## Introduction to Fractional Factorial Designed Experiments

Scientific inquiry is aided by sensible application of statistical tools. I grew up around the best minds in applied statistics. My father was an eminent applied statistican, and George Box (the person in the video) was often around our house (or we were at his). Together they wrote Statistics for Experimenters (along with Stu Hunter, not related to me) the bible for design of experiments (George holds up the 1st edition in the video).

The video may be a bit confusing without at least a basic idea of factorial designed experiments. These introductory videos, by Stu Hunter, on Using Design of Experiments to Improve Results may help get you up to speed.

This video looks at using fractional factorials to reduce the number of experiments needed when doing a multifactor experiment. I grew up understanding that the best way to experiment is by varying multiple factors at the same time. You learn much quicker than One Factor At a Time (OFAT), and you learn about interactions (which are mainly lost in OFAT). I am amazed to still hear scientists and engineers talk about OFAT as a sensible method or even as the required method, but I know many do think that way.

To capture the interactions a full factorial requires an ever larger number of experimental runs to be complete. Assessing 4 factors requires 16 runs, 6 would require 64 and 8 would require 256. This can be expensive and time consuming. Obviously one method is to reduce the number of factors to experiment with. That is done (by having those knowledgable about the process include only those factors worth the effort), but if you still have, for example, 8 very important factors using a fractional factorial design can be very helpful.

And as George Box says “What you will often find is that there will be redundant factors… and don’t forget about those redundant factors. Knowing that something doesn’t matter is almost as important as knowing what does.” If you learn a factor isn’t having an affect you may be able to save money. And you can eliminate varying that factor in future experiments.

## George Box 1919 to 2013 – A Great Friend, Scientist and Statistician

Reposted from my management blog.

I would most likely not exist if it were not for George Box. My father took a course from George while my father was a student at Princeton. George agreed to start the Statistics Department at the University of Wisconsin – Madison, and my father followed him to Madison, to be the first PhD student. Dad graduated, and the next year was a professor there, where he and George remained for the rest of their careers.

George died today, he was born in 1919. He recently completed An Accidental Statistician: The Life and Memories of George E. P. Box which is an excellent book that captures his great ability to tell stories. It is a wonderful read for anyone interested in statistics and management improvement or just great stories of an interesting life.

George Box by Brent Nicastro.

George Box was a fantastic statistician. I am not the person to judge, but from what I have read one of the handful of most important applied statisticians of the last 100 years. His contributions are enormous. Several well know statistical methods are known by his name, including:

George was elected a member of the American Academy of Arts and Sciences in 1974 and a Fellow of the Royal Society in 1979. He also served as president of the American Statistics Association in 1978. George is also an honorary member of ASQ.

George was a very kind, caring and fun person. He was a gifted storyteller and writer. He had the ability to present ideas so they were easy to comprehend and appreciate. While his writing was great, seeing him in person added so much more. Growing up I was able to enjoy his stories often, at our house or his. The last time I was in Madison, my brother and I visited with him and again listened to his marvelous stories about Carl Pearson, Ronald Fisher and so much more. He was one those special people that made you very happy whenever you were near him.

George Box, Stuart Hunter and Bill Hunter (my father) wrote what has become a classic text for experimenters in scientific and business circles, Statistics for Experimenters. I am biased but I think this is acknowledged as one of (if not the) most important books on design of experiments.

George also wrote other classic books: Time series analysis: Forecasting and control (1979, with Gwilym Jenkins) and Bayesian inference in statistical analysis. (1973, with George C. Tiao).

George Box and Bill Hunter co-founded the Center for Quality and Productivity Improvement at the University of Wisconsin-Madison in 1984. The Center develops, advances and communicates quality improvement methods and ideas.

The Box Medal for Outstanding Contributions to Industrial Statistics recognizes development and the application of statistical methods in European business and industry in his honor.

All models are wrong but some are useful” is likely his most famous quote. More quotes By George Box

A few selected articles and reports by George Box

## Solar Powered Water Jug to Purify Drinking Water

Deepika Kurup, a 14-year-old New York student, won the Discovery Education 3M Young Scientist Challenge for her invention of a solar-powered water jug that changes dirty water into purified drinking water. She won the top prize of \$25,000.

During “the 5 minutes of my presentation 15 children have died from lack of clean drinking water.”

I am thankful we have kids like this to create solutions for us that will make the world a better place. We rely on hundreds of thousands of such people to use science and engineering methods to benefit society.

## Capuchin Monkeys Don’t Like Being Paid Less

Quite a fun video. Frans de Waal shows us a task he gave Capuchin monkeys to see if they responded to a sense of fairness. See the rest of the talk.

Frans de Waal is a Dutch primatologist and ethologist. He is the Charles Howard Candler professor of Primate Behavior in the Emory University psychology department in Atlanta, Georgia. His research centers on primate social behavior, including conflict resolution, cooperation, inequity aversion, and food-sharing.

## Majority of Clinical Trials Don’t Provide Meaningful Evidence

The largest comprehensive analysis of ClinicalTrials.gov finds that clinical trials are falling short of producing high-quality evidence needed to guide medical decision-making.

The analysis, published today in the Journal of the American Medical Association, found the majority of clinical trials is small, and there are significant differences among methodical approaches, including randomizing, blinding and the use of data monitoring committees.

This is a critical issue as medical studies continue to leave quite a bit to be desired. Even more importantly the failure to systemically study and share evidence of effectiveness once treatments are authorized leaves a great deal to be desired. On top of leaving quite a bit to be desired, the consequences are serious. If we make mistakes for example in how we date fossils it matters but it is unlikely to cause people their lives or health. Failure to adequately manage and analyze health care experiments may very well cost people their health or lives.

“Our analysis raises questions about the best methods for generating evidence, as well as the capacity of the clinical trials enterprise to supply sufficient amounts of high quality evidence to ensure confidence in guideline recommendations,” said Robert Califf, MD, first author of the paper, vice chancellor for clinical research at Duke University Medical Center, and director of the Duke Translational Medicine Institute.

The analysis was conducted by the Clinical Trials Transformation Initiative (CTTI), a public-private partnership founded by the Food and Drug Administration (FDA) and Duke. It extends the usability of the data in ClinicalTrials.gov for research by placing the data through September 27, 2010 into a database structured to facilitate aggregate analysis.

## Baboons Learn to Recognize Hundreds of Words

The (Monkey) Business Of Recognizing Words by Jon Hamilton

[Jonathan Grainger, researcher, Aix-Marseille University] says a baboon named Dan learned more than 300 words. “Dan’s our star baboon,” he says. “He’s a high-performing individual, basically. He does well in most tasks.”

But here’s the amazing thing: Dan and the other baboons also learned to tell whether a string of letters they’d never seen before was an English word. That’s something first-graders learn to do when they start reading, but scientists had assumed that children were simply sounding out the letters to decide whether they make sense.

Of course, the baboons couldn’t do this because they’re not learning to read a language they already speak. They had to rely on a part of the brain that can tell whether objects fit a known pattern.

Michael Platt, who directs the Duke Institute for Brain Sciences, says he was surprised by what the baboons were able to do.

“I was really looking for holes to poke in this study, but it was very difficult to find any because it was really beautifully done,” he says. “And I think the linchpin here was that the baboons, once they had learned the rule, could generalize to new words that they had not seen before.”

Platt says when you think about it, the finding makes sense, given what’s known about human and animal brains. “Brains are always looking for patterns,” he says. “They are always looking to make some statistical pattern analysis of the features and events that are in the environment. And this would just be one of those.”

Platt says that’s a big departure from the idea that reading is a direct extension of spoken language.

One questions I have, is why the experiment done in France tested wether the Baboons could recognize English words?

## Ritalin Doesn’t Show Long Term Effectiveness for ADHD

From the New York Times opinion piece, Ritalin Gone Wrong, by L. Alan Sroufe is a professor emeritus of psychology at the University of Minnesota’s Institute of Child Development:

Attention-deficit drugs increase concentration in the short term, which is why they work so well for college students cramming for exams. But when given to children over long periods of time, they neither improve school achievement nor reduce behavior problems. The drugs can also have serious side effects, including stunting growth.

To date, no study has found any long-term benefit of attention-deficit medication on academic performance, peer relationships or behavior problems, the very things we would most want to improve. Until recently, most studies of these drugs had not been properly randomized, and some of them had other methodological flaws.

But in 2009, findings were published from a well-controlled study that had been going on for more than a decade, and the results were very clear… At first this study suggested that medication, or medication plus therapy, produced the best results. However, after three years, these effects had faded, and by eight years there was no evidence that medication produced any academic or behavioral benefits.

As I have written before I am skeptical of the amount of drug use our health care system encourages: Lifestyle Drugs and Risk.

## Can Just A Few Minute of Exercise a Day Prevent Diabetes?

That just 1 minute of exercise a day could help prevent diabetes seems to good to be true. But research at the University of Bath indicates it might be true. I am a bit of a soft touch for seeing the benefits of exercise. And I also love health care that focuses on achieving healthy lives instead of what most of the spending focuses on: treating illness.

Performing short cycle sprints three times a week could be enough to prevent and possibly treat Type 2 diabetes researchers at the University of Bath believe.

Volunteers were asked to perform two 20-second cycle sprints, three times per week (but really this works out to under 10 minutes of total time including warm up). After six weeks researchers saw a 28% improvement in their insulin function. Type 2 diabetes occurs when blood sugar levels build up to dangerously high levels due to reduced insulin function, often caused by a sedentary lifestyle. The condition can cause life-threatening complications to the heart, kidneys, eyes and limbs, and has huge costs (monetarily and to people’s lives).

Regular exercise can help keep blood sugar levels low but busy lifestyles and lack of motivation mean 66% of the population is not getting the recommended five 30-minute sessions of moderate exercise a week.

Dr Niels Vollaard who is leading the study, said: “Our muscles have sugar stores, called glycogen, for use during exercise. To restock these after exercise the muscle needs to take up sugar from the blood. In inactive people there is less need for the muscles to do this, which can lead to poor sensitivity to insulin, high blood sugar levels, and eventually type 2 diabetes… We already knew that very intense sprint training can improve insulin sensitivity but we wanted to see if the exercise sessions could be made easier and shorter.”

In the study the resistance on the exercise bikes could be rapidly increased so volunteers were able to briefly exercise at much higher intensities than they would otherwise be able to achieve. With an undemanding warm-up and cool-down the total time of each session was only 10 minutes.

This type of study is very helpful in identifying solutions that will allow more people to lead healthy lives and save our economies large amount of money. Medical studies can’t be accepted on face value. They are often not confirmed by future studies and therefore it is unwise to rely on the results of 1 study. The results provide interesting information but need to be confirmed (and in the area of studies on human health this has been shown to be problematic – are health is quite a tricky area to study).

## Rats Show Empathy-driven Behavior

Rats free trapped companions, even when given choice of chocolate instead

The experiments, designed by psychology graduate student and first author Inbal Ben-Ami Bartal with co-authors Decety and Peggy Mason, placed two rats that normally share a cage into a special test arena. One rat was held in a restrainer device — a closed tube with a door that can be nudged open from the outside. The second rat roamed free in the cage around the restrainer, able to see and hear the trapped cagemate but not required to take action.

The researchers observed that the free rat acted more agitated when its cagemate was restrained, compared to its activity when the rat was placed in a cage with an empty restrainer. This response offered evidence of an “emotional contagion,” a frequently observed phenomenon in humans and animals in which a subject shares in the fear, distress or even pain suffered by another subject.

While emotional contagion is the simplest form of empathy, the rats’ subsequent actions clearly comprised active helping behavior, a far more complex expression of empathy. After several daily restraint sessions, the free rat learned how to open the restrainer door and free its cagemate. Though slow to act at first, once the rat discovered the ability to free its companion, it would take action almost immediately upon placement in the test arena.

“We are not training these rats in any way,” Bartal said. “These rats are learning because they are motivated by something internal. We’re not showing them how to open the door, they don’t get any previous exposure on opening the door, and it’s hard to open the door. But they keep trying and trying, and it eventually works.”

To control for motivations other than empathy that would lead the rat to free its companion, the researchers conducted further experiments. When a stuffed toy rat was placed in the restrainer, the free rat did not open the door. When opening the restrainer door released his companion into a separate compartment, the free rat continued to nudge open the door, ruling out the reward of social interaction as motivation. The experiments left behavior motivated by empathy as the simplest explanation for the rats’ behavior.

“There was no other reason to take this action, except to terminate the distress of the trapped rats,” Bartal said. “In the rat model world, seeing the same behavior repeated over and over basically means that this action is rewarding to the rat.”

As a test of the power of this reward, another experiment was designed to give the free rats a choice: free their companion or feast on chocolate. Two restrainers were placed in the cage with the rat, one containing the cagemate, another containing a pile of chocolate chips. Though the free rat had the option of eating all the chocolate before freeing its companion, the rat was equally likely to open the restrainer containing the cagemate before opening the chocolate container.

“That was very compelling,” said Mason, Professor in Neurobiology. “It said to us that essentially helping their cagemate is on a par with chocolate. He can hog the entire chocolate stash if he wanted to, and he does not. We were shocked.”

Now that this model of empathic behavior has been established, the researchers are carrying out additional experiments. Because not every rat learned to open the door and free its companion, studies can compare these individuals to look for the biological source of these behavioral differences. Early results suggested that females were more likely to become door openers than males, perhaps reflecting the important role of empathy in motherhood and providing another avenue for study…

Interesting study. My guess is this is the kind of thing those that don’t like science would deride. I believe in the value of science. I believe in the value of learning. I believe that such experiments are what drives science forward. I believe if you want your economy to benefit from investing in science you should be encouraging hundreds and thousands of such experiments. Funding for this study was provided by The National Science Foundation (NSF), and others.

I am thankful that more and more countries are willing to invest in science, especially since the USA is showing an increasing anti-science attitude. I would rather the USA continue to believe in the value of science and other countries looked to increase investments. But, it is much better that other countries increase their interest in science, and willingness to invest in science, to more than make up for the USA’s decisions to reduce the appreciation for science than for the world to just lose do to a decrease in investments in science.

YouTube SpaceLab is an open competition inviting 14 – 18 year olds (anywhere in the world) to create an idea for a science experiment in space. You don’t have to actually do the experiment, you just have to record yourself explaining it.

Entries must have be submitted on YouTube by 07:59 GMT on December 8th.

The winning experiments will be conducted on the International Space Station (ISS) and beamed live on YouTube for the whole planet to see.

Winners get the choice to either watch the rocket blast off with your idea on it in Japan or take a specially tailored astronaut training course in Russia when you turn 18. There are other amazing prizes for the runners-up too.

Here is an example entry from 3 students in UK on an experiment to learn about quorum sensing by bacteria in the micro gravity of space.

## Cutting the Boarding Time of Planes in Half

I thought I wrote about this several years ago, but I guess I didn’t (I can’t find it, if I did). Experimental test of airplane boarding methods:

The Ste en method, on the other hand, orders the passengers in such a way that adjacent passengers in line are sitting in corresponding seats two rows apart from each other (e.g., 12A, 10A, 8A, 6A, etc.). This method trades a small number of aisle interferences at the front of the cabin, for the beneﬁt of having multiple passengers stowing their luggage simultaneously. Other methods, such as Wilma and the Reverse Pyramid also realize parallel use of the aisle in a natural way as adjacent passengers are frequently sitting in widely separated rows.

We have seen experimentally that there is a marked difference in the time required to board an aircraft depending upon the boarding method used. The evidence strongly supports the heuristic argument from Ste en that methods that parallelize the boarding process by more efﬁciently utilizing the aisle (having more passengers stow their luggage simultaneously) will board more quickly than those that do not. The relative beneﬁt of the application of this theory will grow with the length of the aircraft. Here, we used a 12-row mock airplane, but a more typical airplane with twice that number of rows will gain more by the implementation of parallelized boarding methods.

How this improvement scales with the cabin length is different for each method. For the Ste en method, the beneﬁt will scale almost linearly. If the airplane is twice as long, the time savings will be nearly twice as much since the density of luggage-stowing passengers will remain the same and the boarding will still be maximally parallel. For Wilma and random boarding the beneﬁt will not be as strong since the beneﬁts of parallel boarding are randomly distributed along the length of the cabin instead of being regularly distributed.

I am not optimistic that airlines will even test out this method. People tend to think companies apply sensible, proven concepts and methods. But that is much less likely to be done than people think. The failure of many places to use simple queuing theory improvement (customers should form one line and be served the next available person not form many individual lines) is one example of failures by companies to apply decades old proven better methods. The poor adoption of multivariate designed experiments is another. Applying better ideas is a process that is not done very efficiently in business, health care, education or even science and engineering – in fact in any human endeavor. This is a waste that impacts each of us every day. It is also an opportunity for you to gain advantages just by applying all the good ideas lying around that others are ignoring. You need to test the ideas out in your setting (using the PDSA cycle in an organizational context a good method).

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