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Dec 28

#78 Two fun (and brief) items

Thanks for reading this, my final blog post for the infamous year 2020.  In contrast to this seemingly unending year*, I will keep this post very brief.  I will conclude this decidedly not-fun year by presenting two fun items that I recently encountered.

* Even though today is December 28th, it feels more like March 303rd.  (I can’t take credit for this joke, but I regret that I cannot remember where I first saw a version of it.)

The first fun item is a quote from American educator Alice Wellington Rollins.  Even though I just learned of this quote within the past two weeks, it’s actually 122 years old, having appeared in the Journal of Education in 1898 (volume 47, issue 22, page 339, available here).  Stacey Hancock brought this to my attention, as she cites this quote in an article about teaching statistics that she has written for the March 2021 issue of the Notices of the American Mathematical Society.  I think this quote offers a valuable perspective on my “ask good questions” refrain:

The test of a good teacher is not how many questions he can ask his pupils that they will answer readily, but how many questions he inspires them to ask him which he finds it hard to answer.

Alice Wellington Rollins, Journal of Education, 1898

The second fun item is a very recent addition to the brilliant* collection of xkcd comics. 

* I like to think that I do not use the adjective brilliant casually.  If you have not seen these comics, consider taking a look.  Some particularly clever ones that address statistical ideas include: Convincing (here), Correlation (here), and Significant (here).

When I look back on this horrible but memorable year, I hope to think of this image and advice from a recent xkcd comic (available here):

Many thanks and best wishes to all who have read this blog in 2019 and 2020.  I hope that you have found something that helps you to ask good questions of your students.  My aspiration remains to write essays about teaching introductory statistics that are practical, thought-provoking, and fun*.

* And, perhaps just this once, brief.

Dec 21

1 Comment

#77 Discussing data ethics

This guest post has been contributed by Soma Roy.  You can contact her at soroy@calpoly.edu.

Soma Roy is a colleague of mine in the Statistics Department at Cal Poly – San Luis Obispo. Soma is an excellent teacher and has been so recognized with Cal Poly’s Distinguished Teaching Award.  She also served as editor of the Journal of Statistics Education.  I recently learned about some of Soma’s ideas for generating student discussions in online statistics courses, and I am delighted that she agreed to write this guest blog post about one such idea, which introduced students to data ethics.

The GAISE (Guidelines for Assessment and Instruction in Statistics Education) College Report (available here) recommends the use of real data with a context and purpose in statistics classes*. One of the ways I achieve this throughout the course, regardless of what statistics topic we are studying at the time, is by always using data (either in raw or summarized form) from research studies published in peer-reviewed journals.

* Just because the recommendation comes in the college report doesn’t mean that the advice couldn’t apply to K-12 classes.

For example, a study I use to motivate the comparison of means between two groups was conducted by Gendreau et al. and published in the Journal of Abnormal Psychology in 1972 (here). In this study, 20 inmates at a Canadian prison were randomly assigned either to be in solitary confinement or to remain non-confined (that is, have contact with others around them) for seven days. Researchers measured each inmate’s EEG alpha frequency on several days* in order to investigate the effect that sensory deprivation can have on one’s EEG alpha frequency**.

* The article provides data for the 20 inmates at three different time periods, but my students only analyze the data from the final (seventh) day of the experiment.

** Alpha waves are brain waves, the predominance of which is believed to indicate that the individual is in a relaxed but aware state. High frequency of alpha waves is considered to be better than low frequency of alpha waves (Wikipedia).

Without fail, one of the first things that students do when they read about this study is ask: How could they just put someone in solitary confinement? That becomes a jumping off point for our discussion on data ethics. This discussion covers the ethics of study design, data collection, data analyses, and publication of findings.

When the COVID-19 pandemic turned my in-person class into an online class, I decided to turn our brief, in-class discussion into an asynchronous, week-long discussion in our learning management system, Canvas. Borrowing from Allan’s style, the questions that I posted appear in italics, below, accompanied by short blurbs on what I was hoping to address with each of the questions, as well as some student responses and comments.

You have read about an experiment conducted on inmates of a Canadian prison, where 20 inmates were randomly split into two groups. One group of 10 inmates was placed in solitary confinement, and the other group was allowed to remain non-confined. 

Are you as struck as I was the first time I read about this experiment, by how unethical and cruel this experiment was, in that people were randomly assigned to be placed in solitary confinement!? 

Unfortunately, there have many, many experiments in the past that violated human rights. That realization has brought about the requirement for all research projects involving human subjects to be reviewed before any data can be collected. 

This discussion is about the ethics to be considered when one decides to carry out a study with human subjects (specifically an experiment that involves manipulating treatment conditions), collect data, or analyze data and publish results from any study. The first few questions below focus on historical studies, while the next few questions in this discussion look into what the process is to propose and carry out human subjects studies, and also what are ethical practices when it comes to data analysis and publication of study results. 

I hope that, going forward, this discussion helps you think critically about any studies that you may be involved in as a researcher, and keep in mind that (to borrow from the great American poet Maya Angelou) when we “know better, (we should) do better.” 

For this discussion, you need to make two (2) posts:

Part 1: First, you will post a response to one of the questions (1) – (10) below. Be sure to copy and paste the question that you are responding to. 

1. Google “Tuskegee Syphilis Study” – describe the study (year(s), methods, participants, objective, etc.). Why is it considered unethical? Cite your source(s). (e.g., Wikipedia link)

2. Google “US apologizes to Guatemalans, 1940s” – describe the study or studies conducted in the 1940s (year(s), methods, participants, objective, etc.). Why are the studies considered unethical? Cite your source(s). (e.g., Wikipedia link)

3. Google “Human Radiation Experiments in the US, 1940s” – describe the study or studies conducted in the 1940s and even later (year(s), methods, participants, objective, etc.). Why are the studies considered unethical? Cite your source(s). (e.g., Wikipedia link) 

4. Google “Project Bluebird, Project Artichoke” – describe the study or studies (year(s), methods, participants, objective, etc.). Why are the studies considered unethical? Cite your source(s). (e.g., Wikipedia link) 

5. Google “The Monster Study” – describe the study (year(s), methods, participants, objective, etc.). Why is the study considered unethical? Cite your source(s). (e.g., Wikipedia link) 

6. Google “Brown eyes, Blue eyes experiment, Jane Elliot” – describe the study (year(s), methods, participants, objective, etc.). What was the objective of the study? Why do some people consider the study to be unethical? Cite your source(s). (e.g., Wikipedia link) 

This first part of my discussion assignment requires students to read up about a particular historical study, identify some of the key elements such as what was the objective of the study, on whom was the study conducted, when it was conducted, how it was conducted, and why the study is considered unethical. Students are required to cite their sources.

All six of these studies have a plethora of information available from multiple reliable sources on the internet. My hope is that as students read about these studies, they will recognize the shortcomings in the study design – where the researchers went wrong in how they treated their subjects or how they recruited their subjects, or just who their subjects were. I also hope that students will recognize the need for an institutional review board (IRB), the need for informed consent, and the need to protect vulnerable populations.

The Tuskegee study, understandably the most infamous of the lot, draws the most outrage from students. Students find the experiment “crazy and insane,” “a great example of raging biases and racism,” and “lacking in decency.” Students are appalled that little to no information was shared with the participants, that a study that was supposed to last only 6 months lasted 40 years, and that even after penicillin was established to be a standard treatment for syphilis, it wasn’t administered to the participants. Students are saddened by the fact that the researchers abused the knowledge that the participants were impoverished by offering incentives such as free meals and free treatment for other ailments in return for their participation in the study.

Students have similar reactions to the other studies as well. Some of their common responses include:

  • Subjects in any study should be told whether any negative outcomes were to be expected.
  • Participation should be voluntary; leaving the study should be easy and come at no cost to the participant.
  • Children should not be experimented on, at least not without permission from a parent or guardian who can make decisions in the child’s best interest.
  • People who are vulnerable, such as children, prisoners, pregnant women, and people from racial and ethnic minorities, should be protected, and not taken advantage of.

The “Brown eyes, blue eyes” experiment draws some interesting responses*. Some of my students write that while the experiment was well meaning, and was trying to teach students about discrimination on the basis of color, conducting an experiment on impressionable children, especially without the consent of their parents, was unethical. 

* For anyone unfamiliar with this experiment: On the day after the assassination of Dr. Martin Luther King, Jr., teacher Jane Elliot repeatedly told students in her all-white third-grade class that brown-eyed people were better than blue-eyed people.  On the next day, she switched to saying that blue-eyed people were better than brown-eyed people. She observed her students’ behaviors toward each other on both days.

Through their answers to the questions above, sometimes directly and sometimes indirectly, students arrive at recognizing the need for an institutional review board, the need for informed consent, and the need to protect vulnerable populations. This leads to the next set of questions in my discussion assignment:    

7. When you conduct research on human subjects, your research protocol needs to be reviewed by an institutional review board, and you need to obtain informed consent from your subjects. Explain what the bold terms mean, when did these procedures start getting enforced in the U.S., and why you need the review or informed consent. Cite your source(s). (e.g., Wikipedia link) 

8. When you conduct research on human subjects, certain sections of the population are referred to as “vulnerable populations” or “protected groups.”  What are these groups, and why do they need to be protected? Give one or two historical examples that were unethically performed on vulnerable populations. Cite your sources (e.g. link from National Institutes of Health) 

For the question about the IRB and informed consent, students are required to describe the terms, why they are needed, and report what year these procedures were put in place in the U.S. Again they are required to provide references. Students discover that concerns about many of the studies referred to in (1) – (6), specifically the Tuskegee Syphilis study and the human radiation experiments, led to the creation of IRBs.

In the wrap-up of this discussion, we revisit the study about the Canadian prisoners, in which some inmates were assigned to solitary confinement to study the effect of sensory deprivation on brain function. The research article mentions that the subjects volunteered to participate, and were told that there were no incentives (e.g. monetary or parole recommendation), that their status in prison would remain unchanged, except for a note in their file mentioning their cooperation. Students discuss whether this is enough of a protection, or enough of an informed consent.

The next two questions touch upon what happens to data after they have been collected. Should the person analyzing the data get to pick and choose which data to include in the analysis, based on what creates a more sensational story? Should studies be published only if they show statistically significant findings? Who stands to lose from violations of the ethics of data analysis? Who stands to lose from publication bias*?

* For class examples, I intentionally use studies that showed statistically significant results as well as studies that didn’t. I also have a separate week-long discussion topic in which students read article abstracts from various peer-reviewed journals, where they see both statistically significant and not significant study results; that discussion touches on one more aspect of data ethics – who funded the study, and why that is important to disclose and to know?

9. What is publication bias? When does it arise? Who stands to benefit from it? More importantly, who stands to lose from it? Give an example of any study or studies where publication bias was present. Cite your source(s). (e.g., Wikipedia link)

10. What is data manipulation (including “selective reporting” and “data fabrication”)? How is it done? Who stands to benefit from it? More importantly, who stands to lose from it? Give an example of any study or studies where the researchers were accused of wrongful data manipulation. Cite your source(s). (e.g., Wikipedia link)

To earn full credit for the discussion assignment, students must also reply to another student’s post.  This is just my way of encouraging them to read and reflect on what other students posted. Students can only reply after they have first submitted their own initial post:

Part 2: Second, respond/reply to a post by another student – adding more detail/insight to their post. (Note: You will need to first post an answer to part 1 before you can see anybody else’s posts.)

I grade these student discussions very generously. Students almost always get full credit as long as they follow the instructions and make reasonable posts, cite their sources, and don’t just copy-and-paste a Wikipedia article.

On my end-of-quarter optional survey about the class this term, students noted this ethics discussion as the discussion they liked the most. Some students said that this discussion topic was the topic from the course that made the biggest impression on them – describing it as “thought-provoking,” “interesting,” and “eye opening.”

In the past I have used this discussion assignment only in introductory classes. But now that I have the online discussion set up in Canvas, I will also use it in my upper-level courses on design of experiments.

Even though I have used these questions as a discussion topic, I can also see using them as a homework assignment, mini-project, or student presentation. For now, I will stick with the online discussion format because my students said they liked reading what other students wrote. While the pandemic keeps us in remote online classrooms, this format provides one more way for students to connect with their peers, as well as learn about some ethical issues associated with collecting and analyzing data.

This guest post has been contributed by Soma Roy.  You can contact her at soroy@calpoly.edu.

Dec 14

3 Comments

#76 Strolling into serendipity

This post is going to meander.  I’ll get to the point right away, but then I’m going to take a long detour before I return to the point.

The point of this post is to let you know about the 2021 U.S. Conference on Teaching Statistics (USCOTS), encourage you to attend and participate in this conference, and urge you to help with spreading the word.  The conference theme is Expanding Opportunities.  It will be held virtually on June 28 – July 1, with pre-conference workshops beginning on June 24.  The conference sessions will be thought-provoking, directly relevant to teaching statistics, and fun!  See the conference website here for more information.

Now I’m going to indulge in a stroll down memory lane before I return to the point.  If you’re in a hurry or don’t feel like accompanying me on this journey, I understand completely and encourage to skip ahead past the next several sections.  You can search for “And then 2020 happened” to find the spot where I conclude my reminiscences and return to discussing the 2021 USCOTS.

I like conferences.  Even though I’m an introvert who feels much more comfortable in a small town than in a big city, I have greatly enjoyed and learned a lot from attending conferences across the country and around the world.  The best part has been meeting, learning from, and befriending people with similar professional goals and interests.

My first conference was the Joint Mathematics Meetings (JMM) held in San Francisco in 1991.  I had never been to San Francisco, and I had only been to California when I was nine years old.  I was in my second year of teaching at Dickinson College in Pennsylvania.  I roomed with my good friend from graduate school Tom Short, who was on the academic job market.  We walked around the city, taking in the sights and remarking that San Francisco is an even hillier city to walk than Pittsburgh, where we had attended Carnegie Mellon University together.  A conference highlight for me was attending a presentation by Tom Moore, whom I had never met.  Tom had written an article with Rosemary Roberts, titled “Statistics at Liberal Arts Colleges” (here), which had inspired me as I finished graduate school and before I started teaching at Dickinson.  I also gave a presentation at the conference, titled “Using HyperCard to teach statistics.”  I remember being extremely nervous before my presentation.  As I refresh my memory by checking the conference program here, I am surprised at not remembering that my presentation was apparently given at 7:05 on a Saturday morning!*

Another memorable conference from early in my career was the ASA’s 1992 Winter Conference, held in Louisville, Kentucky.  I was amazed and delighted to find an entire conference devoted to the theme of Teaching Statistics.  By this time Tom Short was teaching at Villanova University, so he and I drove to Louisville together.  I gave my first conference talk about an early version of Workshop Statistics.  Two presentations had a huge impact on my teaching and stand out in my mind to this day.  Bob Wardrop described his highly innovative introductory course that reimagined the sequencing of topics by using simulation-based inference to present topics of statistical inference from the beginning of the course.   Joan Garfield gave the plenary address, invited and introduced by David Moore, on educational research findings about how students learn statistics.  Joan later wrote an article based on this presentation titled “How Students Learn Statistics” (available here), the general principles of which hold up very well more than 25 years later.

Returning to San Francisco for the Joint Statistical Meetings (JSM) in 1993, I met and chatted with Jeff Witmer, convener of the “isolated statisticians” group and editor of Stats magazine, to which I had recently submitted an article.  I also interacted with Robin Lock for the first time at that conference; he and I have presented in the same sessions of conferences, sometimes with a joint presentation, many times over the years.  The 1993 JSM was also the occasion in which I met a graduate student from Cornell University who was studying both statistics and education, and who had a perfect name for a statistics teacher*.

* Of course, I had no clue at the time that Beth Chance and I would write articles and textbooks together, give conference presentations and conduct workshops together, coordinate the grading of AP Statistics exams, become colleagues in the same department, and eat ice cream together more times than I could count.

In 1994 I traveled outside of North America for the first time, to attend the International Conference on Teaching Statistics (ICOTS) in Marrakech.  Despite tremendously troublesome travel travails*, I greatly enjoyed the exotic locale and the eye-opening experience of meeting and hearing from statistics teachers and education researchers from around the world.  I gave another presentation about Workshop Statistics.  Some specific memories include George Cobb’s talk about workshops for mathematicians who teach statistics and Dick Scheaffer’s presentation about Activity-Based Statistics.

* Try saying (or typing) that ten times fast.

Oh dear, I really could keep writing a full paragraph (or more) about every conference that I’ve attended over the past thirty years.  But I need to remember that I’m writing a blog post, not a memoir.  I hope I’ve made my point that I benefitted greatly from attending and presenting at conferences as I embarked on my career as a teacher of statistics.  Especially for a small-town introvert, these conferences greatly expanded my horizons.  I’m incredibly fortunate and grateful that some of the people I met at these conferences, whose work I admired and had a big impact on me, went on to become lifelong friends and valued collaborators.

I hasten to add that I have continued to enjoy and benefit from conferences throughout my career.  Since 1995, the only JSM that I have missed was in 2016 due to illness.  It took me a few months to recover from my surgery that year, and I considered myself fully recovered when I was able to attend the AMATYC conference in Denver in November of 2016.  I remember feeling very happy to be well enough to walk around a conference hotel and be able to participate in a conference again.  I also recall feeling somewhat silly to consider conference attendance as an important marker of my recovery.

As I continue this stroll down memory lane, I now turn toward USCOTS.  I have attended all eight USCOTS conferences*, which have been held in odd-numbered years since 2005, and I have come to regard USCOTS as my favorite conference. 

* I realize that the word “conference” here is redundant with the C in USCOTS, but I fear that “USCOTSes” looks and sounds ridiculous.

The organizers of the first USCOTS, Dennis Pearl and Deb Rumsey and Jack Miller, did a terrific job of establishing a very welcoming and supportive environment.  Conference sessions were designed to engage participants, and the conference provided provide many opportunities for interaction among attendees, outside of sessions as well as during them.

The inaugural USCOTS in 2005 was the most influential conference my career.  The lineup of plenary speakers was star-studded: Dick Scheaffer and Ann Watkins, Roxy Peck, Cliff Konold, Robin Lock and Roger Woodard, and George Cobb (see the program here).  Roxy’s talk was memorable not only for its enticing title (How did teaching introductory statistics get to be so complicated?) but also for the insights about teaching statistics that Roxy garnered from a famous video of a selective attention test (here).  George’s banquet presentation at this conference, which also featured a provocative title* (Introductory statistics: A saber tooth curriculum?), has achieved legendary status for inspiring a generation of statistics teachers to pursue simulation-based inference**. 

* Of course, I admire that both of these titles ask good questions.

** See here for a journal article that George wrote, based on this presentation, in which he subtly revised to title to ask: A Ptolemaic curriculum?

The next three USCOTS were also very engaging and informative.  I will mention just one highlight from each:

  • In 2007 Dick De Veaux gave a terrific banquet presentation, titled “Math is music; statistics is literature,” that was almost the equal of George’s for its cleverness and thought-provoking-ness. 
  • Chris Wild inspired us in 2009, and provided a glimpse of even more impressive things to come, with his demonstration of dynamic software that introduces young students to statistics, and excited them about the topic, through data visualization. 
  • Rob Gould challenged us in 2011 to think about how best to prepare students to be “citizen statisticians,” arguing that they come to our classes having already experienced immersive experiences with data.

My point here is that USCOTS was designed from the outset as a very engaging and interactive conference, ideal for statistics teachers looking to meet like-minded peers and exchange ideas for improving their teaching.

Following the 2011 USCOTS, I was quite surprised and honored when Deb and Dennis asked me to take on the role of USCOTS program chair.  I have now served in this capacity for four conferences, from 2013 – 2019.  I have tried to maintain the distinctive features that make USCOTS so valuable and worthwhile.  My primary addition to the program has been a series of five-minute talks that comprise opening and closing sessions.  I have been thrilled that so many top-notch statistics educators have accepted my invitations to give these presentations.

If you’ve never given a five-minute presentation, let me assure you that it can be very challenging and nerve-wracking.  Condensing all that you want to say into five minutes forces you to focus on a single message and also to organize your thoughts to communicate that message in the brief time allotted.  

For my first year as program chair in 2013, I went so far as to insist on the “Ignite” format that requires each presenter use 20 slides that automatically advance every 15 seconds.  I have loosened this restriction in subsequent years.  The opening five-minute talks have launched the conferences with energy and fun.  They have generating thought-provoking discussions among attendees.  The closing talks have recapped the conference experience and inspired participants to depart with enthusiasm for implementing some of what they’ve learned with their own students*. 

* You can find slides and recordings for these five-minute talks, along with other conference presentations and materials, by going here, clicking on “years” on the right side, going to the year of interest, then clicking on “program,” and finally clicking on the session link within the program page.  As you peruse the lists of presenters for an opening or closing session, you may notice that I like to arrange the order of presentation alphabetically by first name.

My point in this section is that since I have been entrusted with the keys to the USCOTS program, I have tried to maintain USCOTS as welcoming, engaging, and valuable conference.  Serving as program chair for the past four incarnations of USCOTS has provided me with considerable helpings of both professional pride and enjoyment.

After the 2019 USCOTS, I decided to pass the program chair baton to someone of the next generation who would infuse the conference with new ideas and vitality.

I asked Kelly McConville to take on this role.  Even though Kelly is early in her career as a statistics professor*, she already has considerable experience as a successful program chair.  She has served as program chair for ASA’s Statistics and Data Science Education section at JSM, for the Electronic Undergraduate Statistics Research Conference, and for the Symposium on Data Science and Statistics (see here).  Kelly has attended several USCOTS conferences and gave one of the five-minute talks at the closing session for USCOTS in 2017.

* Congratulations are in order, because Kelly was informed just last week that she has earned tenure in her faculty position at Reed College.

Kelly replied by asking if I would consider co-chairing USCOTS with her in 2021, and I happily agreed.

And then 2020 happened*.

* There’s obviously no need for me to describe how horrible 2020 has been in myriad ways.  But I can’t resist noting that a vaccine has been developed, tested, and approved in less than one year.  This is an incredible achievement, one in which the field of statistics has played an important role. The vaccine is being administered for the first time in the U.S. (outside of trials) on the day that this post appears.

The pandemic required Dennis (who continues to serve as director of CAUSE, the organization that puts on USCOTS) and Kelly and me to decide whether to plan for an in-person, virtual, or hybrid USCOTS.  Spurred on by Camille Fairbourne, Michigan State University had agreed to host USCOTS in late June of 2021.  In August of 2020, we asked statistics teachers to answer survey questions about planning for USCOTS.  Among 372 responses, 50.3% recommended a virtual conference and only 11.8% recommended in-person, with the remaining 37.9% preferring a hybrid.  Mindful of drastic cuts to many schools’ budgets as well as continuing uncertainty about public health, we made the difficult decision to forego an in-person conference and hold USCOTS virtually.

We quickly selected a conference theme: Expanding Opportunities.  Aspects of this timely theme that conference sessions will explore include:

  • How can we increase participation and achievement in the study of statistics by students from under-represented groups?
    • What classroom practices can help with this goal?
    • How can curriculum design increase such participation and achievement?
    • What role can extra-curricular programs play?
    • How can remote learning and new technologies help?
    • How can we collaborate more effectively with colleagues and students in other disciplines to achieve this goal?
  • How can we support and encourage students and colleagues who are beginning, or contemplating, careers in statistics education?
  • Can the emerging discipline of data science help to democratize opportunities for students from under-represented groups?
  • What does educational research reveal about the effectiveness of efforts to expand opportunities?

The conference will feature thought-provoking plenary sessions, interactive breakout sessions, informative posters-and-beyond sessions, and opening and closing sessions with inspiring and lively five-minute presentations. Other highlights include birds-of-a-feather discussions, a speed mentoring session, an awards ceremony*, extensive pre-conference workshops, and sponsor technology demonstrations.

* The USCOTS Lifetime Achievement Award has been renamed the George Cobb Lifetime Achievement Award in Statistics Education, in honor of George, the first recipient of the USCOTS Award, who passed away on May 6, 2020.

One of the plenary sessions will be a panel discussion about fostering diversity in our discipline.  Kelly and I plan to ask the panelists questions such as:

  • What are some barriers to pursuing study of statistics, and succeeding in study of statistics, for students from under-represented groups?
  • What are some strategies for eliminating barriers and expanding opportunities for students from under-represented groups in the following areas?
    • Recruitment
    • Curriculum
    • Individual courses
    • Program/department culture
    • Other?
  • How (if at all) does the emerging discipline of data science offer potential solutions for expanding opportunities and fostering diversity?
  • What are some strategies for encouraging and supporting people from diverse backgrounds to pursue and succeed in careers as statistics teachers and statistics education researchers?

We are determined to reproduce the welcoming, engaging, interactive, and fun aspects of USCOTS as much as possible in a virtual setting.  We also hope that the virtual format will encourage participation from statistics teachers who might not have invested as much time as it takes to travel to an in-person conference.

One of my favorite words is serendipity.  I like the definition from Google’s dictionary almost as much as the word itself: the occurrence or development of events by chance in a happy or beneficial way.  The benefits that I gained from attending conferences early in my career resulted from chance encounters more than from planned meetings.  Serendipity is one of the best aspects of any conference*. 

* Heck, serendipity is one of the best things in life.  Sadly, serendipity has also been one of the biggest casualties of the pandemic.

By definition, serendipity is impossible to plan in advance.  Serendipity is especially challenging to arrange with a virtual conference that people can attend without leaving their homes.  But we’re going to do everything we can to infuse the 2021 USCOTS with opportunities for serendipity, and we welcome suggestions about how to create such opportunities.  I hope that all USCOTS participants in 2021 make new acquaintances and renew friendships with colleagues who are united by a common desire to teach statistics effectively to the next generation of citizens and scholars.

How can you help?  First, mark the dates June 28 – July 1, 2021 on your calendar and plan to attend USCOTS.  Second, consider submitting a proposal to conduct a workshop, lead a breakout session, present a virtual poster, or facilitate a birds-of-a-feather discussion.  Third, please let others know about USCOTS and encourage them to participate.  Spreading the word broadly can expand opportunities to participate in USCOTS, where we can share ideas about expanding opportunities for others to engage in our profession. 

Once again, more information is available at the conference website here.

Dec 7

1 Comment

#75 More final exam questions

I gave my first asynchronous online final exam this past week.  I find writing online exams to be much more time-consuming and stressful than writing good, old-fashioned in-person exams*.  I’ve identified five aspects of writing online exams that take considerable time and effort:

  1. Writing with good multiple-choice questions and answer options;
  2. Creating multiple versions of most questions in an effort to reduce cheating;
  3. Thinking of questions where googling does not provide much of an advantage;
  4. Entering all of the questions into the format required by the learning management system;
  5. Double- and triple- and quadruple-checking everything**

* I’m finding it hard to remember the days of photocopying exams and handing them to students on paper.

** I became obsessed with this last one, because typos and other errors are so much more problematic now than they used to be.  I may not remember photocopying, but I fondly recall the good old days when a student would point out a mistake and I simply had to say: Excuse me, class, please look on the board to see a correction for part c) of question #3.  I really stressed and lost sleep about this.  And somehow I still managed to mess up!  I’m embarrassed to report that despite my efforts, students found an error on both the Wednesday and Friday versions of my final exams.  I was especially grateful to the student who started the exam at 7am on Wednesday and let me know about the error as soon as she finished, so I was able to make the correction before most students began the exam.

Now I’m in the throes of grading.  You may know that when it comes to grading, I enjoy procrastination*.  But the timeline is tight because grades are due on Tuesday.  Without further preamble, I will now discuss some of the multiple-choice questions that I asked my students on this exam.  I will provide answers at the end.

* See post #66, First step of grading exams, here.

1. Suppose that you want to investigate whether Cal Poly students tend to watch more movies than Cal Poly faculty.  Would you collect data to investigate this question using random sampling, random assignment, or both? [Options: A) Random sampling only; B) Random assignment only; C) Both random sampling and random assignment]

I like this question because I try to emphasize the distinction between random sampling and random assignment.  This is a meant to be an easy question.  Students should realize that it’s not reasonable to randomly assign people to the roles of faculty or student.

2. Suppose that the nine current members of the U.S. Supreme Court are still the same nine members of the Supreme Court two years from now. Indicate how the following values will change from now until then (two years from now). a) Mean of ages; b) Standard deviation of ages; c) Median of ages; d) Inter-quartile range of ages [Options: A) Increase; B) Decrease; C) Remain the same]

This is also intended as an easy question.  The mean and median will increase by two years.  But as measures of variability, the standard deviation and inter-quartile range will not change when everyone becomes two years older.

3. a) Which would be larger – the mean weight of 10 randomly selected people, or the mean weight of 1000 randomly selected cats (ordinary domestic housecats)?  b) Which would be larger – the standard deviation of the weights of 1000 randomly selected people, or the standard deviation of the weights of 10 randomly selected cats (ordinary domestic housecats)? [Options: A) Cats; B) People]

I have written about this question before*.  Part (b) is very challenging for students.  Unfortunately, many students come to believe that a larger sample size produces a smaller standard deviation, without realizing that this result applies to the variability of a sample statistic, such as a sample mean, not to variability in the original measurements, such as weights of people and cats.

* See post #16, Questions about cats, here.

4. Suppose that a fair coin is flipped 10 times.  Which is more likely – that the flips result in 5 heads and 5 tails, or that the flips result in 6 of one outcome and 4 of the other? [Options: A) 5 of each; B) 6-4 split; C) These are equally likely.]

Students could answer this by calculating the relevant binomial probabilities.  But they might also realize the key point that a 6-4 split can happen in two different ways.  Even though a particular 6-4 split is less likely than a 5-5 result, a 6-4 split in either direction is more likely than a 5-5 result.  These probabilities turn out to be 0.246 for obtaining 5 heads and 5 tails, 0.410 for achieving a 6-4 split.

5. Suppose that Chiara has a 10% chance of making an error when she conducts a test. If she conducts 10 independent tests, which of the following is closest to the probability that she makes at least one error? [Options: A) 0.10; B) 0.25; C) 0.50; D) 0.65; E) 0.99]

I intend for students to perform the calculation: Pr(at least one error) = 1 – Pr(no errors) = 1 – (0.9)10 ≈ 0.651.  I chose options far enough apart that some students might use their intuition to determine the correct answer, if they realize that making at least one error would be more likely than not without being extremely likely.

6. The United States has about 330 million residents.  Suppose that you want to estimate the proportion of Americans who wore socks yesterday to within a margin-of-error of 3.5 percentage points with 95% confidence.  Which of the following is closest to the number of people that you would need to randomly sample? [Options: A) 30; B) 1000; C) 30,000; D) 1,000,000]

I also discussed this question, which I ask on every final exam, in post #21 here.  Influenced by the 330 million number, many students mistakenly believe that a sample size of 1 million, or at least 30 thousand, people is required.

7. Suppose that Carlos, Dwayne, and Elsa select separate and independent random samples of 50 Cal Poly students each.  They ask each student in the sample how much sleep they got last night, in minutes.  Then they calculate the average amount of sleep for the students in their sample.  How likely is it that Carlos, Dwayne, and Elsa obtain the same value for their sample average? [Options: A) This is very likely. B) There’s about a 50% chance of this. C) There’s a 1 in 3 chance of this. D) This is very unlikely.]

This question addresses the concept of sampling variability, which is even more fundamental than that of sampling distribution.  This is meant to be an easy question that students can answer based on their intuition or by remembering what we discovered when simulating the drawing of random samples with an applet such as this one (here) that randomly samples words from the Gettysburg Address.

8. Suppose that Yasmin and Jade want to select a random sample of San Luis Obispo county residents and ask each person whether or not they spent Thanksgiving in their own home.  Suppose also that Yasmin wants to estimate the population proportion to within ± 0.04 with 95% confidence, and Jade wants to estimate the population proportion to within ± 0.02 with 95% confidence.  Who would need to use a larger sample size?  (You need not calculate any sample sizes to answer this question.)  [Options: A) Jade; B) Yasmin; C) They would both need the same sample size.]

Here is another question for which students could spend a good bit of time performing calculations, but they’re better served by thinking this through.  They need only realize that obtaining a smaller margin-of-error requires a larger sample size.

9. Suppose that you conduct a hypothesis test about a population mean and calculate the t-test statistic to equal 0.68.  Which of the following is the best interpretation of this value?  [Options: A) If the null hypothesis were true, the probability would be 0.68 of obtaining a sample mean as far as observed from the hypothesized value of the population mean. B) The probability is 0.68 that the null hypothesis is true. C) The sample mean is 0.68 standard errors greater than the hypothesized value of the population mean. D) The sample mean is equal to 0.68 times the standard error.]

Students’ ability to interpret the value of a test statistic is worth assessing.  You no doubt realize that I purposefully chose a value less than 1 for the t-test statistic here, partly to see whether students might confuse the interpretation of a test statistic and a p-value.

10. Suppose that you take a random sample of 100 books from a large library.  For each of the following questions, indicate the appropriate inference procedure. a) How old, on average, is a book from this library? b) Are 75% of books in this library less than 20 years old? c) What percentage of books in this library contain fewer than 300 pages? d) How many pages, on average, are contained in a book from this library? e) What percentage of books in this library have been borrowed at least once in the past 10 years? [Options: A) z-interval for proportion; B) z-test for proportion; C) t-interval for mean; D) t-test for mean]

This series of questions is very similar to the questions that I discussed in last week’s post (A sneaky quiz, here), so my students should have expected questions of this type.  I think these questions are a bit harder than the ones I presented in class and on that quiz, though.  Parts (b) and (c) involve a categorical variable, but students might be tempted to think of a numerical variable because the context also refers to a book’s age and number of pages.

I’m selfishly glad that the time I invested into writing multiple-choice questions for my final exam has now served double-duty by providing me with the basis for this blog post.  But I really do need to get back to grading the open-ended questions …

P.S. The correct answers are: 1. A; 2. A, C, A, C; 3. B, B; 4. B; 5. D; 6. B; 7. D; 8. A; 9. C; 10. C, B, A, C, A.