people, even highly educated scientists, get confused about a series of unfortunate or fortunate events (to borrow a phrase from Lemony Snicket).
Yau reports that a noted podcaster with a PhD in neuroscience suggested that chances could be summed, thus if your chance of getting pregnant was 20%, you should see a doctor if not successful after 5 tries. It seems that this should be 100% correct (5 x 20), but not so. By my more productive math (lame pun—taking the product, not summation), the probability of pregnancy comes to 67%. The trick is to multiply the chance of not getting pregnant—0.8—5 times over, subtracting this from 1 and then times 100.
If you remain unconvinced, check out the odds via Yau’s entertaining and enlightening simulation for probability of success for repeated attempts at a binomial process.
Enjoy!