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 http://www.statlit.org/pdf/2004McKenzieASA.pdf . 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.

Pingback: So, you don’t want to teach stats … | Statistical Sage Blog

Coincidence and confounding are others form of variability and may be more common in the everyday media than confidence intervals or statistical significance.

Hi Milo,

Two great points … I will address them both when we get to a section on Variability.

Bonnie

Stat student here.

I think the concept of errors is really difficult to grasp. I guess this falls under variability. However, I think the different kinds of errors, along with its degrees of freedom, are one of the most difficult things i’ve encountered

Hi Stats Student ….

Thank you for the insight. I agree the idea of variability, and then that of different types of error are challenging. Since you are a student, look to the right side of the blog and go to Broken Pencil … it’s a blog specifically for students to learn from. Drew Ziner is a great guy and will help clear up many of those issues.

I, too, will make it a point to do a series of blogs on variability, with a focus on types of error.

Bonnie