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.

Yikes…It’s Been Awile

Apparently our last blog post was in August. Dang. Where did five months go? Blog guilt would be killing me, but I swear it was just yesterday that Mine posted.

I will give a bit of review of some of the books that I read this semester related to statistics. Most recently, I finished Hands-On Matrix Algebra Using R: Active and Motivated Learning with Applications. This was a fairly readable book for those looking to understand a bit of matrix algebra. The emphasis is definitely in economics, but their are some statistics examples as well. I am not as sure where the “motivated learning” part comes in, but the examples are practical and the writing is pretty coherent.

The two books that I read that I am most excited about are Model Based Inference in the Life Sciences: A Primer on Evidence and The Psychology of Computer Programming. The latter, written in the 70’s, explored psychological aspects of computer programming, especially in industry, and on increasing productivity. Weinberg (the author) stated his purpose in the book was to study “computer programming as a human activity.” This was compelling on many levels to me, not the least of which is to better understand how students learn statistics when using software such as R.

Reading this book, along with participating in a student-led computing club in our department has sparked some interest to begin reading the literature related to these ideas this spring semester (feel free to join us…maybe we will document our conversations as we go). I am very interested in how instructor’s choose software to teach with (see concerns raised about using R in Harwell (2014). Not so fast my friend: The rush to R and the need for rigorous evaluation of data analysis and software in education. Education Research Quarterly.) I have also thought long and hard about not only what influences the choice of software to use in teaching (I do use R), but also about subsequent choices related to that decision (e.g., if R is adopted, which R packages will be introduced to students). All of these choices probably have some impact on student learning and also on students’ future practice (what you learn in graduate school is what you ultimately end up doing).

The Model Based Inference book was a shorter, readable version of Burnham and Anderson’s (2003) Springer volume on multimodel inference and information theory. I was introduced to these ideas when I taught out of Jeff Long’s, Longitudinal Data Analysis for the Behavioral Sciences Using R. They remained with me for several years and after reading Anderson’s book, I am going to teach some of these ideas in our advanced methods course this spring.

Anyway…just some short thoughts to leave you with. Happy Holidays.

Pie Charts. Are they worth the Fight?

Like Rob, I recently got back from ICOTS. What a great conference. Kudos to everyone who worked hard to organize and pull it off. In one of the sessions I was at, Amelia McNamara (@AmeliaMN) gave a nice presentation about how they were using data and computer science in high schools as a part of the Mobilize Project. At one point in the presentation she had a slide that showed a screenshot of the dashboard used in one of their apps. It looked something like this.


During the Q&A, one of the critiques of the project was that they had displayed the data as a donut plot. “Pie charts (or any kin thereof) = bad” was the message. I don’t really want to fight about whether they are good, nor bad—the reality is probably in between. (Tufte, the most cited source to the ‘pie charts are bad’ rhetoric, never really said pie charts were bad, only that given the space they took up they were, perhaps less informative than other graphical choices.) Do people have trouble reading radians? Sure. Is the message in the data obscured because of this? Most of the time, no.

plots_1Here, is the bar chart (often the better alternative to the pie chart that is offered) and the donut plot for the data shown in the Mobilize dashboard screenshot? The message is that most of the advertisements were from posters and billboards. If people are interested in the n‘s, that can be easily remedied by including them explicitly on the plot—which neither the bar plot nor donut plot has currently. (The dashboard displays the actual numbers when you hover over the donut slice.)

It seems we are wasting our breath constantly criticizing people for choosing pie charts. Whether we like it or not, the public has adopted pie charts. (As is pointed out in this blog post, Leland Wilkinson even devotes a whole chapter to pie charts in his Grammar of Graphics book.) Maybe people are reasonably good at pulling out the often-not-so-subtle differences that are generally shown in a pie chart. After all, it isn’t hard to understand (even when using a 3-D exploding pie chart) that the message in this pie chart is that the “big 3” browsers have a strong hold on the market.

The bigger issue to me is that these types of graphs are only reasonable choices when examining simple group differences—the marginals. Isn’t life, and data, more complex than that?Is the distribution of browser type the same for Mac and PC users? For males and females? For different age groups? These are the more interesting questions.

The dashboard addresses this through interactivity between the multiple donut charts. Clicking a slice in the first plot, shows the distribution of product types (the second plot) for those ads that fit the selected slice—the conditional distributions.

So it is my argument, that rather than referring to a graph choice as good or bad, we instead focus on the underlying question prompting the graph in the first place. Mobilize acknowledges that complexity by addressing the need for conditional distributions. Interactivity and computing make the choice of pie charts a reasonable choice to display this.

*If those didn’t persuade you, perhaps you will be swayed by the food argument. Donuts and pies are two of my favorite food groups. Although bars are nice too. For a more tasty version of the donut plot, perhaps somebody should come up with a cronut plot.

**The ggplot2 syntax for the bar and donut plot are provided below. The syntax for the donut plot were adapted from this blog post.

# Input the ad data
ad = data.frame(
	type = c("Poster", "Billboard", "Bus", "Digital"),
	n = c(529, 356, 59, 81)

# Bar plot
ggplot(data = ad, aes(x = type, y = n, fill = type)) +
     geom_bar(stat = "identity", show_guide = FALSE) +

# Add addition columns to data, needed for donut plot.
ad$fraction = ad$n / sum(ad$n)
ad$ymax = cumsum(ad$fraction)
ad$ymin = c(0, head(ad$ymax, n = -1))

# Donut plot
ggplot(data = ad, aes(fill = type, ymax = ymax, ymin = ymin, xmax = 4, xmin = 3)) +
     geom_rect(colour = "grey30", show_guide = FALSE) +
     coord_polar(theta = "y") +
     xlim(c(0, 4)) +
     theme_bw() +
     theme(panel.grid=element_blank()) +
     theme(axis.text=element_blank()) +
     theme(axis.ticks=element_blank()) +
     geom_text(aes(x = 3.5, y = ((ymin+ymax)/2), label = type)) +
     xlab("") +



Increasing the Numbers of Females in STEM

I just read a wonderful piece written about how the Harvey Mudd increased the ratio of females declaring a major in Computer Science from 10% to 40% since 2006. That is awesome!

One of the things that they attribute this success to is changing the name of their introductory course. They renamed the course from Introduction to programming in Java to Creative Approaches to Problem Solving in Science and Engineering using Python.

Now, clearly, they changed the language they were using (literally) as well,from Java to Python, but it does beg the question, “what’s in a name?” According to Jim Croce and Harvey Mudd, a lot. If you don’t believe that, just ask anyone who has been in a class with the moniker Data Science, or any publisher who has published a book recently entitled [Insert anything here] Using R.

It would be interesting to study the effect of changing a course name. Are there words or phrases that attract more students to the course (e.g., creative, problem solving)?  Are there gender differences? How long does the effect last? Is it a flash-in-the-pan? Or does it continue to attract students after a short time period? (My guess is that the teacher plays a large role in the continued attraction of students to the course.)

Looking at the effects of a name is not new. Stephen Dubner and Steve Levitt of Freakonomics fame have illuminated folks about research about whether a child’s name has an effect on a variety of outcomes such as educational achievement and future income [podcast], and suggest that it isn’t as predictive as some people believe. Perhaps someone could use some of their ideas and methods to examine the effect of course names.

Has anyone tried this with statistics (aside from Data Science)? I know Harvard put in place a course called Real Life Statistics: Your Chance for Happiness (or Misery) which got good numbers of students (and a lot of press). My sense is that this happens much more in liberal arts schools (David Moore’s Concepts and Controversies book springs to mind). What would good course words or phrases for statistics include? Evidence. Uncertainty. Data. Variation. Visualization. Understanding. Although these are words that statisticians use constantly, I have to admit they all sound better than An Introduction to Statistics.


Conditional probabilities and kitties

I was at the vet yesterday, and just like with any doctor’s visit experience, there was a bit of waiting around — time for re-reading all the posters in the room.


And this is what caught my eye on the information sheet about feline heartworm (I’ll spare you the images):


The question asks: “My cat is indoor only. Is it still at risk?”

The way I read it, this question is asking about the risk of an indoor only cat being heartworm positive. To answer this question we would want to know P(heartworm positive | indoor only).

However the answer says: “A recent study found that 27% of heartworm positive cats were identified as exclusively indoor by their owners”, which is P(indoor only | heartworm positive) = 0.27.

Sure, this gives us some information, but it doesn’t actually answer the original question. The original question is asking about the reverse of this conditional probability.

When we talk about Bayes’ theorem in my class and work through examples about sensitivity and specificity of medical tests, I always tell my students that doctors are actually pretty bad at these, looks like I’ll need to add vets to my list too!

The Future of Inference

We had an interesting departmental seminar last week, thanks to our post-doc Joakim Ekstrom, that I thought would be fun to share.  The topic was The Future of Statistics discussed by a panel of three statisticians.  From left to right in the room: Songchun Zhu (UCLA Statistics), Susan Paddock (RAND), and Jan DeLeeuw (UCLA Statistics).  The panel was asked about the future of inference: waxing or waning.

The answers spanned the spectrum from “More” to “Less” and did so, interestingly enough, as one moved left to right in order of seating.  Songchun staked a claim for waxing, in part because  he knows of groups that are hiring statisticians instead of computer scientists because statisticians’ inclination to cast problems in an inferential context makes them more capable of finding conclusions in data, and not simply presenting summaries and visualizations.  Susan felt that it was neither waxing nor waning, and pointed out that she and many of the statisticians she knows spend much of their time doing inference.  Jan said that inference as an activity belongs in the substantive field that raised the problem.  Statisticians should not do inference.  Statisticians might, he said, design tools to help specialists have an easier time doing inference. But the inferential act itself requires intimate substantive knowledge, and so the statistician can assist, but not do.

I think one reason that many stats educators might object to this because its hard to think of how else to fill the curriculum.  That might have been an issue when most students took a single Introductory course in their early twenties and then never saw statistics again.  But now we must think of the long game, and realize that students begin learning statistics early.  The Common Core stakes out one learning pathway, but we should be looking ahead, and thinking of future curricula, since the importance of statistics will grow.

If statistics is the science of data, I suggest we spend more time thinking about how to teach students to behave more like scientists.  And this means thinking seriously about how we can  develop their sense of curiosity.  The Common Core introduces the notion of a ‘statistical question’– a question that recognizes variability.  To the statisticians reading this, this needs no more explanation.  But I’ve found it surprisingly difficult to teach this practice to math teachers teaching statistics.  I’m not sure, yet, why this is.  Part of the reason might be that in order to answer a statistical question such as “What is the most popular favorite color in this class” we must ask the non-statistical question “What is your favorite color.”  But there’s more to it than that.  A good statistical question isn’t as simple as the one I mentioned, and leads to discovery beyond the mere satisfaction of curiosity.  I’m reminded of the Census at Schools program that encouraged students to become Data Detectives.

In short, its time to think seriously about teaching students why they should want to do data analysis.  And if we’re successful, they’ll want to learn how to do inference.

So what role does inference play in your Ideal Statistics Curriculum?

City Hall and Data Hunting

The L.A. Times had a nice editorial on Thursday (Oct 30) encouraging City Hall to make its data available to the public.  As you know, fellow Citizens, we’re all in favor of making data public, particularly if the public has already picked up the bill and if no individual’s dignity will be compromised.  For me this editorial comes at a time when I’ve been feeling particularly down about the quality of public data.  As I’ve been looking around for data to update my book and for the Mobilize project, I’m convinced that data are getting harder, and not easier. to find.

More data sources are drying up, or selling their data, or using incredibly awkward means for displaying their public data.  A basic example is to consider how much more difficult it is to get, say, a sample of household incomes from various states for 2010 compared to the 2000 census.

Another example is, which has been one of my favorite classroom examples.  (We compare the participatory data in, which lists prices for individual stations across the U.S., with the randomly sampled data the federal government provides, which gives mean values for urban districts. One data set gives you detailed data, but data that might not always be trustworthy or up-to-date. The other is highly trustworthy, but only useful for general trends and not for, say, finding the nearest cheapest gas. )  Used to be you could type in a zip code and have access to a nice data set that showed current prices, names and locations of gas stations, dates of the last reported price, and the username of the person who reported the price.  Now, you can scroll through an unsorted list of cities and states and get the same information only for the 15 cheapest and most expensive stations.

About 2 years ago I downloaded a very nice, albeit large, data set that included annual particulate matter ratings for 333 major cities in the US.  I’ve looked and looked, but the AirData site now requires that I enter the name of each city in one at a time, and download very raw data for each city separately.  Now raw data are good things, and I’m glad to see it offered. But is it really so difficult to provide some common sensically aggregated data sets?

One last example:  I stumbled across this lovely website, wildlife crossing, which uses participatory sensing to maintain a database of animals killed at road crossings.  Alas, this apparently very clean data set is spread across 479 separate screens.  All it needs is a “download data” button to drop the entire file onto your hard disk, and they could benefit from many eager statisticians and wildlife fans examining their data.  (I contacted them and suggested this, and they do seem interested in sharing the data in its entirety. But it is taking some time.)

I hope Los Angeles, and all governments, make their public data public. But I hope they have the budget and the motivation to take some time to think about making it accessible and meaningful, too.

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.