Subject: Re: Eight Features of an Ideal Intro Stat Course
         (Response to comments by Mark Myatt)

     To: sci.stat.edu (July 30, 1998)
         EdStat-L (August 3, 1998)

   From: Donald B. Macnaughton <donmac@matstat.com>

Referring to a July 17 post of mine, Mark Myatt writes (on July 
21)

> I rather liked your list of 8 features

I thank Mark for his positive vote.  Mark continues

> but I think you should not exclude univariate distributions as
> this offers a good avenue into discussions of measures of cen-
> tral tendency and robustness.  You can also use the standard
> deviation to introduce degrees of freedom (an important concept
> later on).  Looking at distributions also allows you to discuss
> test assumptions (i.e., assumption of normality) later and to
> talk about data presentation in graphs and tables. 

I fully agree with Mark that univariate distributions offer a 
good avenue into all the concepts he names -- an avenue I would 
generally follow myself in teaching these important concepts.

But *before* I would teach students any of Mark's follow-on con-
cepts and *before* I would teach students about univariate dis-
tributions, I would first teach another concept -- the concept of 
a relationship between variables.

I believe 

- the usefulness of the field of statistics lies solely in its 
  applications in empirical research

- almost all empirical research projects can be usefully charac-
  terized as studying relationships between variables

- almost all the statistical methods can be usefully character-
  ized as methods for studying relationships between variables.

Thus the concept of a relationship between variables *unifies* 
almost all empirical research projects and almost all the statis-
tical methods.  In view of the broad unifying power of this sim-
ple concept, I suggest we discuss it first.  

(The only concept that needs to come earlier is [obviously] the 
concept of 'variable', which itself necessitates discussion of 
two other concepts, as I discuss in a paper [1998].)

(Of course, although I discuss the concepts here in abstract 
terms, students are much more likely to appreciate statistics if 
we discuss the concepts in the introductory statistics course in 
terms of numerous concrete practical examples.)

If we spend initial time discussing univariate distributions be-
fore we discuss relationships between variables, I believe we 
*alienate* students because students find univariate distribu-
tions to be boring and of little obvious use.  On the other hand, 
students find relationships between variables to be fascinating.  
Relationships are fascinating because study of relationships is 
the only known objective method for accurate prediction and con-
trol, and students are generally very interested in prediction 
and control (of variables that are relevant to them).

(Some readers may know of examples of univariate distributions 
they feel are not boring.  I suggest that some such examples can 
be better characterized as examples of relationships between 
variables.  I discuss two such examples in appendix G of the pa-
per.) 


>    ( snip )
> Throw out univariate distributions and you are well on your way
> to throwing out EDA too.

It is important to note that I do not wish to throw out univari-
ate distributions from the curriculum -- I only wish to move the 
discussion later, *after* students have a good understanding of 
the more interesting and more important concept of a relationship 
between variables.

With respect to EDA (exploratory data analysis), we can break EDA 
into two categories:
- EDA that studies relationships between variables and
- EDA that studies univariate distributions.

Since relationships between variables are much more interesting 
to students than univariate distributions, EDA that studies rela-
tionships between variables is much more interesting to students 
than EDA that studies univariate distributions.  Therefore, even 
in EDA I recommend that the concept of a relationship between 
variables come first.

-------------------------------------------------------
Donald B. Macnaughton   MatStat Research Consulting Inc
donmac@matstat.com      Toronto, Canada
-------------------------------------------------------


REFERENCE

Macnaughton, D. B. 1998.  Eight features of an ideal introductory 
   statistics course.  This paper is available at 
   http://www.matstat.com/teach/