Tag Archives: Statistical Concepts

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

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

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

How wonderful and I wish, I wish …

As I type this, I have one fifty minute class left to teach, and my time with my statistics class will be over. As with anything, each semester is varied. Some semesters I cover more information than other semesters. I liken this semester to driving through the city and hitting all green lights! As such, I believe my students were able to master additional information based on what is probably mostly good fortune.

So, here is my list of things I’m so thrilled I covered:

(1) Effect size statistics, like eta squared: Sure effect size statistics are not used that much, and lets face it, they are super easy to calculate, but my biggest reason for wanting to teach effect size statistics is it helps students to understand what a t-test or F-test can tell us (is there a difference) and what it can’t tell (how big is the effect). In fact, by spending about 20 minutes on the teaching of effect size statistics, students were better able to understand why the “p-value” for an observed t or F score provides us with no information. All we need to know is, did we pass the threshold.

(2) We find the critical value BEFORE calculating the observed value: This discussion helps focus student on the logic of statistical hypothesis testing. Specifically, statistical hypothesis testing works because we assume that the null hypothesis is true, that there is no effect of the independent variable on the dependent variable. With this assumption, we are able to generate the sampling distribution that provides us with information on the standard error. Now, if our sample mean is too extreme, we reject our initial hypothesis, the null, and accept the alternative hypothesis, that is the means are different. By finding the critical value prior to calculating the statistic, it helps focus students on that “line in the sand” to say … my observations are too extreme for me to stay with my current hypothesis. Students are far less likely to fall victim to equating p-value with the strength of the effect of the independent variable, or to conclude … the data is trending because I have a p-value of .07 or some other funky thing far too many people do with null hypothesis testing. By spending a bit more time on the steps involved in hypothesis testing, I think students are less likely to fall victim to the common misconceptions surrounding Statistical Null Hypothesis Testing.

(3) Though not a specific concept, I am pleased that for almost every concept I taught this semester I used new examples. Sure, I’m still a sage in training, no grey hair and all, but I was beginning to find myself using the same examples. As this is the third semester my supplement instructor, Amy, is taking notes in class, I felt I owed it to her, at least, to “keep it fresh.” I also found thinking about this blog helped spur my mind toward different examples. In doing so, I found some worked even better than my “old stand by” examples, but the great things was, when the new example flopped, I just quickly switched to the example I knew helped students.

Now for my Wish List of things I always wished I could have covered, but didn’t.

(1) Though I do get to cover the concepts of the F-test. I teach a three credit class, and only have time to cover the one-factor between subject ANOVA. If only I could cover a two-factor between subject ANOVA and a one-factor within subject ANOVA, I would feel my students would really understand the F-test (and as such, be less incline to misuse or over use it).

(2) Yet, I feel if I could cover non-parametrics, students would better understand the role of the assumptions in parametric tests, and issues like Power and random error could be even better understood. Plus they would get the benefit of learning about a really important class of statistics. Sadly, another semester has passed without me being able to cover this topic with the depth I think it deserves.

(3) I fear I don’t emphasize the weakness of statistics, and that they are only as good as the quality of the theories being tested in the design. They are also only as good as the quality of the sample and the quality of the measure. At least the latter two concepts get covered in classes that will follow the statistics class. But so few people speak of the topic of equifinity, that the same outcome can have multiple explanations. Again, though I touch on this, the idea of developing the alternative rival hypotheses that could explain the same empirical evidence is one I simply don’t have time to cover to the extent I would like. If you have a weak theory or haven’t taken into account the alternative rival hypotheses when designing your study, cool statistics will not improve the quality of your findings.

(4) Though I tell students the hypothesis drive everything, from the selection of the measure and research design, to the specific statistic one would select, and though there are example problems in the textbook (Integrating Your Knowledge) that students have to complete, I really wish we could spend more time on this.

Maybe next semester, I can find a way to reach my wish list … maybe!

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Filed under ANOVA Analysis of Variance, Core Concepts, Curriculum, effect size, Hypothesis Testing, Hypothesis Testing, non-parametric, Sampling Distribution, Statistical Hypothesis Testing, Statistical Tests, t test