The Introductory Statistics Course: The Entity-Property-Relationship Approach Donald B. Macnaughton* introduction to the simplicity, beauty, and truth of the This paper proposes five concepts for discussion at the scientific method. beginning of an introductory statistics course: (1) entities, Teachers must therefore reshape the introductory (2) properties of entities (which are roughly equivalent to course. Many teachers have already contributed to the variables), (3) a major goal of empirical research: to pre- reshaping, as noted below. This paper proposes further dict and control the values of variables, (4) relationships changes. between variables as a key to prediction and control, and I focus on the introductory statistics course for stu- (5) statistical techniques for studying relationships be- dents who are not majoring in statistics or mathematics, tween variables as a means to accurate prediction and whom I call “non-statistics-majors”. Most students who control. After students have learned the five concepts take an introductory statistics course are members of this they learn standard statistical topics in terms of the con- group. The introductory course for non-statistics-majors cepts. It is recommended that students learn the material is important because it is the main seedbed of public through numerous practical examples. It is argued that the opinion about the field of statistics. approach gives students a lasting appreciation of the vital Section 2 recommends two goals for the introductory role of the field of statistics in empirical research. statistics course. Section 3 proposes a sequence of five KEY WORDS: Statistical education; Prediction; Control; concepts for discussion at the beginning of an introductory Role of statistics in empirical research. course. Section 4 argues that the five concepts provide a broad and deep foundation on which to build the field of statistics. Section 5 reports on tests of the approach in 1. INTRODUCTION three courses. Section 6 discusses considerations for Two former presidents of the American Statistical As- teachers wishing to use the approach, and section 7 gives a sociation have stated that “students frequently view statis- summary. tics as the worst course taken in college” (Hogg 1991, Iman 1994). A third former president has stated that the 2. COURSE GOALS field of statistics is in a “crisis” and the subject has be- 2.1 The Value of Emphasizing Goals come “irrelevant to much of scientific enquiry” (Box Emphasizing the goals of any undertaking helps us to 1995). Many statisticians reluctantly agree with these define and focus on what is most important. Otherwise, remarks. we may take a scattershot approach, which is generally In contrast, many statisticians agree that the field of less efficient. Thus, following Hogg (1990, 1992), I rec- statistics is a fundamental tool of the scientific method ommend that all introductory statistics courses have care- which, in turn, plays a key role in modern society. Thus fully stated goals. Ask yourself—what are the goals of the rather than being a worst course and possibly irrelevant, introductory statistics course most familiar to you? the introductory statistics course ought to be a friendly I have observed goal-setting exercises in which the goals were given much attention for a brief period and then forgotten—a waste of a valuable resource. Since a *Donald B. Macnaughton is president of MatStat Research Consulting teacher’s chosen goals are (by the teacher’s own defini- Inc, 246 Cortleigh Blvd., Toronto Ontario, Canada M5N 1P7. E-mail: [email protected] Portions of this material were presented at the Joint tion) what is most important, I recommend that teachers Statistical Meetings in San Francisco, August 11, 1993, at the Joint Statis- regularly revisit their course goals to ask (a) if the goals tical Meetings in Orlando, August 15, 1995, and at the Joint Statistical are still valid and (b) if the day-to-day operations are ef- Meetings in Dallas, August 12, 1998. The author thanks Professor John fectively serving the goals. Flowers of the School of Physical and Health Education, University of Toronto and Professors Donald F. Burrill and Alexander Even of The Ontario Institute for Studies in Education for testing the approach in their 2.2 A Definition of “Empirical Research” statistics courses. Their comments and their students’ comments helped In recommending goals for the introductory statistics substantially to clarify the ideas. The author also acknowledges insightful course I refer to “empirical research”, which thus deserves comments and criticisms from David R. Bellhouse, Carol J. Blumberg, a definition: Christopher Chatfield, George W. Cobb, Sir David Cox, W. Edwards Deming, David J. Finney, Robert W. Frick, Joan B. Garfield, Robert V. Empirical research is any research in which Hogg, Olaf E. Kraulis, Gudmund R. Iversen, William H. Kruskal, Alexan- data are gathered from the external world der M. Macnaughton, Christine E. McLaren, David S. Moore, Thomas L. and then conclusions are drawn from the Moore, Jerry Moreno, John A. Nelder, Ingram Olkin, Allan J. Rossman, data about the external world. Richard L. Scheaffer, Milo A. Schield, Stephen Senn, Gary Smith, and Paul F. Velleman. The Introductory Statistics Course: The Entity-Property-Relationship Approach 2. Empirical research is a key step of the scientific Other writers who discuss goals for the introductory method, which is crucial in many areas of human en- statistics course include Hogg (1990, 1991), Chromiak, deavor, such as in science, education, business, industry, Hoefler, Rossman, and Tesman (1992), Cobb (1992), and government. (No statement of fact in any branch of Iversen (1992), Watkins, Burrill, Landwehr, and Scheaffer science is accepted until it has been verified through care- (1992), Hoerl and Snee (1995), Gal and Garfield (1997a, ful empirical research.) pp. 2 - 5), and Moore (1997a). 2.3 Topic-Based Goals Have a Serious Drawback 3. FIVE CONCEPTS Many introductory statistics courses have what can be To help define the role of statistics, let us consider a called “topic-based” goals. A teacher using such goals sequence of five concepts I recommend for discussion at does not specify general goals, but instead simply speci- the beginning of an introductory statistics course. To fies a list of statistical topics to be covered in the course— make the approach easy for teachers to use, I present each that is, the teacher specifies a syllabus. For example, a concept mainly as a highly condensed version of how it teacher of a traditional introductory course might aim to might be presented to students. cover (in specified amounts of detail) the topics of prob- (In this paper I discuss the five concepts mostly in ab- ability theory, distribution theory, point and interval esti- stract terms because this gives readers a compact over- mation, and so on. Similarly, a teacher of an activity- view of the recommended approach. The abstractness of based course might make a list of statistical topics and my discussion has led readers of an earlier version of the then assign various activities to the students in order to paper to criticize the approach as being too abstract for cover the topics. students to understand [Macnaughton 1998a, app. C]. Unfortunately, topic-based goals have a serious draw- Please note that I am not suggesting that we present the back: By emphasizing lower-level statistical topics, these concepts to students in the compact form in which I de- goals usually fail to emphasize what is essential, which is scribe them below. Instead, I recommend that the con- to help students to appreciate the vital role or use of the cepts be presented in terms of numerous practical exam- field of statistics. Unless students understand and appre- ples. I further discuss presentation issues in section 6 and ciate the general role of statistics, knowledge of statistical I illustrate how the ideas might be presented to students in topics will be both of little interest to them and of little a paper [1996a].) use. Let us begin with what may be the most fundamental concept of human reality. 2.4 Recommended Goals I recommend that the goals of an introductory statis- Concept 1: Entities tics course be If you stop and observe your train of thought at this 1. to give students a lasting appreciation of the vital role moment, you will probably agree that you think about of the field of statistics in empirical research and things. For example, during the course of a minute or so, 2. to teach students to understand and use some useful you might think about, among other things, a friend, an statistical methods in empirical research. appointment, today’s weather, and an idea. Each of these These goals imply a commitment to the practical ap- things is an example of an entity. plication of statistics in empirical research. Emphasis on Many different types of entities exist, for example practical applications is important because the social value • organisms (e.g., people) of statistics is through its practical applications, and not • inanimate physical objects (directly) through theory or mathematics. Thus we stand a • events much better chance of impressing students with the use- • processes fulness of statistics if we discuss practical applications. • ideas, emotions (We must also discuss generalizations that link statis- • societal entities (e.g., educational institutions, govern- tical ideas together, but [to maximize appreciation] practi- ments, businesses) cal applications deserve strong emphasis. More on gener- • symbols alizations below.) • forces The first goal refers to the role of statistics in empiri- • waves cal research. Clearly, to satisfy this goal, we need a pre- • mathematical entities (e.g., sets, numbers, vectors). cise sense of what the role is. I propose a definition of the Entities are fundamental units of human reality be- role in subsection 4.7. I discuss in a paper how we might cause everything in human reality is an entity.