Interpreting Cause and Effect

One big challenge we all face is understanding what’s good and what’s bad for us.  And it’s harder when published research studies conflict. And so thanks to Roger Peng for posting on his Facebook page an article that led me to this article by Emily Oster:  Cellphones Do Not Give You Brain Cancer, from the good folks at the 538 blog. I think this article would make a great classroom discussion, particularly if, before showing your students the article, they themselves brainstormed several possible experimental designs and discussed strengths and weaknesses of the designs. I think it is also interesting to ask why no study similar to the Danish Cohort study was done in the US.  Thinking about this might lead students to think about cultural attitudes towards wide-spread data collection.

PD follow-up

Last Saturday the Mobilize project hosted a day-long professional development meeting for about 10 high school math teachers and 10 high school science teachers.  As always, it was very impressive how dedicated the teachers were, but I was particularly impressed by their creativity as, again and again, they demonstrated that they were able to take our lessons and add dimension to them that I, at least, didn’t initially see.

One important component of Mobilize is to teach the teachers statistical reasoning.  This is important because (a) the Mobilize content is mostly involved with using data analysis as a pathway for teaching math and science and (b) the Common Core (math) and the Next Generation (science) standards include much more statistics than previous curricula.  And yet, at least for math teachers, data analysis is not part of their education.

And so I was looking forward to seeing how the teachers performed on the “rank the airlines” Model Eliciting Activity, which was designed by the CATALYST project, led by Joan Garfield at U of Minnesota.  (Unit 2, Lesson 9 from the CATALYST web site.)  Model Eliciting Activities (MEA) are a lesson design which I’m getting really excited about, and trying to integrate into more of my own lessons.  Essentially, groups of students are given realistic and complex questions to answer.  The key is to provide some means for the student groups to evaluate their own work, so that they can iterate and achieve increasingly improved solutions.  MEAs began in the engineering-education world, and have been used increasingly in mathematics both at college and high school and middle school levels.  (A good starting point is “Model-eliciting activities (MEAs)  as a bridge between engineering education research and mathematics education research”, HamiIton, Lesh, Lester, Brilleslyper, 2008.  Advances in Engineering Education.) I was first introduced to MEAs when I was an evaluator for the CATALYST project, but didn’t really begin to see their potential until Joan Garfield pointed it out to me while I was trying to find ways of enhancing our Mobilize curriculum.

In the MEA we presented to the teachers on Saturday, they were shown data on arrival time delays from 5 airlines. Each airline had 10 randomly sampled flights into Chicago O’Hare from a particular year.  The primary purpose of the MEA is to help participants develop informal ways for comparing groups when variability is present.  In this case, the variability is present in an obvious way (different flights have different arrival delays) as well as less obvious ways (the data set is just one possible sample from a very large population, and there is sample-to-sample variability which is invisible. That is, you cannot see it in the data set, but might still use the data to conjecture about it.)

Before the PD I had wondered if the math and science teachers would approach the MEA differently.  Interestingly, during our debrief, one of the math teachers wondered the same thing.  I’m not sure if we saw truly meaningful differences, but here are some things we did see.

Most of the teams immediately hit on the idea of struggling to merge both the airline accuracy and the airline precision into their ranking.  However, only two teams presented rules that used both.  Interestingly, one used precision (variability) as the primary ranking and used accuracy (mean arrival delay) to break ties; another group did the opposite.

At least one team ranked only on precision, but developed a different measure of precision that was more relevant to the problem at hand:  the mean absolute deviations from 0 (rather than deviations from the mean).

One of the more interesting things that came to my attention, as a designer or curriculum, was that almost every team wrestled with what to do with outliers.  This made me realize that we do a lousy job of teaching people what to do with outliers, particularly since outliers are not very rare.   (One could argue whether, in fact, any of the observations in this MEA are outliers or not, but in order to engage in that argument you need a more sophisticated understanding of outliers than we develop in our students.  I, myself, would not have considered any of the observations to be outliers.)  For instance, I heard teams expressing concern that it wasn’t “fair” to penalize an airline that had a fairly good mean arrival time just because of one bad outlier.  Other groups wondered if the bad outliers were caused by weather delays and, if so, whether it was fair to include those data at all.   I was very pleased that no one proposed an outright elimination of outliers. (At least within my hearing.)  But my concern was that they didn’t seem to have constructive ways of thinking about outliers.

The fact that teachers don’t have a way of thinking about outliers is our fault.  I think this MEA did a great job of exposing the participants to a situation in which we really had to think about the effect of outliers in a context where they were not obvious data-entry errors.  But I wonder how we can develop more such experiences, so that teachers and students don’t fall into procedural-based, automated thinking.  (e.g. “If it is more than 1.5 times the IQR away from the median, it is an outlier and should be deleted.”  I have heard/read/seen this far too often.)

Do you have a lesson that engages students in wrestling with outliers? If so, please share!

Model Eliciting Activity: Prologue

I’m very excited/curious about tomorrow: I’m going to lead about 40 math and science teachers in a data-analysis activities, using one of the Model Eliciting Activities from the University of Minnesota Catalysts for Change Project. (One of our bloggers, Andy, was part of this project.) Specifically, we’re giving them the arrival-delay times for five different airlines into Chicago O’Hare. A random sample of 10 from each airline, and asking them to come up with rules for ranking the airlines from best to worst.

I’m curious to see what they come up with, particularly whether  the math teachers differ terribly from the science teachers. The math teachers are further along in our weekend professional development program than are the science teachers, and so I’m hoping they’ll identify the key characteristics of a distribution (all together: center, spread, shape; well, shape doesn’t play much of a role here) and use these to formulate their rankings. We’ve worked hard on helping them see distributions as a unit, and not a collection of individual points, and have seen big improvements in the teachers, most of whom have not taught statistics before.

The science teachers, I suspect, will be a little bit more deterministic in their reasoning, and, if true to my naive stereotype of science teachers, will try to find explanations for individual points. Since I haven’t worked as much with the science teachers, I’m curious to see if they’ll see the distribution as a whole, or instead try to do point-by-point comparisons.

When we initially started this project, we had some informal ideas that the science teachers would take more naturally to data analysis than would the math teachers. This hasn’t turned out to be entirely true. Many of the math teachers had taught statistics before, and so had some experience. Those who hadn’t, though, tended to be rather procedurally oriented. For example, they often just automatically dropped outliers from their analysis without any thought at all, just because they thought that that was the rule. (This has been a very hard habit to break.)

The math teachers also had a very rigid view of what was and was not data. The science teachers, on the other hand, had a much more flexible view of data. In a discussion about whether photos from a smart phone were data, a majority of math teachers said no and a majority of science teachers said yes. On the other hand, the science teachers tend to use data to confirm what they already know to be true, rather than use it to discover something. This isn’t such a problem with the math teachers, in part because they don’t have preconceptions of the data and so have nothing to confirm. In fact, we’ve worked hard with the math teachers, and with the science teachers, to help them approach a data set with questions in mind. But it’s been a challenge teaching them to phrase questions for their students in which the answers aren’t pre-determined or obvious, and which are empirically oriented. (For example: We would like them to ask something like “what activities most often led to our throwing away redcycling into the trash bin?” rather than “Is it wrong to throw trash into the recycling bin?” or “Do people throw trash into the recycling bin?”)

So I’ll report back soon on what happened and how it went.

Is Data Science Real?

Just came back from the International Conference on Teaching Statistics (ICOTS) in Flagstaff, AZ filled with ideas.  There were many thought-provoking talks, but what was even better were the thought-provoking conversations.  One theme, at least for me, is just what is this thing called Data Science?  One esteemed colleague suggested it was simply a re-branding.  Other speakers used it somewhat perjoratively, in reference  to outsiders (i.e. computer scientists).   Here are some answers from panelists at a discussion on the future of technology in statistics education.  All paraphrases are my own, and I take responsibility for any sloppiness, poor grammar, etc.

Webster West took the High Statistician point of view—one shared by many, including, on a good day, myself: Data Science consists of those things that are involved in analyzing data.  I think most statisticians when reading this will feel like Moliere’s Bourgeois Gentleman, who was pleasantly surprised to learn he’d been speaking prose all his life.  But I think there’s more to it then that, because probably many statisticians don’t consider data scraping, data cleaning, data management as part of data analysis.

Nick Horton offered that data mining was an activity that could be considered part of data science.  And he sees data mining as part of statistics.  Not sure all statisticians would agree, since for many of us, data mining is a swear word used to refer to people who are lucky enough to discover something but have no idea why it was discovered.  But he also offered a broader definition:  using data to answer a statistical question.   Which I quite like.  It leaves open the door to many ways of answering the question; it doesn’t require any particular background or religion, it simply means that those activities used to bring data to bear in answering a statistical question.

Bill Finzer relied on set theory:  data science is a partial union of math and statistics, subject matter knowledge, and computational thinking and programming in the service of making discoveries from data.  I’ve seen similar definitions and have found such a definition to be very useful in thinking about curriculum for a high school data science course.  It doesn’t contradict Nick’s definition, but is a little more precise.  As always, Bill has a knack for phrasing things just right without any practice.

Deb Nolan answered last, and I think I liked her answer the best.  Data science encompasses the entire data analysis cycle, and addresses the issue you face in terms of working with data within that cycle, and the skills needed to complete that cycle.  (I like to use this simplified version of the cycle:  ask questions–>collect/consider/prepare data –>analyze data–> interpret data–>ask questions, etc.)

One reason I like Deb’s answer is that its the answer we arrived at in our Mobilize group that’s developing the Introduction to Data Science curriculum for Los Angeles Unified School District.  (With a new and improved webpage appearing soon! I promise!)  Lots of computational skills appear explicitly in the collect/prepare data bit of the cycle, but in fact, algorithmic thinking — thinking about processes of reproducibility and real-time analyses–can appear in all phases.

During this talk I had an epiphany about my own feelings towards a definition. The epiphany was sparked by an earlier talk by Daniel Frischemeier on the previous day, but brought into focus by this panel’s discussion.   (Is it possible to have a slow epiphany?)

Statistics educators have been big proponents of teaching “statistical thinking”, which is basically an approach to solving problems that involve uncertainty/variation and data.  But for many of us, the bit of problem solving in which a computer is involved is ignored in our conceptualization of statistical thinking.  To some extent, statistical thinking is considered to be independent of computation.  We’d like to think that we’d reach the same conclusions regardless of which software we were using.  While that’s true, I think it’s also true that our approach to solving the problem may be software dependent.  We think differently with different softwares because different softwares enable different thought processes, in the same way that a pen and paper enables different processes then a word processor.

And so I think that we statisticians become data scientists the moment we reconceptualize statistical thinking to include using the computer.

What does this have to do with Daniel’s talk?   Daniel has done a very interesting study in which he examined the problem solving approach of students in a statistics class.  In this talk, he offered a model for the expert statistician problem solving process.  Another version of the data analysis cycle, if you will.  His cycle (built solidly on foundations of others) is Real Problem –> Statistical activity –> Software use–> Reading off/Documentation (interpreting) –> conclusions –> reasons (validation of conclusions)–> back to beginning.

I think data scientists are those who would think that the “software use” part of the cycle was subsumed by the statistical activity part of the cycle. In other words, when you approach data cleaning, data organizing, programming, etc. as if they were a fundamental component of statistical thinking, and not just something that stands in the way of your getting to real data analysis, then you are doing data science.  Or, as my colleague Mark Hansen once told me, “Teaching R  *is* teaching statistics.”  Of course its possible to teach R so that it seems like something that gets in the way of (or delays) understanding statistics.  But it’s also possible to teach it as a complement to developing statistical understanding.

I don’t mean this as a criticism of Daniel’s work, because certainly it’s useful to break complex activities into smaller parts.  But I think that there is a figure-and-ground issue, in which statisticians have seen modeling and data analysis as the figure, and the computer as the ground.  But when our thinking unites these views, we begin to think like data scientists.  And so I do not think that “data science” is just a rebranding of statistics. It is a re-consideration of statistics that places greater emphasis on parts of the data cycle than traditionally statistics has placed.

I’m not done with this issue.  The term still bothers me.  Just what is the science in data science?  I feel a refresher course in Popper and Kuhn is in order.  Are we really thinking scientifically about data?  Comments and thoughts welcome.

Fathom Returns

The other shoe has fallen.  Last week (or so) Tinkerplots returned to the market, and now Fathom Version 2.2 (which is the foundation on which Tinkerplots is built) is  available for a free download.  Details are available on Bill Finzer‘s website.

Fathom is one of my favorite softwares…the first commercially available package to be based on learning theory, Fathom’s primary goal is to teach statistics.  After a one-minute introduction, beginning students can quickly discuss ‘findings’ across several variables.  So many classroom exercises involve only one or two variables, and Fathom taught me  that this is unfair to students and artificially holds them back.

Welcome back, Fathom!

Tinkerplots Available Again

Very exciting news for Tinkerplots users (and for those who should be Tinkerplots users).  Tinkerplots is highly visual dynamic software that lets students design and implement simulation machines, and includes many very cool data analysis tools.

To quote from TP developer Cliff Konold:

Today we are releasing Version 2.2 of TinkerPlots.  This is a special, free version, which will expire in a year  — August 31, 2015.

To start the downloading process

Go to the TinkerPlots home page and click on the Download TinkerPlots link in the right hand panel. You’ll fill out a form. Shortly after submitting it, you’ll get an email with a link for downloading.

Help others find the TinkerPlots Download page

If you have a website, blog, or use a social media site, please help us get the word out so others can find the new TinkerPlots Download page. You could mention that you are using TinkerPlots 2.2 and link to www.srri.umass.edu/tinkerplots.

Why is this an expiring version?

As we explained in this correspondence, until January of 2014, TinkerPlots was published and sold by Key Curriculum, a division of McGraw Hill Education. Their decision to cease publication caught us off guard, and we have yet to come up with an alternative publishing plan. We created this special expiring version to meet the needs of users until we can get a new publishing plan in place.

What will happen after version 2.2 expires?

By August 2015, we will either have a new publisher lined up, or we will create another free version.  What is holding us up right now is our negotiations with the University of Massachusetts Amherst, who currently owns TinkerPlots.  Once they have decided about their future involvement with TinkerPlots, we can complete our discussions with various publishing partners.

If I have versions 2.0 or 2.1 should I delete them?

No, you should keep them. You already paid for these, and they are not substantively different from version 2.2. If and when a new version of TinkerPlots is ready for sale, you may not want to pay for it.  So keep your early version that you’ve already paid for.
Cliff and Craig

Lively R

Next week, the UseR conference comes to UCLA.  And in anticipation, I thought a little foreshadowing would be nice.  Amelia McNamara, UCLA Stats grad student and rising stats ed star, shared with me a new tool that has the potential to do some wonderful things.  LivelyR is a work-in-progress that is, in the words of its creators, a “mashup of R with packages of Rstudio.” The result is a highly interactive.  I was particularly struck by and intrigued by the ‘sweeping’ function, which visually smears graphics across several parameter values.  The demonstration shows how this can help understand the effects of bin-width and off-set changes on a histogram so that a more robust sense of the sample distribution shines through.

R is beginning to become a formidable educational tool, and I’m looking forward to learning more at UseR next week. For those of you in L.A. who can attend, Aron Lunzer will be talking about LivelyR at 4pm on Tuesday, July 1.

Data Privacy (L.A. Times)

The L.A. Times ran an article on data privacy today, which, I think it’s fair to say, puts “Big Data” in approximately the same category as fire. In the right hands, it can do good. But…

http://www.latimes.com/nation/politics/politicsnow/la-pn-white-house-big-data-privacy-report-20140501,0,5624003.story