Category Archives: Randomness

First Day of Class — starting off right

How do students comes to us on the first day of class? Yes, I can just about hear you mumbling …

(1) They wonder why they even have to take this class … after all they are a [non-quantitative] major. Why does [psychology, sociology, business, education, etc] need statistics?

(2) They may have had really bad math experiences in the past leading to (a) math anxiety (b) poor math attitudes including a low self efficacy and/or (c) weak math skills.

(3) They have heard lots and lots of stories as to how hard or useless or manipulative statistics can be. We have all heard the quote … and so have they … “There are lies, … , and statistics!”

But the first thing I want to let you know is … instructors of applied statistics may be over estimating the negative thinking of their students. Mills (2004);col1 found that, in general, students attitudes towards statistics tended to be more positive then negative. Now, granted, that could simply be the case at Mill’s school. Yet, it is worth challenging … what do our students really think? How is this impacting their academic success? Is there anything we can do to get them from less adaptive to more adaptive ways of approaching this class?

If you would like to specifically see what attitudes your students have, the Mills (2004) article includes an abstract with a validated and reliable measure of  Survey of Attitudes Toward Statistics (SATS). 

Though I do find that there are some positive attitudes regarding statistics in the students I see, the majority of students are still coming in with negative attitudes and ways of thinking about the class. Almost importantly, my first day of class activities do as much to help the students with positive attitudes as it does for the negative ones.  

In short … I try to start of the first day of my semester differently than any other class students may have experienced.

I often start by asking students to describe what a typical first day of class look like. That is right, I don’t even introduce myself or the class. I walk in and say, “So … what does the first day of class typically look like.” After a few blank stares, and me having to repeat the question. The students start talking.  There are many types of descriptions … for which I then define variability. We often talk about what is the most typical? Students respond by raising their hands (of course, I have to instruct this) High means strongly agree, low means mildly agree or disagree. Moderately high hands mean that you moderately agree. Sitting on one’s hands means you completely disagree (thus everyone has to do something, everyone has to actively participate. The student with his hands on the desk is ask to participate.)

Yes, as we discuss “typical,” I will often tell students my name, hand out the syllabus and tell them to put it away, and briefly describe things like … there will be four exams, as they state that professors tell them about how the class will be graded. So, the students end up getting the “typical” information from me in an atypical manner.

 Then, I ask students’ their personal preferences of the activities they listed, again  having them to respond with their hands.  This activity really helps to focus on the concept of individual differences, which I define. As individual differences is a precursor to sampling error, which will follow weeks from the first day of class, students are already beginning to conceptualize this class.

I then define statistics as a tool to help us to answer questions by making sense of variability, taking into account individual differences of the subjects we are working with.

Yes, I start the class by forcing students to respond verbally and with voting using their hands … From the first minutes of class, students realize that they have to be engaged in this class … there are no other options. From the first minutes of class, they are beginning to understand two of the most critical concepts … variability and individual differences!

So, why start off the class so differently than most? Because, in the event students are not excited about taking an Applied Statistics class, may be down right afraid of this class, and/or think the class is unnecessary, right from the start, they start to recognize this class is unlike any others.   By starting off so differently, I can challenge their preconceived notions regarding classes in general, and statistics in particular.

At this point, I tend to talk to them about what they had heard or how do they feel about statistics, thus making them face their preconceived notions right away. Again, we conduct another hand poll … and I define for them the concepts of data and sample.

This opening exercise involves kinesthetic action, thus, forces student engagement. Moreover, it takes the abstract concept of variability, individual differences, data, and sampling and puts it into a context of something all of your students can understand, the first day of class. It provides students for context in which statistics functions.

I follow this first day of activities up with Assignments and Exercises 1.1, 1.2, 1.3, & 1.4 all requiring students to think about their behavior and attitude for class. Instructors who are using Kiess and Green (2010) as their statistics textbook can access those assignments at

Will one day be enough? Of course not … but it’s always the first step!

As always, I would love to hear from others regarding their first day activities!

Green, B. A., & Sandry, J. D. (2010) Assignments and Exercises for Students for Statistical Concepts for the Behavioral Sciences, 4/E . Boston: Pearson.

Mills, J. D. (2004). Students’ attitudes toward statistics: implications for the future. College Student Journal. 29 Jan, 2011.



Filed under Engaging students, Introduction, Pedagogy, Randomness, Variability

Core Statistical Concepts

I have been spending the week thinking about what I consider to be the “core concepts” that need to be covered in an applied statistics class, be it in psychology, health, business, or education. However, before I post my personal thoughts, I felt it necessary to see what other applied statisticians had to say. In my search, I found . This work was conducted by John McKenzie (2004), Conveying the Core Concepts, is from the Proceedings of the ASA Section on Statistical Education, pages 2755-2757.

In reading what  McKenzie, and several other professors of applied statistics identified as the core concepts in statistics, I must say … I concur. Listed below are the core concepts in applied statistics … the information that, in my opinion, simply has to be covered regardless of illness, snow days, or anything else that could interrupt a professors’ teaching schedule.

Variability: Students cannot understand the purpose of statistics unless they get the concept of variability. Within this, we can further talk about variability due to chance and variability due to effect. Including in the discussion of variability should be the difference between systematic and random variability. I would have to say that not a class period goes by without me spending at least a little time on helping students to focus on issues of variability (especially variability due to the individual differences of the subjects who just happen to be in our sample). 

Randomness: Though I would see randomness and variability as being part of the same large concept, McKenzie’s work identified the concept of randomness as not only separate from variability but also critical for students to master.

Sampling Distribution: Along with Hypothesis Testing, the teaching of sampling distribution is considered to be one of the most complicated to teach.  I would concur, which is why I spend an entire class period just on a single activity with M&M’s to demonstrate the concept of sampling distribution. (Please see a prior blog entry for details on this tactile activity).

Hypothesis Testing: The sages and I spent the month of October and much of November discussing whether Hypothesis Testing is critical and if so, how to best tackle the teaching of this complex topic. Not surprising, McKenzie identified the teaching of hypothesis testing as being one of the two most difficult concepts to teach in applied statistics (the other being sampling distribution). Though there may be several published articles on hypothesis testing no longer being a critical concept to teach, the individuals who were surveyed for McKenzie’s work, certainly consider it to be a critical concepts.

Data Collection Methods: Though I have said to my students more times that I can count, “the quality of our statistics is limited by the quality of our sample,” I must admit to being a bit surprised that this was considered critical by others, especially since when I look at many undergraduate statistics textbooks, data collection methods are barely mentioned. Kiess and Green’s (2010) Statistical Concept for the Behavioral Sciences, 4/e, certainly tackles the issue of data collection methods.

Association vs. Causality: This core concept makes me smile, as often when I meet someone for the first time, and they ask me what I do … my response is often met with one of two comments … “Oh, I hated statistics” or “Correlation does not mean causation.” It’s kind of like me recalling how to greet a person in German, a class that I had for three years, and yet recall so little. We, as applied statisticians, certainly engrave this concept into the minds of our students, but I’m sure most of you are like me, hoping student get more than a “pat phrase” out of our classes.

 Significance (Statistical vs. Practical): This is a critical concept in applied statistics and one that is probably not mentioned in theoretical statistics classes. Sure, we delineate a mark in which we have to say … these results are too extreme for us to attribute them to “chance” … but just because we found a statistically significant difference, doesn’t mean it’s a difference that truly matters. In applied statistics, it’s not enough to understand how statistical significance works, but to be able to interpret the results to determine practical difference. I must admit to not covering this core concept to the same extent I cover the others.

As I think of other “critical concepts” they tend to be a bit more specific and fall under the larger concepts listed above (e.g., understanding what a standard deviation can tell us, clearly falls under the concept of variability. I invite all of you, to comment on what concepts, if any, are missing from this list.


Filed under Association vs. Causality, Core Concepts, Curriculum, Hypothesis Testing, Hypothesis Testing, Methods of Data Collection, Randomness, Sampling Distribution, Significance (Statistical/ Practical), Variability