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

     To: EdStat-L and

   From: Donald B. Macnaughton <>

   Date: Wednesday November 25, 1998

     cc: Rossi Hassad <>

In a November 23 post I recommend that statistics teachers omit 
discussing univariate distributions near the beginning of the in-
troductory course.  I recommend that teachers instead concentrate 
on discussing relationships between variables.  Quoting that post 
(and taking an opposing point of view), Rossi Hassad writes (on 
November 23)

> This is all very stimulating.  I strongly support the logical
> progression from univariate to bivariate.

As I note in a paper (1998a, sec. 9.1), I agree with Rossi that 
univariate distributions *logically* precede relationships be-
tween variables.  However, it is possible -- and, I believe, emi-
nently practical -- to begin the introductory course by discuss-
ing relationships with NO reference to univariate distributions.

I recommend concentrating first on relationships because students 
find univariate distributions to be *boring* -- students can see 
little or no obvious practical use of the study of univariate 

(I am NOT saying that univariate distributions have no practical 
uses -- they have many important uses in statistics.  I am only 
saying that univariate distributions have few uses that can be 
readily appreciated by students at the beginning an introductory 
statistics course.)

On the other hand, relationships between variables have many ob-
vious practical uses, as can be seen by their use across almost 
all empirical research.  

For example, ALL reputable medical research into the effective-
ness of new treatments for diseases can be easily viewed as 
studying relationships between variables.  The response variable 
reflects the amount of disease patients have (possibly in terms 
of the length of their survival), and the predictor variable(s) 
reflect the amount(s) of treatment(s) administered to the pa-

I submit that it is difficult to find examples of univariate dis-
tributions that are of real practical interest to beginning stu-
dents.  I invite Rossi and other proponents of teaching univari-
ate distributions near the beginning of the introductory statis-
tics course to describe some such examples.  (I discuss some pu-
tative examples in the earlier post [1998b] and in the paper 
[1998a, appendix G].)

Anyone proposing examples of interesting univariate distributions 
may also wish to consider the idea that we can make *any* inter-
esting univariate distribution of a variable substantially *more* 
interesting by studying the *relationship* between that distribu-
tion and some other variable(s) -- that is, by studying the rela-
tionship between the variables.

> Students learn best when our teaching strategies are based on
> the "constructivist learning theory", 

Under the constructivist view of learning the teacher structures 
the course in a way that encourages students to construct their 
own knowledge through active participation (Moore 1997, sec. 3).  
I agree that it is important to encourage students to construct 
their own knowledge.


- many statistics teachers will agree that a reasonable first 
  goal for the introductory course is to give students a lasting 
  appreciation of the vital role of the field of statistics in 
  empirical research

- most empirical research projects can NOT be viewed as studying 
  univariate distributions, but can be easily viewed as studying 
  relationships between variables

- relationships between variables are easy to understand (espe-
  cially when taught in terms of practical examples) and

- it appears that students can construct their own knowledge of 
  relationships between variables at least as easily as they can 
  construct their own knowledge of univariate distributions (be-
  cause relationships are more interesting -- they lead to accu-
  rate prediction and control).

Therefore, I believe it is more effective to encourage students 
to construct knowledge about relationships between variables than 
to encourage them to construct knowledge about (boring) univari-
ate distributions.

> that is they would quickly link Bi to Uni and get the big pic-
> ture.  

There are indeed strong linkages between relationships between 
variables and univariate distributions.  Specifically, relation-
ships between variables can be viewed as a *generalization* of 
univariate distributions.  Conversely, univariate distributions 
can be viewed as a *special case* of relationships between vari-
ables.  (I discuss these linkages further in the earlier post 

Thus we can introduce either of the two concepts in terms of the 
other.  However, since relationships between variables are much 
more interesting and more useful (because they allow more accu-
rate prediction and control), I suggest it is more reasonable to 
start with relationships.  

After students have a good sense of the use of the concept of a 
relationship between variables in empirical research, we can then 
discuss univariate distributions as a special case of relation-
ships.  At that point we can exploit the linkages Rossi mentions.  
In addition, we can show students the small but important roles 
that univariate distributions play in the study of relationships 
between variables.

> Believe me it's as simple as this.

Given that two presidents of the American Statistical Association 
have stated that "students frequently view statistics as the 
worst course taken in college" (Hogg 1991, Iman 1994), I suggest 
that the issues are not as simple as Rossi (with his traditional 
approach) would like us to believe.

However, I suggest a solution to the "worst course" problem is 
available:  If we focus on the *practical* study of relationships 
between variables as a means to accurate prediction and control, 
I believe we can move statistics from its current sometime back-
water status to its rightful role as a respected cornerstone of 
all empirical research.

Donald B. Macnaughton   MatStat Research Consulting Inc      Toronto, Canada


Hogg, R. V. (1991), "Statistical education: Improvements are 
   badly needed," _The American Statistician,_ 45, 342-343.

Iman, R. L. (1994), "The importance of undergraduate statistics," 
   _Amstat News,_ Number 215, December 1994, 6.

Macnaughton, D. B. 1998a. "Eight features of an ideal introduc-
   tory statistics course."  This paper is available at

Macnaughton, D. B. 1998b. "Re: Eight features of an ideal intro 
   stat course (response to comments by Gary Smith)."  Posted to 
   EdStat-L and on November 23, 1998.  Available at

Moore, D. S. 1997. "New pedagogy and new content: The case of 
   statistics (with discussion)." _International Statistical Re-
   view,_ 65, 123-165.

Home page for Donald Macnaughton's papers about introductory statistics