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

     To: edstat-l@jse.stat.ncsu.edu
         sci.stat.edu Usenet newsgroup

   From: Donald Macnaughton <donmac@matstat.com>
                   (formerly donmac@hookup.net)

   Date: Monday December 16, 1996 22:27 EDT

     Cc: Rex Boggs <rex@rocknet.net.au> 
         Graham Wood <g.wood@cqu.edu.au>

On Monday December 2, 1996 Rex Boggs, in apparent reference to my 
post of December 1 (1996a), wrote

> [Graham Wood] at Central Queensland University is developing a
> quite radical course and text for introductory statistics
> based on teaching students to use statistics as a tool to solve
> problems.

Clearly, a good introductory statistics course should show stu-
dents how to "solve problems".  In fact, I believe a focus on 
solving practical problems with statistics is essential for a 
successful introductory course.

However, in view of the title of this thread, Rex seems to be 
suggesting that we can *motivate* students to study statistics by 
telling them they are going to learn how to "solve problems".  I 
suggest that "solving problems" is not a good motivating concept 
because it is much too vague.  That is, just about *any* disci-
pline can be characterized as "solving problems" of one form or 
another.  

Instead of trying to motivate students with the concept of "solv-
ing problems", I believe we should motivate them by focusing on 
the essential *role that statistics plays* in solving problems.  
This role can be characterized in terms of the study of variables 
and relationships between variables as a means to accurate pre-
diction and control (Macnaughton 1996b).  

To illustrate the effectiveness of this approach, let me use it 
to discuss the four examples of problems that Rex gives in his 
post.  The first example is

>    ( snip )
> how a TV rental company used statistics to increase the per-
> centage of the bills that were paid on time;

This is clearly a study of a relationship between variables as a 
means to controlling the values of a variable.  Specifically,

    response variable:  percentage of bills paid on time

predictor variable(s):  although not identified in the example, 
                        the predictor variables are presumably 
                        something like:
                        1. variables reflecting the methods used 
                           to encourage customers to pay their 
                           bills
                        2. variables reflecting characteristics 
                           of the customers that a company might 
                           use as a basis for accepting or re-
                           jecting customers for rentals
                        3. variables reflecting other methods of 
                           managing customers.

statistical questions:  1. Is there a relationship between the 
                           response variable and the predictor 
                           variables in the population of custom-
                           ers?
                        2. If there is a relationship, how can we 
                           best control (i.e., maximize) the 
                           value of the response variable (per-
                           centage of bills paid on time) for 
                           members of the population on the basis 
                           of the relationship?

Thus Rex's first example can be easily characterized as a study 
of a relationship between variables.  His second example is

> how statistics was used to help determine how genetic material
> from the parents combines in an offspring;

This example is difficult to characterize because Rex does not 
identify either the response variable(s) or the predictor vari-
ables(s) that were used in the research.  However, it seems cer-
tain that the example is concerned either with one or more vari-
ables or (more likely) with one or more relationships between 
variables, because Rex notes that statistics was used.  Statis-
tics *invariably* concerns itself with variables or relationships 
between variables.

(Rex and other readers with access to Graham Wood's as-yet unpub-
lished text will have the best grasp of the details of Rex's four 
examples.  I hope these readers will let this newsgroup/mail-list 
know if they feel that my characterization of the examples in 
terms of relationships between variables is untenable.  See the 
appendix for a technical note.)

Thus Rex's second example can be characterized as a study of var-
iables or relationships between variables as a means to predict-
ing or controlling the values of variables.  His third example is

> and using statistics to help determine the assessed needs of
> old folks in rest homes and geriatric hospitals.

Again, Rex does not identify the actual variables, but it seems 
likely that this is another study of relationships between vari-
ables.  In one possible form of the example the response variable 
might be some measure of "quality of life" and the predictor var-
iables might be variables that reflect
- demographic properties of the patients
- attitudes of the patients
- properties of the facilities and care of the institutions.
The goal of this research would be to discover a relationship be-
tween the response variable and the predictor variables in order 
to learn how to control (i.e., maximize) the value of the re-
sponse variable (quality of life).

Thus Rex's third example can be characterized as a study of a re-
lationship between variables.  His final example is how

>    ( snip )
> one student set up a factorial experiment to determine the best
> combination of cam shaft, exhaust manifold and carburetttor for
> 'hotting up' his Cortina.

This is another example of a relationship between variables.  The 
response variable is some measure of the performance of the car, 
and the predictor variables are three nominal-level variables 
that reflect respectively the different cam shafts, exhaust mani-
folds, and carburetors that were used in the experiment.  


Thus each of Rex's four examples can be characterized as studying 
variables or relationships between variables as a means to pre-
dicting or controlling the values of variables.  Thus note how 
the concepts of variables, relationships, prediction, and control 
*unify* all the examples.  This unification can be applied to 
most (all?) empirical research projects and most statistical 
methods (Macnaughton 1996b).  The unification makes the field of 
statistics substantially easier for students to understand.


Let us return to the question of how we should *motivate* stu-
dents to study statistics.  Since 
- the concept of prediction is pivotal in empirical research
- the concept of prediction is pivotal in statistics
- the concept of prediction is simpler than the concept of con-
  trol
- students are keenly interested in knowing how to make accurate 
  predictions
therefore, I believe we can best motivate introductory students 
by telling them they will learn how to make accurate predictions. 


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

               http://www.matstat.com/teach/

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


APPENDIX
Some readers may wonder whether Rex's genetic material problem is 
purely a problem in probabilities and thus not a problem with 
variables.  I suggest that it is useful to view probabilities as 
*being* variables (i.e., formal representations of a particular 
property of "events").  From this point of view, even if the 
problem is purely a problem in probabilities, it is still a study 
of one or more variables or relationships between variables.


REFERENCES
Macnaughton, D. B. (1996a) "How Should We *Motivate* Students in 
   Intro Stat?"  Posted to the sci.stat.edu Usenet newsgroup on 
   December 1, 1996.  Available at http://www.matstat.com/teach/

Macnaughton, D. B. (1996b), "The Introductory Statistics Course:  
   A New Approach."  Available at http://www.matstat.com/teach/