Experimentation: An Introduction to Measurement Theory and Experiment Design

225 Pages·1994·7.134 MB·English

by  David C. Baird

EXPERIMENTATION
An Introduction to Measurement Theory
and Experiment Design
Third Edition
D. C. Baird
Royal Military’ College
Kingston, Ontario
^ ♦
Prentice-Hall, Inc.
Englewood Cliffs, New Jersey 07632
Library of Congress Cataloging-in-Publication Data
Baird, D. C. (David Carr)
(Experimentation : an introduction to measurement theory and
experiment design / D. C. Baird. — 3rd ed.
p. cm.
Includes bibliographical references and index.
ISBN 0-13-303298-1
1. Physical measurements. I. Title.
QC39.B\1 1995
507'.24—dc20 94-13384
CIP
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© 1995 by Prentice-Hall, Inc.
A Paramount Communications Company
Englewood Cliffs, New Jersey 07632
All rights reserved. No part of this book may be
reproduced, in any form or by any means,
without the permission in writing from the publisher.
Printed in the United States of America
10 9 8 7 6 5 4 3 2
ISBN D-lB-aOBaTfl-l
Prentice-Hall International (UK) Limited, London
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To Margaret
Contents
Preface, vii
Chapter 1: Approach to Laboratory Work, 1
1 -1 Nature of Scientific Knowledge, 2
1- 2 Role of the Physics Laboratory, 4
Chapter 2: Measurement and Uncertainty, 10
2- 1 Basic Nature of Measuring Process, 10
2-2 Digital Display and Rounding Off, 12
2-3 Absolute and Relative Uncertainty, 13
2-4 Systematic Errors, 14
2-5 Uncertainty in Calculated Quantities, 15
2-6 Uncertainty in Functions of One Variable Only, 16
2-7 General Method for Uncertainty in Functions of a Single
Variable, 17
2-8 Uncertainty in Functions of Two or More Variables, 20
2-9 General Method for Uncertainty in Functions or Two or
More Variables, 22
2-10 Compensating Errors, 25
2- 11 Significant Figures, 26
Problems, 26
Chapter 3: Statistics of Observation, 29
3- 1 Statistical Uncertainty, 29
3-2 Histograms and Distributions, 30
3-3 Central Values of Distribution, 32
3-4 The Breadth of Distributions, 34
3-5 Significance of the Mean and Standard Deviation, 35
IV
CONTENTS
3-6 Gaussian Distributions and Sampling, 37
3-7 Relation Between Gaussian Distributions and Real
Observations, 40
3-8 Sample Means and Standard Deviation of the Mean, 41
3-9 Sample Standard Deviation, 43
3-10 Application of Sampling Theory to Real
Measurements, 43
3-11 Effect of Sample Size, 45
3-12 Standard Deviation of Computed Values, 47
3-13 Standard Deviation of Computed Values: Special
Cases, 50
3-14 Combination of Different Types of Uncertainty, 53
3- 15 Rejection of Readings, 54
Problems, 55
Chapter 4: Scientific Thinking and Experimenting, 57
4- 1 Observations and Models, 57
4-2 Construction of Models, 64
4-3 Testing Theoretical Models, 73
4-4 Use of Straight-Line Analysis, 77
4- 5 Case of Undetermined Constants, 79
Chapter 5: Experiment Design, 84
5- 1 To Text and Existing Model, 85
5-2 Straight-Line Form for Equations, 86
5-3 Planning and Experiments, 93
5-4 Experiment Design When There is No Existing Model, 99
5-5 Dimensional Analysis, 100
5-6 Difference-Type Measurements, 104
5-7 Experimenting with No Control Over Input Variables, 107
Problems, 109
Chapter 6: Experiment Evaluation, 113
6-1 General Approach, 113
6-2 The Stages of Experiment Evaluation, 115
6-3 Graphs, 118
6-4 Comparison Between Existing Models and Systems, 119
6-5 Calculation of Values from Straight-Line Analysis, 123
6-6 Cases of Imperfect Correspondence Between System and
Model, 128
6-7 The Principle of Least Squares, 129
6-8 Least-Squares Fit to Nonlinear Functions, 133
6-9 Precautions with Least-Squares Fitting, 134
VI CONTENTS
6-10 Function Finding, 135
6-11 Polynomial Representation, 137
6-12 Overall Precision of the Experiment, 138
6-13 The Concept of Correlation, 140
6- 14 Use of Computers in Experiment Evaluation, 145
Problems, 152
Chapter 7: Writing Scientific Reports, 157
7- 1 Good Writing Does Matter, 157
7-2 Title, 158
7-3 Format, 159
7-4 Introduction, 160
7-5 Procedure, 162
7-6 Results, 164
7-7 Graphs, 166
7-8 Discussion, 168
Appendix 1: Mathematical Properties of the Gaussian or
Normal Distribution, 171
A1-1 The Equation of the Gaussian Distribution Curve, 171
A1-2 Standard Deviation of the Gaussian Distribution, 176
A1-3 Areas Under the Gaussian Distribution Curve, 177
Appendix 2: The Principle of Least Squares, 179
A2-1 Least Squares and Sample Means, 179
A2-2 Least-Squares Fitted to Straight Lines, 180
A2-3 Weighting in Statistical Calculations, 183
Appendix 3: Difference Tables and the Calculus of Finite
Differences, 186
A3-1 Mathematical Foundations, 186
A3-2 Application of Difference Tables to Measured
Values, 193
Appendix 4: Specimen Experiment, 195
A4-1 Experiment Design, 195
A4-2 Report, 203
Bibliography, 208
Answers to Problems, 211
Index, 215
Preface
The first edition of this book was written with the conviction that, regardless
of the chosen objectives for an introductory physics laboratory, the basic
principles of experimenting should not be neglected and could in fact become
the principal topic. Introductory laboratories in physics are particularly suited
to this purpose since the systems and theories found there are usually simple
enough that the basic characteristics of measurement and experimenting can
easily be made visible and understandable Such an approach to physics
laboratory work can, therefore, be beneficial for a wide range of students, not
only those who will proceed to professional work in physics.
That purpose on which the 1962 edition was based seems still to be
valid. Many changes have taken place in the practice of experimenting, partly
through the introduction of new instrumentation, but mostly because of the
revolutionary impact of computing. Not only can we easily attain a level of
post-experiment data analysis that would have been completely impracticable
30 years ago, but the possibilities for the conduct of the experiment itself
have been enormously expanded by the availability of on-line data analysis
and computer-based control of the apparatus.
VII
VIII PREFACE
Revolutionary though such changes have been in the actual conduct of
experiments there has, nevertheless, been little or no change in the basic
principles underlying the experimenting, and training in these basic principles
is still required. Indeed, emphasis on these basic principles may be even more
necessary today than it was 30 years ago on account of the present-day pos­
sibility than an experimenter can be completely insulated from the phenom­
ena under study by an almost impenetrable barrier of data processing equip­
ment and procedures. Under these circumstances, wholly invisible defects
can produce final results with little or no meaning. Unless we have complete
and clear understanding of all phases of our experiment and data analysis, we
turn over our experiment wholly to the computer at our peril.
The plan of the present edition is largely the same as in that first edition
but the text has been almost completely rewritten. Chapter 1 gives an outline
of an approach to introductory physics laboratory work that emphasizes the
basic nature of experimenting. Chapters 2, 3, and 4 provide the information
on measurement, statistics, and scientific procedures that is needed to
understand the basic principles of experiment design. Chapter 5 treats in a
step-by-step way the practical requirements in designing an experiment, and
Chapter 6 provides the corresponding procedures for evaluating the results of
the experiment after the measurements have been made. At the end of the
main text. Chapter 7 contains some suggestions for writing laboratory
reports. The main addition to the present edition is material on computer
processing of experimental observations.
The appendices contain material which, although desirable in itself, would
have interrupted the development within the main text. This includes
mathematical derivation of some of the equations quoted in the main text. In
addition, a sample experiment is described in extensive detail, starting at the
beginning of the experiment design, continuing through the conduct of the actual
experiment and the evaluation of results, and ending with the final report.
The material in the text has been based on many years of teaching in
our First Year Physics Laboratory, and I am grateful to the generations of
students whose sometimes painful experience with it provided the opportu­
nity for continued refinement. I wish to express my appreciation, too, to Mr.
Peter Snell for valuable discussions and review of the text.
D.C. Baird
1
Approach
to Laboratory Work
This book is intended for use in introductory physics laboratories. It was
written, however, in the hope that it will serve a much wider purpose. It
provides an introduction to the study of experimenting in general, irrespec­
tive of the area in which the experimenting is carried out. Some students in
an introductory physics laboratory may pursue careers in physics research,
and it is hoped that the book will serve as a suitable introduction to their
continued studies. Many others will pursue careers in completely different
areas, perhaps in other sciences, or perhaps in areas outside science alto­
gether. Whatever the need, the introductory physics laboratory can, if suitably
oriented, provide a useful introduction to the fundamental principles that
underlie experimenting of any kind. For our purposes, the word ex­
perimentation has a very broad definition. By it we mean the whole process
of identifying a portion of the world around us, obtaining information from it,
and interpreting that information. This definition covers a wide range of
activities—all the way from the traditional picture of a biologist in a white
coat splicing DNA molecules to a manufacturer taking a poll to determine
individual preferences in toothpaste. This book is intended to meet the needs
of all who are either engaged themselves in any kind of study of the world
around us, or who must form a judgment on scientific statements made by
others.