Tuesday, February 28, 2012
Reflections upon Teaching Statistics Again
This semester I find myself again in the enviable position of teaching statistics to psychology graduate students. My cohort is over age 30 and has not studied math for more years than we can count. So how do we teach them? I can tell you what not to do! First, don't assume they know anything, even what an average is! Assume no knowledge until proven otherwise! We don't currently have a placement exam, though I have recommended one now, since the assumption that undergraduate statistics has been retained has proven false. I am finding myself teaching basic ideas, dividing cake, flipping coins, telling them that statistics has to do with proportionality. Second, assume no interest, either! My second surprise was to learn how uninterested my students were in statistics. I suppose I should have known better since anyone with any interest would know something and these students largely knew nothing. To know nothing about statistics, as common as it is in modern life requires an active effort to avoid learning. I should have suspected this. We all have stories to explain our behavior and avoiding statistics is no exception. These stories included "I don't do numbers"; "Knowing statistics has nothing to do with being a good psychologist"; "I can't do math"; "My brain can't comprehend math"; and "I don't have time for this", among other good summary lines. Math education in North America is seriously flawed and biased against women. We know this. Malcolm Gladwell explored math education in Asia and discovered that most of the advantage that Asian students have in understanding math over their North American counterparts comes from their going to school around the entire year and not taking a summer vacation in which they forget what was learned the preceding year. Apparently Asian students didn't have to stop school to help their family with the planting, growing, harvesting, butchering, and other farm chores. Math education has changed, however, even if summer vacation is still observed. We now teach math visually and kinesthetically. We use Lego - to model probability distributions. We cut pieces of pie to teach children about fraction and percent. And, we try to make it interesting. To be most successful, science education has moved to problem-based learning. Except in the most conservative bastions of pre-med student screening in which courses are designed to fail more students than pass, we've abandoned rote memorization as a technique. One, there's too much to memorize. Two, no one remembers what they memorize after the test. Studies have shown that lectures using power point and other visual aids result in 15% the retention of knowledge that occurs when students work together in small interactive groups to solve a problem. Therefore, statistics is being approached as learning how to solve problems together, interactively. The problem solving approach more closely mirrors how science and math are really done and how they arose. The neat linear textbook with tight principles and theorems that people of my age encountered in high school geometry and algebra is an artifact. It's a story made up years later to explain what happened in a way in which it clearly never happened. Statistics, for example, was born in the gambling dens of France. Noblemen were losing their shirts (and estates) at the gaming tables. They came to mathematicians like Pascal and de Moivre to solve their problem. A famous initiating problem was, "what are the odds of rolling 4 sixes in a row with a die?". No one had thought about this before, so experimentation was required. The mathematicians rolled dice and collected data. They didn't actually go into a state of deep meditation and receive the answers from another dimension (though that's been known to happen in science and math as in the solution to the problem of the structure of the benzene ring or a recent development in the theory of black holes). They collected data and examined their results for patterns. This is what we humans do very well. They counted the number of times that each combination of dots on the dice appeared. Pascal invented a triangular table for predicting the number of times any number would occur given successively increasing numbers of rolls of the dice. Of course, it's called Pascal's table. In that table the expected number of times that a "3" for instance would appear in 20 rolls would be the sum of the two numbers above and adjacent (to the right and to the left) of the desired number. Wow, who knew that would happen! Then they could really inform the noblemen what their odds were of success. And, of course, we all know the answer -- don't gamble; odds always favor the house. This is one statistical result that almost everyone in North America has heard; though not many follow its advice. And, actually, there's another way to interpret the results, which I follow. If the odds of winning the lottery are quite small, then buying enough tickets to make a difference would be prohibitively expensive. Therefore, buy one ticket and ask the spirits (Forces, God, Ancestors, Lady Luck, etc.) to rig the game and help you win. This is my approach each week. It hasn't worked yet, either, but then, neither have I lost much money. The Gallup polling organization uses a similar approach. Instead of increasing the number of people they poll over 4,000, they work at reducing the bias and the error from how they select the people which they poll -- a much less expensive strategy. Statistics, then, was discovered as a way to answer practical questions. At the Guinness Brewery, for example, a statistician named Gossett invented a way to reduce the number of beers that had to be sampled (drank!) to do quality control. Apparently, the makers of Guinness were so incensed that anyone would suggest that any of their beers were not perfect, that they demanded that Gossett publish his results under a pseudonym. He chose the name Student -- hence, Student's t-test. Using the t-test and it's t-table, Guinness could waste fewer beers on their employees and still achieve an acceptable degree of quality control. The problem, I discovered with my students, is that they wished certainty. They wanted to know exactly how things worked including the basic principles for going from a to b to c before they attempted to solve any problems. I suspect this is a function of age. My younger acquaintances handle problems very differently. If given new software, for example, my son tries everything to see what it does. He'd never consider reading a manual. He just plays until he feels like he knows what it does. He doesn't have the belief that many people my age have -- that we will somehow screw up things. He comes from the generation that simply knows that pushing the "reset" button will solve everything and we just start over again. My generation is not so sure of that. Nevertheless, teaching statistics has generated some philosophical ideas for me. First, we live in a probabilistic universe as much as we try to avoid thinking about it. The future is not determined. In fact, the most parsimonious theory of quantum physics predicts that every time we make a decision our universe divides into two copies -- one in which we leave New York to open up a restaurant in Santa Fe (see the musical, Rent) and one in which we don't. The possibilities are endless giving an almost uncountable number of parallel universes arranged in some probability distribution. Some parallel universes are more likely than others. For example, there can't be too many parallel universes in which I won the lottery since it hasn't happened yet. For every parallel universe in which I do win the lottery, there must be many in which I don't. Some occurrences are more likely than others. Here's where probability enters. I say to my newest client, what are the odds that your Toyota Camry is not a hovercraft and won't stay afloat if you drive it over a cliff. He has to think about this for some time because he was quite convinced of its anti-gravity drive and its cosmic multi-dimensional nature. Finally he agrees that there might be some parallel universes in which it's only a car and that it might behoove him to be aware of which universe he's in when he turns on the ignition. (Seeing more than one dimension at a time is often problematic for those without the training of a holy person or a culturally sanctioned inter-dimensional traveler.) So, many of the forces in our lives are random and we do what we can to rig the outcome. We do this through visualizing the probable future in which we wish to arrive, through prayer, through taking action when we can envision what to do, and more. Many of my patients are patients because they spend much of their time visualizing the most negative outcome that could happen. As Mark Twain once said, "Now that I'm old, I've lived through countless disasters, most of which never happened." Many of my patients spend hours each day imagining probable futures in which the direst events transpire. My job is to help them redirect their attention. I do believe that their visualizing in this way increases the likelihood of negative (from their value system) events happening to them, but I don't know how much. I also believe that prayer increases our likelihood of being pulled into the probable future into which we hope to arrive, but, again, I'm not sure how much. It's uncertain. I'm more certain that exercise increases my likelihood of staying healthier for longer, but it's certainly no guarantee. A myriad of other random forces could intervene. That's why it's important to me to express gratitude each day for my life and my health and all my many blessings and to not dwell too long on what I don't have but to focus on what I do have. Mark Twain also said, "The easiest way to be happy is to be content with what you have." I'm not a statistician though I enjoy learning. I have used statistics extensively in my research work and I appreciate the beauty of numbers and equations. I confess to not know fully the basis for every technique that I use. I know enough to get by, and, actually, learn more and more every time I teach statistics and every time I read about statistics. Learning, it turns out, is a life-long process. We've done a disservice to students by assisting them to feel that they can actually know a field or a subject. Just when we think we know something, the rug gets pulled from beneath us and all of the old concepts are null and void. Many of us avoid this by pretending that the rug is still there. For example, nearly everyone I meet believes that low levels of serotonin in the synaptic cleft in the brain causes depression even though we've known for years that this isn't true and the drug companies get fined regularly for implying it in their ads. Yet, it's a story that simplifies the complex, generates an air of certainty, and certainly sells drugs, so it remains part of the general knowledge base. It's a story that serves regardless of its lack of validity. What I can't do, apparently, is to give my students an interest in numbers. I've tried such things as using the Beastie Boys in calculating confidence intervals, discussing probability from the standpoint of the Cat in the Hat, and analyzing a database with them of meditators in Los Angeles trying to affect the growth rate of bacteria in Oakland through intent. I thought this last exercise would be really exciting, but no one even came to that lecture (since it wasn't part of the homework). It does, by the way, turn out that meditators in Los Angeles can influence the growth rate of bacteria in Oakland, and, thanks to the need to entertain my students, I will get to be part of a publication about that finding, so boring statistics students isn't all bad. What worries me, however, is how rigged research is. The knowledge generating empire is set to crank out certain kinds of knowledge that matches its biases. Funding will go to those who comply with the invisible rules for what you can study. Some of us at the margin find ways to do small studies to challenge this status quo. We don't typically score the large grants to do big randomized controlled trials because the questions we ask are too weird. Good questions related to drugs' effectiveness compared to placebo or sometimes the effectiveness of cognitive behavior therapy for specific (and relatively minor) conditions, but a study of psychotherapy and healing for psychosis, for example, is probably not going to get funding. Nevertheless, I can do small studies at the margins and even publish them as I have been doing and thereby support a small, but hopefully growing number of people who think like me. I wish my graduate students had this desire and interest, or even the interest to critique the available research to understand how it's rigged. My favorite example currently of this rigging is the study that facilitated the FDA's approving the drug, quetiapine, for monotherapy for bipolar depression. The study requirements meant that to be a suitable candidate, the participants could have never considered suicide, never used a substance of abuse, have no other mental health or medical problems, and so on. It took 43 academic centers to recruit just under 250 patients with bipolar depression that met this description. I believe we could help this population with almost any intervention and show better results than placebo, including gluten-casein free diets, reiki energy healing, or homeopathy. They certainly don't match virtually any of the patients I routinely see in my office who do misuse substances, consider suicide, and have a host of other problems. Just like my clients, my students feel only average and believe that they would do better with a great teacher. Unfortunately, I'm an average teacher looking for great students in the same way that I'm an average healer/clinician looking for the best patients. Because I'm not the one to change! Effort must be made and many students, like many patients, don't want to make that effort. We'd all prefer to be passively entertained and just learn or heal without having to show up and do the hard work of focusing and shifting our attention and trying things that are outside our comfort zone. One of my current patients believes he's invisible and will not do anything to increase his visibility. Consequently, he spends a lot of time sitting in his mother's basement -- one way to become invisible. The hard work, in teaching statistics or doing healing or medicine is inspiring people to believe that they can make a difference in their lives, their learning, their outcomes, their level of suffering, and to take action to do so. Here is where story emerges. We need good stories to help people move outside their comfort zone. I'm looking for better stories for motivating students to learn statistics. I'm thinking that quantum physics and Heisenberg's Uncertainty Principle coupled with the Quantum Zeno Effect is the way to go. Mystical physics is usually a good source of inspiration as we say in the movie, "What the bleep"". Maybe this will work for clients as well. Therefore, I conclude, that we should all learn more quantum physics, and that's all I have to say about that.