Subject: EPR Approach to Intro Stat: Relationships Between Variables

Date: 14 Jul 1996 15:02:25 GMT

From: Don Macnaughton <donmac@matstat.com>
(formerly donmac@matstat.com)

Newsgroups: sci.stat.edu

In an earlier posting to this newsgroup I suggested that it is useful to begin an introductory statistics course by discussing the concepts of entities, properties of entities, and values of properties of entities. I suggested that this approach is useful because it helps students understand the important concept of a "variable".

I also proposed a definition:

A variable is equivalent to a property of an entity.

[Note added on December 1, 1996: I now believe a more precise definition is: A variable is a formal representation of a property of entities.]

The present posting describes how a teacher can usefully extend these ideas in an introductory course. To facilitate seeing the ideas from the students' point of view, I have presented the material below as a condensed version of how I recommend it be taught.

## A Goal of Empirical Research: Prediction and Control

An important goal of empirical research is to discover how to accurately predict and control the values of properties of entities. In other words, the goal is to predict and control the values of variables in entities. For example, a goal of medical science is to discover how to accurately predict and control the state of the human body, where the state is reflected by various medical properties or variables, such as blood pressure, white blood count, and other indicators of health or disease.

Society supports empirical research aimed at developing the ability to predict and control the values of variables because instances of such ability often yield substantial social or commercial benefits. For example, if medical scientists can discover how to better predict and control a person's predisposition to heart attacks, then their discovery will yield the social benefit of saving lives.

## Relationships Between Variables as a Key to Accurate Prediction and Control

Given the goal of predicting and controlling the values of variables, an obvious question is How can we predict and control the values of variables? The answer is by studying the distributions of the values of variables and (much more importantly) by studying relationships between variables.

For example, medical scientists have discovered that a relationship exists between the amount of fat ingested by a person and a person's predisposition to heart attacks. Knowledge of this relationship helps doctors and patients to predict and control heart attacks.

The concept of a relationship existing between variables pervades all branches of empirical research (including all "scientific" research). In fact, most (all?) empirical research can be viewed as the study of variables and relationships between variables.

We can convince students of the pervasiveness of relationships between variables by discussing various socially or commercially important empirical research projects, including research projects chosen by the students. In each case we can discuss

• the entities that were studied in the research project
• the variables (properties of the entities) that were measured
• the relationships between the variables that were discovered or analyzed and
• how knowledge of the relationships between the variables helps researchers and others to predict or control the values of important variables.

## Statistical Techniques for Studying Relationships Between Variables

After we have illustrated for students the vital role that the concept of a relationship between variables plays in empirical research, we can then bring the field of statistics out on the stage. We can introduce and teach the field to students as a set of rigorously developed techniques to help empirical researchers study variables and relationships between variables, as a means to accurately predicting and controlling the values of variables.

## Is It Useful to Emphasize Relationships Between Variables in the Introductory Course?

Given the vital role that the concept of a relationship between variables plays in empirical research, and given that most of the field of statistics can be viewed as providing techniques for studying relationships between variables, I believe that we should build the introductory statistics course around the concept of a relationship between variables.

I invite readers who disagree to present their views in this newsgroup.