Subject: Re: Eight Features of an Ideal Intro Stat Course (Response to comments by Dennis Roberts) To: EdStat-L (July 23, 1998) sci.stat.edu (July 28, 1998) From: Donald B. Macnaughton <donmac@matstat.com>

In a July 17 post I recommend that teachers emphasize the concept of a relationship between variables and I recommend a de-emphasis of less important topics such as univariate distributions ... Referring to this text, Dennis Roberts writes (on July 20) > ( snip ) > i disagree .... i find it hard to think that you will be able > to cogently discuss relationships between variables without > first having studied such mundane issues as central tendency, > or variability, or position measures (i.e., z scores for exam- > ple) ... on single variables ... > > these form the foundation of higher level things. Dennis' comments reflect traditional thinking about the introduc- tory statistics course. This thinking holds that students must understand univariate distributions before they can understand the main ("higher level") ideas of statistics. While I fully agree that the concept of a univariate distribution is necessary to understand the main *mathematical* ideas of statistics, I do not believe the concept is necessary to understand the main ideas of statistics *as they are used in empirical research*. As I discuss in a paper (1998), I believe the concept of a rela- tionship between variables is a candidate for the most important concept in both empirical research and statistics. Thus I be- lieve it is important to emphasize this concept in an introduc- tory statistics course. It is clear that students can understand the concept of a rela- tionship between variables without understanding the concept of a univariate distribution. We can see this by noting that students learn and understand many examples of relationships between vari- ables in high school *before* they know much about univariate distributions. For example, students in high school physics courses learn about the relationship between acceleration (a) and force (f) with the model equation f = ma where m is the mass of the body being accelerated. Students seem quite capable of understanding this relationship without knowl- edge of univariate distributions. Similarly, we can easily talk with students about the relationship in people between the vari- ables EDUCATION and INCOME without reference to the concept of a univariate distribution. Similarly, although they are generally not specifically characterized as such, many high school mathe- matics problems are problems of relationships between variables -- these problems make no reference to univariate distributions. Thus we can discuss relationships between variables in the intro- ductory statistics course with almost no reference to the concept of a univariate distribution. (I demonstrate one approach in a paper for students [1996].) In section 9.1 of the 1998 paper I note that univariate distribu- tions - play only a *peripheral conceptual role* in real empirical re- search - are *not necessary* for initial study and understanding of the concept of a relationship between variables - are *boring* for students because students see no practical use of univariate distributions - are *less accurate* for making predictions than predictions based on relationship between variables. I believe we alienate students by burdening them with concepts of univariate distributions that are boring and have no obvious practical use. (I discuss two examples of univariate distribu- tions a teacher submitted that are clearly not boring in appendix G of the 1998 paper. I suggest that both examples are better viewed as examples of relationships between variables.) Studying univariate distributions certainly *was* necessary when students had to do all the mathematical computations of statis- tics themselves because many of the underlying mathematical ideas rely on the concept of a univariate distribution. But nowadays a computer can do all the standard computations, so it is no longer necessary to understand the underlying mathematical ideas right from the start. Finally, as I say in the paper, an understanding of univariate distributions is *mandatory* for full understanding of the field of statistics. Therefore, I am not suggesting that the topic of univariate distributions be removed from the curriculum -- I am only suggesting that it be moved later, *after* students have a good understanding of the more interesting and more important concept of a relationships between variables. Because this approach is more closely tied to the use of statis- tics in actual empirical research, I suggest that the approach is more likely to give students a lasting appreciation of the vital role of our field. ------------------------------------------------------- Donald B. Macnaughton MatStat Research Consulting Inc donmac@matstat.com Toronto, Canada ------------------------------------------------------- REFERENCES Macnaughton, D. B. 1996. The entity-property-relationship ap- proach to statistics: An introduction for students. Avail- able at http://www.matstat.com/teach/ Macnaughton, D. B. 1998. Eight features of an ideal introductory statistics course. Available at http://www.matstat.com/teach/

Home page for Donald Macnaughton's papers about introductory statistics