Subject: Re: How Should We *Motivate* Students in Intro Stat?

     To: Usenet newsgroup

   From: Donald Macnaughton <>

   Date: December 16, 1996, 22:31 EDT

     Cc: Dennis Roberts <>

On December 3, 1996 Dennis Roberts wrote (in reference to my post 
of December 1, 1996)

> Unfortunately ... to tell students that they are going to be
> able to make "accurate predictions" is for the most part ... a
> myth.

I suspect Dennis may have written somewhat hastily because it 
seems quite reasonable to me to view almost *everything* that the 
field of statistics does in empirical research as revolving 
around the concepts of accurate prediction and control on the ba-
sis of study of variables and relationships between variables.  
Let me give examples in terms of two statistical cornerstones:

If we (or students) properly perform a linear regression and find 
a new relationship between the response variable and the predic-
tor variables, are we not better able to *predict* the value of 
the response variable?  Or is this just a myth?

If we (or students) properly perform an analysis of variance and 
find a new relationship between the response variable and a ma-
nipulated variable, are we not better able to *control* the value 
of the response variable?  Or is this just a myth?  

Dennis may be worried about the word "accurate" in "accurate pre-
dictions".  Of course, the phrase "accurate predictions" does not 
mean *perfect* predictions.  However, it can be shown that the 
predictions made with proper statistical analysis are the *most 
accurate predictions currently possible* under various reasonable 
definitions of the term "accurate".  

Dennis may also be worried that students won't be able to make 
accurate predictions immediately.  This is so because of the many 
pitfalls both in empirical research and in statistical analysis 
of the results of empirical research.  Therefore, the necessary 
work to make accurate predictions is complicated and time-consum-
ing.  This difficulty (together with the cost of performing use-
ful empirical research) puts the use of statistical analysis in 
real empirical research out of the reach of most students.  How-
ever, this does not prevent us from beginning to equip students 
with the *ability* to understand and use empirical research and 
statistical analysis to make the most accurate possible predic-
tions (and exercise the most accurate possible control).

1. Most students are keenly interested in knowing how to make ac-
   curate predictions.  
2. Most empirical research projects can be viewed as being aimed 
   at determining how to make accurate predictions (or aimed at 
   determining how to exercise accurate control).  
3. Most statistical procedures can be viewed as methods for accu-
   rate prediction or control.  
Therefore, if we teach the field of statistics to students as a 
set of methods to help make accurate predictions and control, we 
can, in one swoop, thread three important needles with the same 
strong thread.  We are thus guaranteed that students will obtain 
a lasting appreciation of our field.

The ideas in this post are part of a broader discussion of an ap-
proach to the introductory statistics course available at


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