Tag Archives: Teaching Statistics

Great Resource for the Teaching of Applied Statistics

Hello All,

The Society for the Teaching of Psychology has an office dedicated to great, peer-reviewed resources for teaching called the Office of Teaching Resources in Psychology.

Two such (free) resources for those of us teaching applied statistics include the free on-line book, Teaching Statistics and Research Methods: Tips from TOPS. http://teachpsych.org/ebooks/stats2012/index.php

Another such resource, is Statistical Literacy in Psychology: Resources, Activities, and Assessment Methodshttp://teachpsych.org/Resources/Documents/otrp/resources/statistics/STP_Statistical%20Literacy_Psychology%20Major%20Learning%20Goals_4-2014.pdf

The web site housing these two resources is filled with great ideas, all of which have been peer-reviewed. You can find teaching resources including example syllabi as well as article on how to maximize your students’ learning. Even if you are teaching applied statistics in an area outside of psychology, I encourage you to make use of this value set of tools. ( http://teachpsych.org/ )

Happy Teaching!



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Filed under Applied Statistics, Curriculum, Engaging students, Pedagogy, Preparing to Teach, Professional Development

Tackling the tough concepts

Hello All.

I apologize for our absence over the last several weeks. Though it was my intention to work on “tackling the tough concepts in statistics.” I’ve, instead, been tackling the tough concepts of life and death, as my father died following a battle with cancer.  However, though I miss my Dad tremendously, it is time to continue with this blog.

Last year, I  posed a question to the sages … What are the critical concepts in applied statistics. Their response was an overwhelming … it’s not a matter of individual concepts but the overall application of statistics that is necessary for true understanding.

Of course, I wholeheartedly support this assertion, and yet, as I look at how people come across this blog, they almost always do so by searching for specific statistical concepts. I also have to argue that we have to make sure students understand certain concepts before they can grasp the larger application of statistics. Taken together, I think it is a worthwhile endeavor for a few blogs to be focussing on how to teach the critical concepts in statistics.

A search of the literature failed to yield a complete list of concepts. However, when looking at the website CAUSEweb.org, the Consortium for the Advancement of Undergraduate Statistics Education, they have resources on statistical concepts divided into eight sections, and I added one. Those concepts are Data, Central Tendency, Correlation and Covariation, Distribution and Graphs, Variability, Sampling, Sampling Distribution, and Inferences. However, I would also add to this list, Error, as though it overlaps with several of the prior concepts, it is a critical concept that requires direct attention.

Over the next several weeks, I will be addressing each of these concepts and provide information on how to best teach it.  Of course, if you feel I’m missing a concept, I encourage you to let us know.

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Filed under Core Concepts

Prezi … a different tool


Math is not linear. This Prezi file reviews a concept we all know is true not only about Mathematics, but also about statistics. I know, as I spend the first three weeks of a regular semester (or the first two class periods or so of the summer semester) providing students with foundational knowledge to help them to better conceptualize statistics. While this is happening students seem to beg for a step by step linear sequence, but statistics simply doesn’t work like that, as concepts and practices are often interrelated, and hardly linear.  Of course, we all know that if students are missing a fundamental concept, whether it is order of operations or sampling error, their ability to understand statistical hypothesis testing is minimized, so there is some temporal requisites.

As I was looking at this Prezi demonstration, thinking about how math and statistics are not linear, I wondered … is this why I do not care for using PowerPoint in the classroom? As I thought, I realized it is precisely because PowerPoint doesn’t permit me to have the flexibility to circle around easily or in a visual way that the chalk and chalk board does. I also find that I tend not to provide enough background knowledge, or even, for that matter, go off on a student driven, yet appropriate tangent, those “Teachable Moments” where students seem to learn so much more in a 10 minutes than they often learn in an entire class period simply because they want to know the answer to a question. Yes, I have yet to find the means to build a PowerPoint slide that provides me with that kind of flexibility in teaching.

However, then I saw a student presentation using the software Prezi. (Prezi.com) This presentation software is, as you can see from the sample link above, more flexible and enables a less linear presentation and a more structural one.  Though I will admit to not using it in teaching statistics … it certainly seems worth mentioning in the blog for those of you looking toward updating your technological presentations in your applied statistics classes. As statistics is not linear nor is Prezi, it very way may help students get a better “big picture” / “fine detailed” conceptual understanding of statistics.

I encourage anyone who has used Prezi in teaching applied statistics to share your experiences with us.

Today, we end our month of discussing technology in the teaching of applied statistics. I do encourage all of you to get “unplugged” at least for a little bit during this summer.

For the months of June and July we will be talking about how to teach the difficult topics in applied statistics. If you have a topic you would like for us to address, please let us know.

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Filed under Engaging students, Pedagogy, Uncategorized

Evaluating the implementation of Mathematica Demonstrations … next semester, deliberate practice

Before the spring semester started, I promised to try Mathematica demonstrations with my applied statistics class with the intention of helping them better understand the concepts of statistics. You can access that blog at this link: https://statisticalsage.wordpress.com/wp-admin/post.php?post=256&action=edit.

Well, I did what I had intended, but not in the manner in which I had hoped. You see, we ended up with my students missing almost a week and half of the semester due to school being closed. So, I had my students “explore” the Mathematica Demonstrations that I outlined in my prior blog. I felt pretty good, as I thought my students wouldn’t fall too far behind in their course work, and their exploration could be even more beneficial than being in class … right? Wrong …

Students logged on and looked at the demonstration. Most reported (cut this in half?) working with each demonstration for less then 6 minutes (ouch). They all said favorable things about Mathematica, but I saw no carry over to questions in class or on exams.

I suppose as I look at the practice of using technology in teaching applied statistics, simply providing students with the tools does not assure cognitive development — and yes, I knew that, and was planning on integrating it during class time, but snow days got in the way. In a few days, I have asked a guest blogger, Livie Carducci, who is experienced in using Mathematic demonstrations in teaching statistics to talk about some techniques to maximize student engagement.

Not surprising, what I noticed this semester is that some students will naturally explore, but others will put forth the minumum effort. I became motivated to figure out a way to assure students will be intellectually engaged in thi assignment. I thought of the new pedagogical practice of Deliberate Practice. Thus, for this summer, I plan on working on developing assignments around each of the Mathematica Demonstrations that increases the likelihood of students engaging in deliberate practice through the application of Deliberate Practice.

So, let me review this for you … first of all, as a pedagogical tool, Deliberate Practice is in its infancy. It is based off of the cognitive developmental research of Ericcson on expertise. http://projects.ict.usc.edu/itw/gel/EricssonDeliberatePracticePR93.pdf Briefly, in the early 1990’s Ericcson and others noticed that people who truly became experts in an area, often devoted a tremendous amount of time and effort over the course of at least a decade before they hit a level of expertise. Ericcson hypothesized that we were born to excel, but through deliberate practice could become experts in areas of music, thinking, physical activity and the like.

Not all practice is deliberate. For practice to be considered deliberate it seems that it requires the following.

(1) We must first not only establish our desired outcome, but establish a means of reaching that outcome, thus we must specify the process.

So, I have a goal: I want to master the pedagogical practice of increasing my students participate in Deliberate Practice when interacting with the Mathematca Demonstrations, but in order to do that I must (a) study about deliberate practice, which will mean reading about it and talking to others who have tried it (b) specify the components of deliberate practice that I need to have my students accomplish (c) look at each Mathematica Demonstration I have selected for my students, and come up with an activity that will increase students’ deliberate practice (d) as I am going to have to assess my students implementation of Deliberate Practice, I should design a quick survey. (e) Immediately, my mind ponders about whether or not I should set this up as a research study … and I say, if I will, I’ll make that a new goal. (f) After looking at the students’ responses to the survey in the fall semester, see about making revisions to improve these assignments.

(2) The established goal must take us to a higher level of attainment.

Let’s face it, we can’t just stay right were we all … deliberate practice is all about hitting a higher level of expertise.  In my example, I’m clearly going outside of my prior experiences, but not too far to make this an unattainable goal.

(3) Now, as you implement your plan, you have to be formally and informally evaluating your progress.

Often this will require the use of an expert to provide you with feedback. Of course, you also have to have a keen sense of your own metacognition and progress. Though I haven’t read this in the literature, yet, I would suspect that individuals with weakened self esteems might have a tough time implementing Deliberate Practice, as you must have clear (and honest) insight into what you are doing, why you are doing it, and how you can do it better. We simply have to be cautious of our own bias to see everything as great. In hypothesis testing, this is called validation testing … where you look for signs that you are right! Instead, people who make strides in increasing their expertise through Deliberate Practice should make use of a practice more akin to “falsification hypothesis testing” where you look for how  you are wrong, and what you must do to get better.

My plan for preparing to implement deliberate practice as a way of maximizing the use of the Mathematica demonstrations will involve a self designed survey, specifically geared to look for how my practice is weak and what I can do to make it better. Of course, I’m also putting my efforts out in this blog, where I invite other statistics professors to comment.

(4) Then, you must … practice, practice, practice … but notice, that practice, alone isn’t enough … you must have a detailed and well thought out plan that takes you to a higher level, and  be critically evaluated by both yourself and an expert.

I would love to say … provide students with the Mathematica Demonstrations and the students will naturally enter into Deliberate Practice, but my experience this semester has been that most will not. So, I will establish an assignment that puts students on the right path. As I work on that over this summer, I will update my prior Mathematica Blog with a new one including the activities that go along with the demonstrations.

As always, I welcome your expertise on this topic! I also encourge you to look at Livie’s post on how she uses Mathematica to get students to master concepts of statistics.


Filed under Engaging students, Homework/ Assignments, Maximizing Cognitive Development, Pedagogy

Teaching Large Classes

This has been a rough couple of weeks at the state and state related universities throughout Pennsylvania. The Governor has proposed a new budget that will cut 54% of the state’s funding to the state universities, like the one where I teach. The state related universities, like Penn State, Pitt, Temple, and Lincoln are receiving cuts in the neighborhood of 50% assuming the budget goes through as proposed, which, at this point seems more likely than unlikely.

As of right now, much of the changes that will be taking place will require increased class sizes, the elimination of all new hires and of adjuncts (even for sabbatical or maternity leave replacement). The good news (as least for my students) is that the applied statistics class I teach is not increasing in size, but many other classes are, including a class that I teach in development.

As such, I have been spending my time seeking pedagogical techniques that help maximize student learning in larger classes. As I have two sections of 40 students every semester in statistics, I have realized that I implement techniques that help engage students without overwhelming me. Here are two of my favorites, plus some good references.

(1) I do not correct homework, and yet it is clear that students who complete their homework are more likely to get an A in the class, and students who do not complete ALL of their homework are more likely to not pass the class. I do provide students with answers, and for longer problems, I include the intermediate answers. This really seems to help motivate students to complete the homework, as it helps them to identify what they are doing right.

(2) Every pupil response — by having students respond with their hands or speaking an answer out loud, I have a very quick feeling of what students are understanding. It also helps keep students’ focused.

(3) As a Penn State grad, I can tell you, PSU is home of the super huge classes. It shouldn’t be shocking to find a great reference from PSU on how to teach large classes:  http://www.schreyerinstitute.psu.edu/Tools/Large/

(4) As I find additional resources I will add them here: http://serc.carleton.edu/NAGTWorkshops/earlycareer/teaching/LargeClasses.html     or      http://teaching.uncc.edu/resources/best-practice-articles/large-classes/handbook-large-classes

(5) A link to a list of books:   http://www.facultyfocus.com/articles/teaching-professor-blog/a-lifeline-for-those-teaching-large-classes/

Teach well!

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Filed under Engaging students, Pedagogy

More than calculations? Guiding students to thinking with statistics

I am currently on spring break, and yet … with 4 snow days that have canceled classes this semester, I am keenly thinking about what I need to do to get to the end of the semester. As my university doesn’t make up missed snow days … I  have been thinking about what is the most important “thing” that students should leave an applied statistics class with? My answer is … the foundational knowledge to be able to make use of, interpret, and learn more about applying statistics to answer questions. I am expecting that they go beyond regurgitation of information or following of strict steps on how to answer questions using statistics. In short, I want them to be able to think with statistics as one of their tools!

As these thoughts swim through my mind, I continued reading a book, “What the Best College Teacher’s Do!” by Ken Bains. I got to a section of the book on how the best college teachers help students to develop a deeper level of knowing.  To summarize Bains (2004), there are 4 different levels of knowing student vacillate through in a non-linear manner, some times being at the two different levels at the same time. Using terms coined by the great teachers Bain’s researched, here are the four developmental levels of knowing:

The Banking Level where teachers deposit information into the students’ brains for later withdraw.

Does it Feel Right Level where students start to believe that all knowledge is subjective and as such merely a matter of opinion, thus the best knowledge can pass the “feels right” test.

Procedural Level is the point where students can apply their discipline specific rubrics, schemata, scripts in order to “know” or communicate information. Of course, this is discipline specific, with little or no carry over to other disciplines.

Commitment Knowers are students who reach the “highest” level of knowing. Such students have mastered a level of metacognition, that is awareness of their own thinking and how knowledge came to be in their mind. These students are creative and critical thinkers, and have developed a sense of independent thinking. Thus, students can take this knowledge and synthesize it with knowledge gathered from other disciplines and over time to truly result in more advanced cognitive processes. If I were to name this, I would call is The Thinker Level!

Commitment Knowers can be further classified into two components: the Separate Knowers who are emotionally detached from what knowledge they are seeking, and seem to follow a “falsificaction” process of hypothesis testing  and the Connected Knowers who are really don’t ever want to shoot anyone’s idea down, and instead seek to validate or find support for a hypothesis that has been put forward.

My philosophy of science and the application of statistics for the purpose of answering questions and testing hypotheses is fairly clear in that it is best to approach these situations as the Separate Knower. Thus, it’s not surprising that this is where I am guiding my students.

As I review the assignments students are expected to complete, I can see that I am taking students through these levels.   I am truly trying to move students up (within a single semester) from the “Banking” level of knowing, where students work to memorize terms and symbols, to the level of being a “separate – commitment knowing,”  where students know how to apply statistical concepts when answering questions or testing hypotheses.

In looking at the assignments I use (e.g., Assignments and Exercises for Students) the assignments for each chapter start out at the Banking Level, then move to the Procedural Level. It seems by looking at my assignments I don’t care if students “feel it’s right” this may require some reflection on my part. However, for students to hit the Commitment Level, they have to not only complete the assignments within the chapter of the textbook I use (Kiess and Green, 2010, Statistical Concepts for the Behavioral Science, 4/e), but them most certainly have to complete the Integrating Your Knowledge assignments that occur every two to three chapters in Kiess and Green’s textbook. It is then that students are lead to that highest level.

Yet, as I think of the final exam, I see something a bit different. For the final exam, students are given four scenarios, and they have to select the appropriate statistics (all problems require the calculation of several statistics), calculate it, make a decision regarding the results, and when appropriate draw a conclusion.  Of all the exams I give, it is the most calculation rich exam. Yet, I tell students, it is not the step by step procedures involved in the calculations that are most important, but understanding the concepts of what statistics can tell us, what they can’t, when we can use them, when we shouldn’t, and yes, how do they tell us what they tell us. It is the latter reason why I have students complete hand calculations using definitional formulas, but the rest of it is, as the prior sages have stated, relates to the conceptual and contextual understanding of the application of statistics. It is safe to say, students can’t merely regurgitate out how to complete this exam. Though, it seems possible for students who have only reached the level of “Procedural Knower”  to be able to follow the procedures, select the right statistic, follow the steps to calculations and interpretation … and not yet hit that level of “separate-commitment knowing.”

As such, through reading Ken Bair’s text, and thinking about what I really want students to be able to do, and what they are demonstrating … I want them to be Commitment Knowers, and yet, it is possible for them to be successful in my class while being only at the Procedural Level. So now … I’m four classes down due to snow, AND am in the middle of a quandary … am I taking the students’ far enough?

I welcome comments!

Bains, K. (2004). What the Best College Teachers Do. Cambridge, MA: Harvard Press.


Filed under Core Concepts

Exposing students to Diversity while teaching the t-test

There are a lot of ways we can approach diversity in the statistics classroom, as even the term “diversity” can be operationally defined in so many ways. One method is to use research on diversity as a basis of an example when teaching statistics in context.

Often the complexity of the statistics used in a published journal article are beyond what would be taught in an introductory course in applied statistics, however, what I often do is take the research hypothesis and design and simplify it a bit. Yes, this is an example of scaffolding. So, I structure the study to fit the concept I am teaching (e.g., making a multivariate research student univariate, or making a two-way factorial a one-way). Keeping the general structure of the study intact, I often shorten the task so it will take less than 10 minutes to run through the mock study, collect the data, and then provide students with critical conceptual background information. This still gives me enough time (in a 50 minute class) to have students work through the problem, while I model it, and go from question to answer through the use of hypothesis testing.

In this example, the concept I will be teaching is the independent t-test, a form of null hypothesis testing. The study I am using is Apfelbaum, Pauker, and Sommer’s (2010) study of 4th and 5th grade students which examined the effects of color-blind thinking and value-diversity thinking on bias.

In short, color-blind thinking is simply ignoring race as a variable worth attending to, as in doing so, issues of bias will be minimized. (For my social scientist readers … this is a very etic way of approaching the potential of racial bias.)

Value-diversity thinking (emic) actively recognizes differences within each racial and ethnic group.

As we are comparing two different conditions, this study can easily be adapted to an independent t-test.

So, during class, we could quickly, and randomly provide students with one of two sheets of paper.

Borrowing phrased directly from the published study, the students in the color-blind condition would see phrases like:

  • We need to focus on how we are similar to our neighbors rather than how we are different.
  • We want to show everyone that race is not important and that we’re all the same.

Meanwhile, the students in the value diversity condition would see phrases like:

  • We need to recognize how we are different from our neighbors and appreciate those differences.
  • We want to show everyone that race is important because our racial differences make each of us special.

In the actual study, Apfelbaum, Pauker, and Sommer’s (2010) looked at both implied and explicit racial biases. For the in-class activity, as this is being conducted with college students instead of 4th and 5th graders, we could just use the implied bias. Read to students the following scenario (slightly modified from the article): “Most of Brady’s classmates got invitations to his birthday party, but Terry was one of the kids who did not. Brady decided not to invite him because he knew that Terry would not be able to buy him any of the presents on his ‘wish list.’”

Then ask students to write down an answer on a scale from 1 – 10, 1 being completely inappropriate and 10 being completely appropriate. Typically, my class size is too large to collect data from all of the students, so I would randomly select 5 students from each condition, and write their responses on the chalk board. Now, we can model how to answer the question: is encouraging people to ignore race a way to increase bias or decrease it, compared to encouraging people to factor race into evaluating situations.

Of course, one of the problems in using “real data” in a study with so few subjects is that you will never be certain if the test statistic will support the same conclusion as the research article. There are two ways to deal with this problem, acknowledge the potential for low power right from the start, or have the students complete the activity, but use data that you selected to model how to answer this question with the use of an independent t-test. The latter might be best for individual’s new to teaching, as you can come to class with your calculations prepared.

In closing, it is easy to bring diversity into a classroom, even if you are that “scoop of vanilla ice cream.” One of the best ways is to make use of published research studies on cultural or racial diversity as a way of modeling critical concepts in statistics.

Apfelbaum, E. P., Pauker, K., & Sommers, S. R. (2010) In blind pursuit of racial equality? Psychological Science, 21, 1587-1592. http://pss.sagepub.com/content/21/11/1587.full

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Filed under Engaging students, Hypothesis Testing, Statistical Hypothesis Testing, t test