Magic of multifactor testing revealed by fun physics experiment: Part Three—the details and data
Posted by mark in design of experiments, Education, Uncategorized on September 2, 2020
Detail on factors:
- Ball type (bought for $3.50 each from Five Below (www.fivebelow.com)):
- 4 inch, 41 g, hollow, licensed (Marvel Spiderman) playball from Hedstrom (Ashland, OH)
- 4 inch, 159 g, energy high bounce ball from PPNC (Yorba Linda, CA)
- Temperature (equilibrated by storing overnight or longer):
- Freezer at about -4 F
- Room at 72 to 76 F with differing levels of humidity
- Drop height (released by hand):
- 3 feet
- 6 feet
- Floor surface:
- Oak hardwood
- Rubber, 3/4″ thick, Anti Fatigue Comfort Floor Mat by Sky Mats (www.skymats.com)
Measurement:
Measurements done with Android PhyPhox app “(In)Elastic”. Record T1 and H1, time and height (calculated) of first bounce. As a check note H0, the estimated drop height—this is already known (specified by factor C low and high levels).
Data:
| Std # | Run # | A: Ball type | B: Temp deg F | C: Height feet | D: Floor type | Time seconds | Height centimeters |
| 1 | 16 | Hollow | Room | 3 | Wood | 0.618 | 46.85 |
| 2 | 6 | Solid | Room | 3 | Wood | 0.778 | 74.14 |
| 3 | 3 | Hollow | Freezer | 3 | Wood | 0.510 | 31.91 |
| 4 | 12 | Solid | Freezer | 3 | Wood | 0.326 | 13.02 |
| 5 | 8 | Hollow | Room | 6 | Wood | 0.829 | 84.33 |
| 6 | 14 | Solid | Room | 6 | Wood | 1.119 | 153.54 |
| 7 | 1 | Hollow | Freezer | 6 | Wood | 0.677 | 56.17 |
| 8 | 4 | Solid | Freezer | 6 | Wood | 0.481 | 28.34 |
| 9 | 5 | Hollow | Room | 3 | Rubber | 0.598 | 43.92 |
| 10 | 10 | Solid | Room | 3 | Rubber | 0.735 | 66.17 |
| 11 | 2 | Hollow | Freezer | 3 | Rubber | 0.559 | 38.27 |
| 12 | 7 | Solid | Freezer | 3 | Rubber | 0.478 | 28.03 |
| 13 | 15 | Hollow | Room | 6 | Rubber | 0.788 | 76.12 |
| 14 | 11 | Solid | Room | 6 | Rubber | 0.945 | 109.59 |
| 15 | 9 | Hollow | Freezer | 6 | Rubber | 0.719 | 63.43 |
| 16 | 13 | Solid | Freezer | 6 | Rubber | 0.693 | 58.96 |
Observations:
- Run 7: First drop produced result >2 sec with
height of 494 cm. This is >16 feet! Obviously something went wrong. My guess
is that the mic on my phone is having trouble picking up the sound of the
softer solid ball and missed a bounce or two. In any case, I redid the bounce.
- Starting run 8, I will record Height 0 in Comments as a check against bad readings.
- Run 8: Had to drop 3 times to get time
registered due to such small, quiet and quick bounces.
- Could have tried changing setting for threshold provided by the (In)Elastic app.
- Run 14: Showing as outlier for height so it was re-run. Results came out nearly the same 1.123 s (vs 1.119 s) and 154.62 cm (vs 153.54). After transforming by square root these results fell into line. This makes sense by physics being that distance for is a function of time squared.
Suggestions for future:
- Rather than drop the balls by eye from a mark on the wall, do so from a more precise mechanism to be more consistent and precise for height
- Adjust up for 3/4″ loss in height of drop due to thickness of mat
- Drop multiple times for each run and trim off outliers before averaging (or use median result)
- Record room temp to nearest degree
Magic of multifactor testing revealed by fun physics experiment: Part Two—the amazing results
Posted by mark in design of experiments, Uncategorized on August 31, 2020
The 2020 pandemic provided a perfect opportunity to spend time doing my favorite thing: Experimenting!
Read Part One of this three-part blog to learn what inspired me to investigate the impact of the following four factors on the bounciness of elastic spheroids:
A. Ball type: Hollow or Solid
B. Temperature: Room vs Freezer
C. Drop height: 3 vs 6 feet
D. Floor surface: Hardwood vs Rubber
Design-Expert® software (DX) provides the astonishing result: Neither the type of ball (factor A) nor the differing surfaces (factor D) produced significant main effects on first-bounce time (directly related to height per physics). I will now explain.
Let’s begin with the Pareto Chart of effects on bounce time (scaled to t-values).
First observe the main effects of A (ball type) and D (floor surface) falling far below the t-Value Limit: They are insignificant (p>>0.05). Weird!
Next, skipping by the main effect of factor B (temperature) for now (I will get back to that shortly), notice that C—the drop height—towers high above the more conservative Bonferroni Limit: The main effect of drop height is very significant. The orange shading indicates that increasing drop height creates a positive effect—it increases the bounce time. This makes perfect sense based on physics (and common knowledge).
Now look at a multi-view Model Graphs for all four main effects.
The plot at the lower left shows how the bounce time increased with height. The least-significant-difference ‘dumbbells’ at either end do not overlap. Therefore, the increase is significant (p<0.05). The slope quantifies the effect—very useful for engineering purposes.
However, as DX makes clear by its warnings, the other three main effects, A, B and D, must be approached with great caution because they interact with each other. The AB and BD interactions will tell the true story of the complex relationship of ball type (A), their temperature (B) and the floor material (D).
See by the interaction plot how the effect of ball type depends on the temperature. At room temperature (the top red line), going from the hollow to the solid ball produces a significant increase in bounce time. However, after being frozen, the balls behaved completely opposite—hollow beating solid (bottom green line). These opposing effects caused the main effect of ball type (factor A) to cancel!
Incredibly (I’ve never seen anything like this!), the same thing happened with the floor surface: The main effect of floor type got washed out by the opposite effects caused by changing temperature from room (ambient) to that in the freezer (below 0 degrees F).
Changing one factor at a time (OFAT) in this elastic spheroid experiment leads to a complete fail. Only by going to the multifactor testing approach of statistical DOE (design of experiments) can researchers reveal breakthrough interactions. Furthermore, by varying factors in parallel, DOE reveals effects far faster than OFAT.
If you still practice old-fashioned scientific methods, give DOE a try. You will surely come out far ahead of your OFAT competitors.
P.S. Details on elastic-spheroid experiments procedures will be laid out in Part 3 of this series.
Magic of multifactor testing revealed by fun physics experiment: Part One—the setup
Posted by mark in design of experiments, Education on August 23, 2020
The behavior of elastic spheres caught my attention due to a proposed, but not completed, experiment on ball bounciness turned in by a student from the South Dakota School of Mines and Technology.* I decided to see for myself what would happen.
To start, I went shopping for suitable elastic spheres. As pictured, I found two ball-toys with the same diameter—one of them with an eye-catching Spider-Man graphic.
My grandkids all thought that “Spidey” would bounce higher than the other ball—the one in swirly blue and yellow. Little did they know just by looking that “Swirley” was the one with superpowers, it being made from exceptionally elastic, solid synthetic rubber. Sadly, Spidey turned out to be a hollow airhead. This became immediately obvious when I dropped the two balls side by side from shoulder height. Spidey rebounded only to my knee while Swirley shot all the way back to nearly to the original drop level, which really amazed the children.
My next idea for the bouncy experiment came from Frugal Fun for Boys and Girls, a website that provides many great science projects. Their bouncy ball experiment focuses on the effect of temperature as seen here.
However, I could see one big problem straight away: How can you get an accurate measure of bounce height? That led me an amazing cell-phone app called Phyphox (Physics Phone Experiments) which provided an ingenious way to calculate how high a ball bounces by listening to them hit the floor.** Watch this short video to see how. (If you are a physicist, stay on for how the narrator of the demo, Sebastian Staacks, worked out all his calculations for the Phyphox (In)elastic tool.)
The third factor came easy: Height of drop. To make this obvious but manageable, I chose three versus six feet.
The fourth and final factor occurred to me while washing dishes. We recently purchased a thick rubber mat for easy cleanup and comfortable standing in front of our sink. I realized that this would provide a good contrast to our hardwood floors for bounce height, the softer surface being obviously inferior.
To recap, the four factors and their levels I tested were:
A. Ball type: Hollow or Solid
B. Temperature: Room vs Freezer
C. Drop height: 3 vs 6 feet
D. Floor surface: Hardwood vs Rubber
Using Design-Expert® software (DX) I then laid out a two-level, full factorial of 16 runs in random order. To be sure of temperature being stabilized, I did only one run per day, recording the time the first bounce and its height (calculated by the Phypox boffins as detailed in the videos).
When I completed the experiment and analyzed the results using DX, I was astounded to see that neither the type of ball nor the differing surfaces produced significant main effects. That made no sense based on my initial demonstrations on side-by-side bounce for the two balls on the floor versus the rubber mat.
Keeping in mind that my experiment provided a multifactor test of two other variables, perhaps you can guess what happened. I will give you a hint: Factors often interact to produce surprising results, such as time and temperature suddenly coming together to create a fire (or as I would say as a chemical engineer—an “exothermic reaction”).
Stay tuned for Part 2 of this blog on my elastic spheroid experiment to see how the factors interacted in delightful ways that, once laid out, make perfect sense to even for non-physicists.
*For background on my class and an impressive list of home experiments, see “DOE It Yourself” hits the spot for distance-learning projects.
**I credit Rhett Alain of Wired for alerting me to Phyphox via his 8/16/18 post on Three Science Experiments You Can Do With Your Phone. From there he provides a link to a prior, more detailed, post on Modeling a Bouncing Ball.
Butterfly effect debunked (but, even so, best you not step on them)
It’s peak butterfly season—a beautiful time of the year to watch for these wonderfully winged insects, such as the Tiger Swallowtail caught on camera this week by my son-in-law Ryan Bretzel.
Coincidentally, physicists from the Los Alamos National Laboratory just announced* that we need not worry about butterflies in Minnesota setting off hurricanes in Florida, as speculated by chaoticians (such as Dr. Ian Malcolm in the movie Jurassic Park).
“For those interested in the technical details, a number of entangled qubits were run through a set of logic gates before being returned to their initial setup.”
– Mike McRae, Science Alert, 7/31/20, Time Travel Simulation Shows Quantum ‘Butterfly Effect’ Doesn’t Exist
That’s one less thing to worry about for Floridians! They need all the help they can get, being at the peak of pandemic and hurricane season.
* Recovery of Damaged Information and the Out-of-Time-Ordered Correlators, Bin Yan and Nikolai A. Sinitsyn, Physical Review Letters, 125, 040605 – Published 24 July 2020.
Humans cannot wolf down hot dogs as fast as a wolf, scientist calculates
Here at the heart of summer in middle America, hot dogs reign supreme (or at least as co-rulers with hamburgers and brats). Their tubular geometry facilitates ingestion with minimal obstacles as attested by Joey Chestnut—winner again of the Nathan’s Famous Hot Dog Eating Contest on this year’s Independence day. His new record of 75 consumed in 10 minutes probably approaches the theoretical maximum, according to a statistical study by a veterinarian and human biomechanics researcher.
The author, Professor James Smoliga from High Point University in North Carolina, worked out 83 as the number of hot dogs being humanly possible to eat in such a short time. My hunch is that Chestnut and his fellow competitors will be working-out all year to demolish this ‘Smoliga’ bar.
For all the scientific details see the July 15 Royal Society publication of Modelling the maximal active consumption rate and its plasticity in humans—perspectives from hot dog eating competitions.
“These contests provide each individual with an unlimited, ready-to-consume food supply. Thus, participants can focus all of their efforts on maximizing consumption, rather than investing energy into foraging, chasing prey or competing with others for access to a dwindling supply.”
Dr. James Smoliga speaking on the advantages of human hot-dog eaters at a staged event such as the 2020 Nathans Famous event (check out the wacky hats worn by the spectators—gotta love that mustard!)
Even a glutton for statistics gets choked up by the feast of analysis provided by Smoliga, but I did find the comparison between species very tasty, especially the bit about grizzly bears being on par with humans for active consumption rate (ACR). However, having owned a number of big dogs and seen them demolish entire platters of barbecued meats left within reach, I was not surprised that, per Smoliga’s calculations, a grey wolf can eat meaty foods at more than double the rate of a person.
I suggest putting Smoliga’s speculations to the test at next year’s event: Pit the winner against a wolf and a grizzly for the interspecies champion of hot dog eating.
Being kind pays off—wear a mask for the sake of others and earn positive returns
Posted by mark in Consumer behavior, Uncategorized on July 6, 2020
Last month I reported the positive news that people really do like to help others. I figured it would be best to focus on the kind behavior seen even in the most troubling times of tensions here in Minneapolis and around the world.
Since then the coronavirus flared up across the USA. Despite this, many Americans remain adamant against wearing masks, even though this would be kind to their fellow citizens.
I get it—no one likes to be told what to do and the face coverings create a lot of hot and bother. My approach, being committed to kindness, is to always wear a mask in public indoor spaces while steering clear of anyone going without one, choosing times and stores that provide plenty of maneuvering room.
Two books coming out this month provide some hope that mask-averse people may come around to kindly covering up on Covid-19: Survival of the Friendliest and The Kindness of Strangers. They generated a buzz for kindness that got amplified by the Associated Press last week in their report on Not so random acts: Science finds that being kind pays off.
“Doing kindness makes you happier and being happier makes you do kind acts.”
Economist Richard Layard
For those of you who seek data on why people are kind or unkind, check out Oliver Scott Curry’s Kindlab. I love the graphic showing the scientist measuring the height of the “K: Check it out for laughs! Then follow the link to “doing a kind act has a significant effect on well-being” for results gleaned from 27 experimental studies.
There are some caveats, however. The effects reported by Curry et al are small. Also, the individual studies tend to be underpowered—averaging only about a third of the number of subjects needed to detect effects of interest.
Furthermore, it’s clear from Kindlab and other sources (for example, my prior blog noted at the outset of this post), that many people lack a motivation to be kind.
For example, a twenty-something bar-hopper is very unlikely to wear an unfashionable, drink-inhibiting mask. Why bother to protect his or her peers from a disease that probably won’t kill them anyways (never mind the grandparents).
How can this dangerously unkind behavior be turned around?
Fun with colors
Posted by mark in pop, Uncategorized on June 26, 2020
Download one of these color-identifier apps to your cell phone for some summer ‘staycation’ fun. Stop and measure the roses!
I did so with the top-rated Color Grab. It reported “Brilliant Rose” and “Golden Yellow” for the flowers in my vase.
The ‘heads-up’ about Color Grab came from Oliver Thunich—a master statistician who teaches DOE for our German affiliate Statcon. He came up with an innovative way to demonstrate mixture design for optimal formulation by blending three juices: clear apple, passion fruit, and pink grapefruit.
Using Design-Expert® software Oliver developed an experiment with 20 recipes that varied the ingredients in an optimal way to model the resulting color in RGB (three responses).
Based on the results, I came up with the ideal formulation (flagged on the 3d graph) to produce a Pure Red color with as little of the expensive passion fruit as possible.
My high point in coloring came in kindergarten when the teacher sent me home after coloring with a black crayon on black paper—just too dark by her reckoning. However, now that I know that color can be engineered, I may pick it up again. In any case, I do appreciate an array of red, green and blue (i.e., RGB) and all that’s in between, especially in a floral display.
P.S. A hummingbird just flew up to my home-office screen window—just a foot away from where I sit. It would be interesting to see what the color identifier comes up with for this iridescent-feathered friend.
Positive news for troubling times: People really do like to help others
Posted by mark in Consumer behavior on June 19, 2020
Being Minneapolis based and seeing all the strife these last few weeks, it was heartening to see that this Large-Scale Experiment Shows People Want to Help Each Other, Even When It Costs Them Something.
“It [prosocial behavior] means doing something for someone else at a cost to yourself. One example would be paying for the person behind you’s order at the coffee shop. Or right now, wearing your mask in public. It’s a cost to you; it’s uncomfortable. But you contribute to the public good by wearing it and not spreading the virus. From an evolutionary perspective, it’s kind of perplexing that it even exists, because you’re decreasing your own fitness on behalf of others.”
– David Melamed, Associate Professor of Sociology at The Ohio State University, lead author of “The robustness of reciprocity”, Science Advances, 6/3/20
The experiment, which involved 700 people, showed prosocial behavior persisted no matter what the mix of motivators. It is very sweet to see anyone of any age, from toddler to senior, help one another. I don’t know of many things that give me more satisfaction than lending a hand. Come on everyone, be nice—you will feel better for it! It’s time we turned all the frowns upside down.
Baking bread breaks up boredom of being home bound, but baffles many
Market research firm Nielsen reported sales of baking yeast surging by over 600% when the coronavirus cooped up most of America in March. It seemed like a good idea to pass the time. However, as I can attest, getting a loaf to rise can be frustratingly hit-or-miss. The Wall Street Journal described botched breads as “hockey pucks”—my words exactly when describing too-frequent failures with machine-made bread.
“We’ve all decided to bake bread, but a lot of us are ending up with hockey pucks.”
Annie Gasparro and James R. Hagerty, “We’re All Baking Bread Now (And Many of Us Are Failing at It)”, Wall Street Journal, April 2, 2020 (updated web post)
It turns out that multifactor design of experiments (DOE) provides an ideal way to troubleshoot baking problems. See in this show-and-tell* how I successfully applied DOE to rise above (pun intended) the hockey pucks. that provided.
All the best for your baking. We all need some levity nowadays, which can be accomplished with the proper leavening (dough!). Enjoy!
*Published by Quality Progress: “Augmented Ruggedness Testing To Prevent Failures”, Vol. 36, Nº 5, 2003, pp. 38-45, and posted by them for subscribers-only in this archival site.
“DOE It Yourself” hits the spot for distance-learning projects
Every spring for the last two decades I travel to Rapid City to teach design of experiments (DOE) for the Department of Chemical and Biological Engineering at the South Dakota School of Mines and Technology (SDSMT). The highlight of these classes comes when students compete in a flyoff of their paper helicopters developed via the multifactor tools of DOE. They provide an awesome demonstration of design of experiments.
Unfortunately, the Covid-19 pandemic made it impossible for students to team up this year. However, this provided the opportunity for them to each do their their own experiments. I provided an extensive number of suggestions via this DOE It Yourself compilation. Most of the students chose one of these, but a few came up with new ones, such as the one of legal drinking age who sipped tiny amounts (for tasting only, I was assured) of variously concocted Margaritas. The variety of experiments amazed me:
- Cooking eggs to perfection
- Playing tabletop hockey
- Blending a most refreshing Margarita
- Shooting Nerf arrows
- Sharpening up hand-eye coordination
- Flying paper helicopters
- Soaking colors into celery
- Finding fabrics with maximum absorbency
- Making the perfect cup of coffee
- Baking delicious cookies (I asked to be on the taste panel for round 2)
- Mixing good Gatorades
- Producing the perfect puffed rice
- Manufacturing fearsome fighter jets
- Catapulting projectiles with a clothes-pin
- Chipping golf balls more accurately (I wish this could translate to my game)
- Breaking paper clips for stress relief
- Creating craters in the kitchen
- Spinning balls down a funnel
- Sinking boats with too much treasure (see video by Nghia Thai )
Congratulations to SDSMT and their students of DOE for such great work—them not letting the pandemic get in the way for learning how to experiment more effectively via these statistically rigorous, multifactor methods.