```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.

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
-------------------------------------------------------

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/

```