Community Colleges and the ASA

Rob will be be participating in this event, organized by Nicholas Horton:

CONNECTION WITH COMMUNITY COLLEGES: second in the guidelines for undergraduate statistics programs webinar series

The American Statistical Association endorses the value of undergraduate programs in statistical science, both for statistical science majors and for students in other majors seeking a minor or concentration. Guidelines for such programs were promulgated in 2000, and a new workgroup is working to update them.

To help gather input and identify issues and areas for discussion, the workgroup has organized a series of webinars to focus on different issues.

Connection with Community Colleges
Monday, October 21st, 6:00-6:45pm Eastern Time

Description: Community colleges serve a key role in the US higher education system, accounting for approximately 40% of all enrollments. In this webinar, representatives from community colleges and universities with many community college transfers will discuss the interface between the systems and ways to prepare students for undergraduate degrees and minors in statistics.

The webinar is free to attend, and a recording will be made available after the event.  To sign up, please email Rebecca Nichols (rebecca@amstat.org).

More information about the existing curriculum guidelines as well as a survey can be found at:

http://www.amstat.org/education/curriculumguidelines.cfm

Crime data and bad graphics

I’m working on the 2nd edition of our textbook, Gould & Ryan, and was looking for some examples of bad statistical graphics.  Last time, I used FBI data and created a good and bad graphic from the data. This time, I was pleased to see that the FBI provided its own bad graphic.fbi crime bad graph

This shows a dramatic decrease in crime over the last 5 years.  (Not sure why 2012 data aren’t yet available.) Of course, this graph is only a bad graph if the purpose is to show the rate of decrease.  If you look at it simply as a table of numbers, it is not so bad.

Here’s the graph on the appropriate scale.

fbi crimes improved

Still, a decrease worth bragging about.  But, alas, somewhat less dramatic.

Statistics, the government shutdown, and causality.

There’s a  statistical meme that is making its way into pundits’ discussions (as we might politely call them) that is of interest to statistics educators.  There are several variations, but the basic theme is this:  because of the government shutdown, people are unable to benefit from the new drugs they receive by participating in clinical trials.  The L.A Times went so far as to publish an editorial from a gentleman who claimed that he was cured by his participation in a clinical trial.

Now if they had said that future patients are prevented from benefiting from what is learned from a clinical trial, then they’d nail it.  Instead, they seem to be overlooking the fact that some patients will be randomized to the control group, and probably get the same treatment as if there were no trial at all.  And in many trials (a majority?), the result will be that the experimental treatment had little or no effect beyond the traditional treatment.  And in a very small number of cases, the experimental effect will be found to have serious side effects.  And so the pundits should really be telling us that the government shutdown prevents patients from a small probability of a benefitting from experimental treatment.

All snarkiness aside, I think the prevalence of this meme points to the subtleties of interpreting probabilistic experiments, in which outcomes contain much variability, and so conclusions must be stated in terms of group characteristics.  This came out in the SRTL discussion in Minnesota this summer, when Maxinne Pfannkuch, Pip Arnold, and Stephanie Budgett at the University of Auckland  presented their work leading towards a framework for describing students’ understanding of causality.  I don’t remember very well the example they used, but it was similar to this (and was a real-life study):   patients were randomized to receive either fish oil or vegetable oil in their diet.  The goal of the study was to determine if fish oil lowered cholesterol.  At the end of the study, the fish oil group had a slightly lower average cholesterol levels.  A typical interpretation was, “If I take fish oil, my cholesterol will go down.”

One problem with this interpretation is that it ignored the within-group variation.  Some of patients in the fish oil group saw their cholesterol go up; some saw little or no change.  The study’s conclusion is about group means, not about individuals.  (There were other problems, too.  This interpretation ignores the existence of the control group: we don’t really know if fish oil improves cholesterol compared to your current diet; we know only that it tends to go down in comparison to a vegetable-oil diet.  Also, we know the effects only for those who participated in the study. We assume they were not special people, but possibly the results won’t hold for other groups.)

Understanding causality in probabilistic settings (or any setting) is a challenge for young students and even adults.  I’m very excited to see such a distinguished group of researchers begin  to help us understand.  Judea Pearl, at UCLA, has done much to encourage statisticians to think about the importance of teaching causal inference.  Recently, he helped the American Statistical Association establish the Causality in Statistics Education prize, won this year by Felix Elwert, a sociologist at the University of Wisconsin-Madison.  We still have a ways to go before we understand how to best teach this topic at the undergraduate level and even further before we understand how to teach it at earlier levels.  But, as the government shut down has shown, understanding probabilistic causality is an important component of statistical literacy.

My first Shiny experience – CLT applet

When introducing the Central Limit Theorem for the first time in class, I used to use applets like the SOCR Sampling Distribution Applet or the OnlineStatBook Sampling Distribution Applet. If you are reading this post on Google Chrome, chances are those previous links did not work for you. If on another browser, they may have, but you may have also seen warnings like this one:

java_warning

Last year when I tried using one of these applets in class and had students pull it up on their own computers as well, it was a chaos. Between warnings like this and no simple way for everyone in their various computers and operating systems to update Java, most students got frustrated. As a class we had to give up playing with the applet, and the students just watched me go through the demonstrations on the screen.

In an effort to make things a little easier this year, I searched to see if I could find something similar created using Shiny. This one, created by Tarik Gouhier, looked pretty promising. However it wasn’t exactly what I was looking for. For example, it’s pretty safe to assume that my students have never heard of the Cauchy distribution, and I didn’t want to present something that might confuse them further.

Thanks to the code being available on GitHub, I was able to re-write the applet to match the functionality of the previous CLT applets: http://rundel.dyndns.org:3838/CLT.

clt_applet

I’m sure I’ll make some edits to the applet after I class-test it today. Among planned improvements are:

  • an intermediary step between the top (population distribution) and the bottom (sampling distribution) plots: the sample distribution.
  • sliders for input parameters (like mean and standard deviation) for the population distribution.

None of this is revolutionary, but it’s great to be able to build on someone else’s work so quickly. Plus, since all of the code is in R, which the students are learning anyway, those who are particularly motivated can dive deeper and can see the connection between the demonstration and what they’re doing in lab.

If you use such demonstrations in your class and have suggestions for improvements, leave a comment below. If you’d like to customize the applet for your use, the code is linked on the applet page, and I’ll be transitioning it to GitHub as I work on creating a few more of such applets.

(I should also thank Colin Rundel who helped with the implementation and is temporarily hosting the applet on his server until I get my Shiny Server set up — I filled out the registration form last night but I’m not yet sure what the next step is supposed to be.)

Thinking with technology

Just finished a stimulating, thought-provoking week at SRTL —Statistics Research Teaching and Learning conference–this year held in Two Harbors Minnesota, right on Lake Superior. SRTL gathers statistics education researchers, most of whom come with cognitive or educational  psychology credentials, every two years. It’s more of a forum for thinking and collaborating than it is a platform for  presenting findings, and this means there’s much lively, constructive discussion about works in progress.

I had meant to post my thoughts daily, but (a) the internet connection was unreliable and (b) there was just too much too digest. One  recurring theme that really resonated with me was the ways students interact with technology when thinking about statistics.
Much of the discussion centered on young learners, and most of the researchers — but not all — were in classrooms in which the students used TinkerPlots 2.  Tinkerplots is a dynamic software system that lets kids build their own chance models. (It also lets them build their own graphics more-or-less from scratch.) They do this by either dropping “balls” into “urns” and labeling the balls with characteristics, or through spinners which allow them to shade different areas different colors. They can connect series of spinners and urns in order to create sequences of independent or dependent events, and can collect outcomes of their trials. Most importantly, they can carry out a large number of trials very quickly and graph the results.

What I found fascinating was the way in which students would come to judgements about situations, and then build a model that they thought would “prove” their point. After running some trials, when things didn’t go as expected, they would go back and assess their model. Sometimes they’d realize that they had made a mistake, and they’d fix it. Other times, they’d see there was no mistake, and then realize that they had been thinking about it wrong.Sometimes, they’d come up with explanations for why they had been thinking about it incorrectly.

Janet Ainley put it very succinctly. (More succinctly and precisely than my re-telling.)  This technology imposes a sort of discipline on students’ thinking. Using the  technology is easy enough  that they can be creative, but the technology is rigid enough that their mistakes are made apparent.  This means that mistakes are cheap, and attempts to repair mistakes are easily made.  And so the technology itself becomes a form of communication that forces students into a level of greater precision than they can put in words.

I suppose that mathematics plays the same role in that speaking with mathematics imposes great precision on the speaker.  But that language takes time to learn, and few students reach a level of proficiency that allows them to use the language to construct new ideas.  But Tinkerplots, and software like it, gives students the ability to use a language to express new ideas with very little expertise.  It was impressive to see 15-year-olds build models that incorporated both deterministic trends and fairly sophisticated random variability.  More impressive still, the students were able to use these models to solve problems.  In fact, I’m not sure they really know they were building models at all, since their focus was on the problem solving.

Tinkerplots is aimed at a younger audience than the one I teach.  But for me, the take-home message is to remember that statistical software isn’t simply a tool for calculation, but a tool for thinking.

Paint and Patch

IMG_0591

The other day I was painting the trim on our house and it got me reminiscing. The year was 2005. The conference was JSM. The location was Minneapolis. I had just finished my third year of graduate school and was slotted to present in a Topic Contributed session at my first JSM. The topic was Implementing the GAISE Guidelines in College Statistics Courses. My presentation was entitled, Using GAISE to Create a Better Introductory Statistics Course.

We had just finished doing a complete course revision for our undergraduate course based on the work we had been doing with our NSF-funded Adapting and Implementing Innovative Material in Statistics (AIMS) project. We had rewritten the entire curriculum, including all of our assessments and course activities.

The discussant for the session was Robin Lock. In his remarks about the presentations, Lock compared the re-structuring of a statistics course to the remodeling of a house. He described how some teachers restructure their courses according to a plan doing a complete teardown and rebuild. He brought the entire room to laughter as he described most teachers’ attempts, however, as “paint and patch,” fixing a few things that didn’t work quite so well, but mostly just sprucing things up.

The metaphor works. I have been thinking about this for the last eight years. Sometimes paint-and-patch is exactly what is needed. It is pretty easy and not very time consuming. On the other hand, if the structure underneath is rotten, no amount of paint-and-patch is going to work. There are times when it is better to tear down and rebuild.

As another academic year approaches, many of us are considering the changes to be made in courses we will soon be teaching. Is it time for a rebuild? Or will just a little touch-up do the trick?

Free Book—Statistical Thinking: A Simulation Approach to Modeling Uncertainty

CATALST-Textbook-Cover-v2

Catalyst Press has just released the second edition of the book Statistical Thinking: A Simulation Approach to Modeling Uncertainty. The material in the book is based on work related to the NSF-funded CATALST Project (DUE-0814433). It makes exclusive use of simulation to carry out inferential analyses. The material also builds on best practices and materials developed in statistics education, research and theory from cognitive science, as well as materials and methods that are successfully achieving parallel goals in other disciplines (e.g., mathematics and engineering education).

The materials in the book help students:

  • Build a foundation for statistical thinking through immersion in real world problems and data
  • Develop an appreciation for the use of data as evidence
  • Use simulation to address questions involving statistical inference including randomization tests and bootstrap intervals
  • Model and simulate data using TinkerPlots™ software

Why a cook on a statistics book? It is symbolic of a metaphor introduced by Alan Schoenfeld (1998) that posits many introductory (statistics) classes teach students how to follow “recipes”, but not how to really “cook.” That is, even if students leave a class able to perform routine procedures and tests, they do not have the big picture of the statistical process that will allow them to solve unfamiliar problems and to articulate and apply their understanding. Someone who knows how to cook knows the essential things to look for and focus on, and how to make adjustments on the fly. The materials in this book were intended to help teach students to “cook” (i.e., do statistics and think statistically).

The book is licensed under Creative Commons and is freely available on gitHub. If physical copies of the book are preferred, those are available for $45 at CreateSpace (or Amazon) in full color. All royalties from the book are donated to the Educational Psychology department at the University of Minnesota.

JSM 2013 – Days 4 and 4.5

I started off my Wednesday with the “The New Face of Statistics Education (#480)” session. Erin Blackenship from UNL talked about their second course in statistics, a math/stat course where students don’t just learn how to calculate sufficient statistics and unbiased estimators but also learn what the values they’re calculating mean in context of the data. The goal of the course is to bring together the kind of reasoning emphasized in intro stat courses with the mathematical rigor of a traditional math/stat course. Blackenship mentioned that almost 90% of the students taking the class are actuarial science students who need to pass the P exam (the first actuarial exam) therefore the probability theory must be a major component of the course. However UNL has been bridging the gap between these demands and the GAISE guidelines by introducing technology to the course (simulating empirical sampling distributions, checking distributional assumptions, numerical approximation) as well as using writing assessments to improve and evaluate student learning. For example, students are asked to explain in their own words the difference between a sufficient statistic and minimal sufficient statistic, and answers that put things in context instead of regurgitating differences are graded highly. This approach not only allows students who struggle with math to demonstrate understanding, but it also reveals shallow understanding of students who might be testing well in terms of the math by simply going through the mechanics.

In my intro stat class I used to ask similar questions on exams, but have been doing so less and less lately in the interest of time spent on grading (they can be tedious to grade). However lately I’ve been trying to incorporate more activities into the class, and I’m thinking such exercises might be quite appropriate as class activities where students work in teams to perfect their answers and perhaps even teams then grading each others’ answers.

Anyway, back to the session… Another talk in the session given by Chris Malone from Winona State was about modernizing the undergraduate curriculum. Chris made the point that we need much more than just cosmetic changes as he believes the current undergraduate curriculum is disconnected from what graduates are doing when they get their first job. His claim was that the current curriculum is designed for the student who is going on to graduate school in statistics, but that that’s only about a fifth of the students in undergraduate majors. (As an aside, I would have guessed the ratio to be even lower.) He advocated for more computing in the undergrad curriculum, a common thread among many of the education talks at JSM this year, and described a few new programs at Winona and other universities on data science. Another common thread was this discussion of “data science” vs. “statistics”, but I’m not going to go there – at least not in this post. (If you’re interested in this discussion, this Simply Statistician post initiated a good conversation on the topic in the comments section.) I started making a list of Data Science programs I found while searching online but this post seems to have a pretty exhaustive list (original post dates back to 2012 but it seems to be updated regularly).

Other notes from the day:
- R visreg package looks pretty cool, though perhaps not necessarily very useful for an intro stat course where we don’t cover interactions, non-linear regression, etc.
- There is another DataFest like competition going on in the Midwest: MUDAC – maybe we should do a contributed session at JSM next year where organizers share experiences with each other and the audience to solicit more interest in their events or inspire others.

On Thursday I only attended one session: “Teaching the Fundamentals (#699)” (the very last session, mine). You can find my slides for my talk on using R Markdown to teach data analysis in R as well as to instill the importance of reproducible research early on here.

One of the other speakers in my session was Robert Jernigan, who I recognize from this video. He talked about how students confuse “diversity” and “variability” and hence have a difficult time understanding why a dataset like [60,60,60,10,10,10] has a higher standard deviation than a dataset like [10,20,30,40,50,60]. He also mentioned his blog statpics.com, which seems to have some interesting examples of images like the ones in his video on distributions.

John Walker from Cal Poly San Luis Obispo discussed his experiment on how well students can recognize normal and non-normal distributions using normal probability plots — a standard approach for checking conditions for many statistical methods. He showed that faculty do significantly better than students, which I suppose means that you do get better at this with more exposure. However the results aren’t final, and he is considering some changes to his design. I’m eager to see the final results of his experiment, especially if they come with some evidence/suggestions for what the best method to teach this skill is.