Subject: Re: EPR Approach to Intro Stat: 
             Relationships Between Variables

   Date: July 18, 1996 22:48 EDT

   From: Donald Macnaughton <>


On July 16, 1996, Will G Hopkins wrote about my posting of July 

> if you present this sort of stuff to students in those words
> you'll lose them, IMHO.  

I agree.  However, my discussion in the posting is for teachers 
and (as I note in the posting) is condensed.  I discuss in refer-
ences 1 and 2 below how I recommend the material be presented to 

> I agree with your concepts, but the way to get it across is to
> use the vernacular and concrete examples.

I believe that when we are presenting statistical concepts to 
students we must use carefully chosen familiar terminology.  Thus 
it's very important to use the vernacular when possible, although 
some new terms must be introduced because not all statistical 
concepts have names in the vernacular.

I also agree that it's important to use concrete examples.  I 
recommend that teachers use two types:
1. Teacher-chosen examples are helpful for introducing new con-
2. Student-chosen examples are helpful because they ensure that 
   the students are considering examples that are of interest.

Extensive class discussion of both types of examples is important 
because it helps the teacher to determine when the students have 
mastered the concepts.  Because the concepts of statistics build 
on one another, an introductory statistics course can be success-
ful only if the teacher ensures that the students have mastered 
each concept before moving on to the next.

I further discuss terminology and examples in references 1 and 2 
below.  I shall discuss the use of "frivolous" examples in sta-
tistics courses in my paper at the Joint Statistical Meetings in 

>                 <snip>
> I teach that a variable is something that can take on various
> values.

This is correct, of course.  But if a teacher doesn't attach var-
ables *to* something, the variables are left floating in a haze, 
completely disconnected, which is certainly not correct.  Instead 
(as I discuss further in reference 3), whenever you have a vari-
able in empirical research, entities are always present and the 
variable is always associated with a property of these entities.  
Because the entities are often the most tangible aspect of em-
pirical research, I believe that we should make them explicit, 
hence the 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.]

I emphasize that the teacher must precede this definition with a 
characterization of entities and properties of entities (using 
carefully chosen terminology and many examples), and follow this 
definition with a careful discussion of examples of variables and 
their values.

>                 <snip>
> I then go on to say that stats is all about:
> (a) Finding one or two numbers to summarise the values of a
> variable (e.g. mean and SD for a numeric variable;  frequency
> table for a nominal variable).  These numbers are called simple
> statistics.
> (b) Finding one or two numbers to summarise the relationship
> between two or more variables (e.g. correlation coefficient,
> effect size, relative risk).  There's no agreement as to what
> to call these, so I call them effect statistics. (I saw a paper
> lately in which they were called measures-of-effect statistics,
> but that's too much of mouthful.)
> (c) Estimating likely values of these statistics in a
> population on the basis of a sample of that population.  I
> emphasise the importance of confidence intervals here, and I
> have few kind words for hypothesis testing.
> That's it.  The end.  No more mystery.

Although this description certainly characterizes some of the ac-
tivities of statistics, I think it can be enhanced by showing 
students the role that the field of statistics plays in empirical 
research.  That role is to provide a broad set of techniques that 
help satisfy an important goal of empirical research, which is to 
study relationships between variables as a means to predicting 
and controlling the values of variables.

Material about the entity-property-relationship approach to the 
introductory statistics course is available at

Donald B. Macnaughton      MatStat Research Consulting Inc.         Toronto, Canada

1. Macnaughton, D. B. (1996) "The Introductory Statistics Course:  
   A New Approach."  This 8000-word draft paper is available at 
   the web site above.
2. Macnaughton, D. B. (1996) "The Entity-Property-Relationship 
   Approach to Statistics:  An Introduction for Students."  This 
   21,000-word draft paper is available at the web site above.
3. Macnaughton, D. B. (1996) "EPR Approach to Intro Stat:  Enti-
   ties and Properties.  Posted to the UseNet news-
   group (= EdStat-L) on June 25/26, 1996.  Available at the web 
   site above.