Subject: Re: How Should We *Motivate* Students in Intro Stat? To: edstat-l@jse.stat.ncsu.edu sci.stat.edu Usenet newsgroup From: Donald Macnaughton <donmac@matstat.com> (formerly donmac@hookup.net) Date: Monday December 16, 1996 22:27 EDT Cc: Rex Boggs <rex@rocknet.net.au> Graham Wood <g.wood@cqu.edu.au>

On Monday December 2, 1996 Rex Boggs, in apparent reference to my post of December 1 (1996a), wrote > [Graham Wood] at Central Queensland University is developing a > quite radical course and text for introductory statistics > based on teaching students to use statistics as a tool to solve > problems. Clearly, a good introductory statistics course should show stu- dents how to "solve problems". In fact, I believe a focus on solving practical problems with statistics is essential for a successful introductory course. However, in view of the title of this thread, Rex seems to be suggesting that we can *motivate* students to study statistics by telling them they are going to learn how to "solve problems". I suggest that "solving problems" is not a good motivating concept because it is much too vague. That is, just about *any* disci- pline can be characterized as "solving problems" of one form or another. Instead of trying to motivate students with the concept of "solv- ing problems", I believe we should motivate them by focusing on the essential *role that statistics plays* in solving problems. This role can be characterized in terms of the study of variables and relationships between variables as a means to accurate pre- diction and control (Macnaughton 1996b). To illustrate the effectiveness of this approach, let me use it to discuss the four examples of problems that Rex gives in his post. The first example is > ( snip ) > how a TV rental company used statistics to increase the per- > centage of the bills that were paid on time; This is clearly a study of a relationship between variables as a means to controlling the values of a variable. Specifically, response variable: percentage of bills paid on time predictor variable(s): although not identified in the example, the predictor variables are presumably something like: 1. variables reflecting the methods used to encourage customers to pay their bills 2. variables reflecting characteristics of the customers that a company might use as a basis for accepting or re- jecting customers for rentals 3. variables reflecting other methods of managing customers. statistical questions: 1. Is there a relationship between the response variable and the predictor variables in the population of custom- ers? 2. If there is a relationship, how can we best control (i.e., maximize) the value of the response variable (per- centage of bills paid on time) for members of the population on the basis of the relationship? Thus Rex's first example can be easily characterized as a study of a relationship between variables. His second example is > how statistics was used to help determine how genetic material > from the parents combines in an offspring; This example is difficult to characterize because Rex does not identify either the response variable(s) or the predictor vari- ables(s) that were used in the research. However, it seems cer- tain that the example is concerned either with one or more vari- ables or (more likely) with one or more relationships between variables, because Rex notes that statistics was used. Statis- tics *invariably* concerns itself with variables or relationships between variables. (Rex and other readers with access to Graham Wood's as-yet unpub- lished text will have the best grasp of the details of Rex's four examples. I hope these readers will let this newsgroup/mail-list know if they feel that my characterization of the examples in terms of relationships between variables is untenable. See the appendix for a technical note.) Thus Rex's second example can be characterized as a study of var- iables or relationships between variables as a means to predict- ing or controlling the values of variables. His third example is > and using statistics to help determine the assessed needs of > old folks in rest homes and geriatric hospitals. Again, Rex does not identify the actual variables, but it seems likely that this is another study of relationships between vari- ables. In one possible form of the example the response variable might be some measure of "quality of life" and the predictor var- iables might be variables that reflect - demographic properties of the patients - attitudes of the patients - properties of the facilities and care of the institutions. The goal of this research would be to discover a relationship be- tween the response variable and the predictor variables in order to learn how to control (i.e., maximize) the value of the re- sponse variable (quality of life). Thus Rex's third example can be characterized as a study of a re- lationship between variables. His final example is how > ( snip ) > one student set up a factorial experiment to determine the best > combination of cam shaft, exhaust manifold and carburetttor for > 'hotting up' his Cortina. This is another example of a relationship between variables. The response variable is some measure of the performance of the car, and the predictor variables are three nominal-level variables that reflect respectively the different cam shafts, exhaust mani- folds, and carburetors that were used in the experiment. Thus each of Rex's four examples can be characterized as studying variables or relationships between variables as a means to pre- dicting or controlling the values of variables. Thus note how the concepts of variables, relationships, prediction, and control *unify* all the examples. This unification can be applied to most (all?) empirical research projects and most statistical methods (Macnaughton 1996b). The unification makes the field of statistics substantially easier for students to understand. Let us return to the question of how we should *motivate* stu- dents to study statistics. Since - the concept of prediction is pivotal in empirical research - the concept of prediction is pivotal in statistics - the concept of prediction is simpler than the concept of con- trol - students are keenly interested in knowing how to make accurate predictions therefore, I believe we can best motivate introductory students by telling them they will learn how to make accurate predictions. LINK The ideas in this post are part of a broader discussion of an ap- proach to the introductory statistics course available at http://www.matstat.com/teach/ -------------------------------------------------------- Donald B. Macnaughton MatStat Research Consulting Inc. donmac@matstat.com Toronto, Canada -------------------------------------------------------- APPENDIX Some readers may wonder whether Rex's genetic material problem is purely a problem in probabilities and thus not a problem with variables. I suggest that it is useful to view probabilities as *being* variables (i.e., formal representations of a particular property of "events"). From this point of view, even if the problem is purely a problem in probabilities, it is still a study of one or more variables or relationships between variables. REFERENCES Macnaughton, D. B. (1996a) "How Should We *Motivate* Students in Intro Stat?" Posted to the sci.stat.edu Usenet newsgroup on December 1, 1996. Available at http://www.matstat.com/teach/ Macnaughton, D. B. (1996b), "The Introductory Statistics Course: A New Approach." Available at http://www.matstat.com/teach/

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