INTRODUCTION
The aim of this book is to present to statisticians, and to
statistics instructors, ideas and data relevant to teaching
statistical inference - especially at the introductory level -
using resampling methods in addition to, or in place of,
conventional methods.
Before proceeding further, here are a problem in
probability, and one in statistics, to show you what we mean by
simulation (in probability) and resampling simulation (in
statistics):
P: INSERT ? Three girls from statbook?
P: INSERT ? Bush-Dukakis from statbook?
Part I introduces resampling and its teaching to that large
part of humanity, and even of the statistics profession, that is
still unaware of resampling. We begin in Chapter I-1 with the
results of studies of resampling in the classroom (and a bit of
data for afterwards, too) from the early 1970s to the present; if
there were no demonstrated successes or proven superiority over
the conventional method, there would be no reason to read
further. Chapter I-2 then describes the resampling method
itself. And Chapter I-3 tells some of the history of the
development of resampling method.
Part II discusses methods of teaching statistical inference
with resampling. Resampling is best understood by seeing it
being learned. Hence Chapter II-1 transcribes an edited taped
class, to give the sense of the class atmosphere. Chapter II-2
discusses the teaching of resampling in a fashion complementary
with the conventional method and books. And Chapter II-3
discusses some of the benefits and costs of teaching the
resampling method - the spontaneity of the give-and-take between
students and teachers being both a benefit to students and a cost
to the teacher because it demands more effort than does a
standard structured class hour.
Part III analyses the resampling method from the point of
view of its effectiveness for users and students, and the nature
of the cognitive processes involved in carrying out statistical
inference with resampling and with the conventional method.
Chapter III-1 looks into the nature of statistical inference to
ascertain why it is such a difficult subject, and discusses how
resampling allows the student to focus on the true inherent
difficulties without getting distracted by unnecessary
mathematical difficulty and obscurity using the formulaic
approach. Chapter III-2 discusses why simulation can sensibly
attack some problems that the formal sample-space approach cannot
address. Chapter III-3 analyses several famous problems and
shows how the simulation approach that solves them also eases
problems in statistics. An afternote shows - half seriously,
half in jest - how a "try it" simulation approach can hugely
raise students' IQ (as defined by a newspaper IQ test) in a
matter of minutes; this typifies the effect of resampling on
one's intellectual capabilities.
Part IV takes up some special topics. Chapter IV-1
discusses the relationship between mathematicians and the
teaching of statistics; their love of the esthetics of
mathematics is a major barrier against teaching the simulation
approach, which (to mathematicians) lacks the beauty of formal
equations and proofs. Chapter IV-2 describes a computer-based
tutor that uses artificial intelligence to detect whether a
student's program is correct, and if not, to tell the student
where errors in logic have been made; the nature of the
resampling approach uniquely enables the operation of such a
tutor that works understandably, rather than a mere dumb device
that finds deviations from the formula that is demanded. Chapter
IV-3 discusses the nature of the Resampling Stats program that
emobdies the resampling approach; it and other parallel languages
such as Mathematica and APL work in an entirely different fashion
from Basic and Pascal because they closely mimic the operations
in simulation. (Resampling Stats has the additional advantage
over Mathematica and APL that it is designed only for statistics
and probability, and therefore is much less difficult to master.)
Part V discusses the future of resampling, and the barriers
it must overcome before it is adopted widely or universally for
instruction and everyday use - as it surely will be. Chapter V-1
discusses students' reactions to conventional statistics teaching
in the general context of the teaching of mathematics. And
Chapter V-II discusses the short-run prospects for resampling
instruction.
These chapters may seem as if they are an argument for the
use and teaching of resampling methods. But if that is so, we
believe, the reason is the characteristics of the resampling and
the conventional parametric methods, rather than our partiality
to resampling. And we do our very best to present all the
relevant material, pro and con, in as unbiased a manner as
possible, though we are certainly are adherents of resampling -
because of its characteristics, we believe.
The reader who is interested in learning more about the
practical procedures of resampling methods may consult
Resampling: The New Statistics by Julian L. Simon. And the same
author's The Philosophy and Practice of Statistics and Resampling
discusses the philosophical foundations of the subject.
page # teachbk introtch May 6, 1996