Introduction to Statistics in Metrology Stephen Crowder

Introduction to Statistics in Metrology Stephen
Crowder download
https://textbookfull.com/product/introduction-to-statistics-in-
metrology-stephen-crowder/
Download more ebook from https://textbookfull.com

Stephen Crowder
Collin Delker
Eric Forrest
Nevin Martin
Introduction
to Statistics
in Metrology

Introduction to Statistics in Metrology

Stephen Crowder • Collin Delker • Eric Forrest
Nevin Martin
Introduction to Statistics in
Metrology

Stephen Crowder
Sandia National Laboratories
Albuquerque, NM, USA
Collin Delker
Eric Forrest
Nevin Martin
ISBN 978-3-030-53328-1 ISBN 978-3-030-53329-8 (eBook)
https://doi.org/10.1007/978-3-030-53329-8
© Springer Nature Switzerland AG 2020
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the
material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,
broadcasting, reproduction on microfilms or in any other physical way, and transmission or information
storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology
now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication
does not imply, even in the absence of a specific statement, that such names are exempt from the relevant
protective laws and regulations and therefore free for general use.
The publisher, the authors, and the editors are safe to assume that the advice and information in this
book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or
the editors give a warranty, expressed or implied, with respect to the material contained herein or for any
errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional
claims in published maps and institutional affiliations.
This Springer imprint is published by the registered company Springer Nature Switzerland AG
The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To Lee, Leah, Stephen, Colleen, and Anna—S.V.C.
To Kim, David, and Shawn—C.J.D.
To Lisa, Cari, and Lyla—E.C.F.
To Zane, Andy, and Josie—N.S.M.

Preface
This book is the result of many years of collaboration between the Primary Standards
Laboratory and the Statistical Sciences Department at Sandia National Laboratories.
Project work together, publications, and many discussions regarding how to best use
statistics in metrology have culminated in this manuscript. With this book, we wish
to present statistical best practices to both students and practitioners of metrology.
The book brings together in one place many of the basic statistical methods that have
been applied to problems in metrology, plus much more. It not only includes
methods presented in the JCGM 100 “Guide to the Expression of Uncertainty in
Measurement” (aka, the GUM), but also presents topics in metrology seldom
covered elsewhere. These topics include the design of experiments and statistical
process control in metrology, uncertainties in curve ﬁtting, assessment of binary
measurement systems, and sample size determination in metrology studies. The
book is not intended as a replacement for the GUM or other guiding documents
from metrology bodies. Rather, it is intended as a companion resource for the
student, technologist, engineer, or scientist involved in measurement studies. The
chapters were chosen to provide a blend of topics that will both inform and challenge
students and practitioners of metrology.
As a textbook, it is intended for junior or senior level college students studying
engineering, statistics, or metrology within a speciﬁc discipline. It can also be used at
the graduate level for students in instrumentation and measurement classes who are
learning the basics of metrology and the statistical methods behind uncertainty
analyses. As a prerequisite, readers should have a basic knowledge of calculus and
probability and statistics. Related readings that go beyond the scope of the book are
included in each chapter. We have also included exercises at the end of each chapter
to further illustrate and emphasize material in the body of the book.
Statistical techniques are emphasized throughout, with appropriate engineering
and physics background provided as needed. Most of the methods covered in the
book are illustrated with case studies from our work in the Nuclear Security
Enterprise. The case studies should provide the reader with a solid foundation for
vii

applying the techniques to a wide variety of metrology problems. Many end-of-
chapter exercises also rely on these case studies.
The statistical topics in metrology are presented by first introducing the basic
theory and models necessary to complete an uncertainty analysis. These topics are
then followed by case studies illustrating the approach.
Noteworthy highlights of the book include:
• Measurement uncertainty as a part of everyday life.
• Basic measurement terminology and types of measurement.
• Role of measurement uncertainty in decision-making.
• Direct and indirect measurement models.
• Analytical methods for the propagation of uncertainties.
• Design of experiments in metrology.
• Uncertainties in curve fitting.
• Statistical process control in metrology.
• Evaluation of binary measurement systems.
• Sample size determination and allocation in metrology experiments.
• R-Code and Python Uncertainty Calculator used in metrology studies.
Of course, we have not covered all possible topics involving statistics in metrol-
ogy. For example, we have chosen not to cover interlaboratory comparisons or
proficiency tests, as these topics are more relevant for calibration laboratories and
are well-covered in other sources such as the NCSLI’s RP-15. We have also chosen
not to cover in detail the metrology of system-level measurements. A system-level
approach would include a broader understanding of topics such as frequency
responses, sampling rates, aliasing, sensor placement and mounting, cables, and
connectors. These topics are well-covered in various books and short courses. Other
fields such as healthcare and analytical chemistry will have specialized extensions of
statistics in metrology that are beyond the scope of this book. The many intricacies of
discipline-specific metrology practices such as these are learned only through years
of training and hands-on experience.
Chapter 1 of the book includes a brief history of measurement and the develop-
ment of measurement science and technology. In Chap. 2, we introduce measure-
ment terminology, types of measurement, and sources of uncertainty. Chapter 3
covers the International System of Units (SI), traceability, and calibrations. The SI
base units and derived units are presented, along with the notion of unit realization.
Measurement standards and various aspects of calibration are also presented. These
three chapters are included to establish the background and language of metrology
used throughout the book.
An introduction to probability and statistics is given in Chap. 4. Topics include
types of data, summary statistics, graphical displays of data, and an introduction to
the probability distributions most often used in metrology. In Chap. 5, we provide an
overview of measurement uncertainty in decision-making, including risk, error
probabilities, test uncertainty ratios, and guardbanding.
Chapter 6 develops both direct and indirect measurement models and their roles
in an uncertainty analysis. Type A and Type B uncertainty evaluations, standard
viii Preface

uncertainties, combined standard uncertainties, and expanded uncertainties are
introduced here. The GUM approach to quantifying uncertainty is presented, and
the methods are illustrated with an uncertainty analysis of a neutron yield measure-
ment. Chapter 7 presents the analytical methods used to propagate uncertainties
through an indirect measurement model, including both first-order and higher order
models, with both uncorrelated and correlated inputs. Measurement examples are
given for each case.
Chapter 8 introduces the Monte Carlo method for uncertainty analysis, beginning
with a discussion of random number generation followed by a discussion of the
techniques found in the JCGM 101 (aka, the GUM Supplement 1). Measurement
examples and a case study are used to illustrate this approach. Chapter 9 presents the
basic experimental designs that can be used in the evaluation of uncertainty.
Emphasis is on full factorial, fractional factorial, and ANOVA-based designs. A
step-by-step approach to designing an experiment is given, along with case studies to
illustrate the design and analysis techniques.
In Chap.10, we present the methods for determining uncertainties in fitted curves,
including both linear and nonlinear least squares. The Monte Carlo method is also
applied to curve fitting, and examples are given for each approach. Finally, in
Chap. 11, we cover special topics in metrology that have been important in our
work. These topics include statistical process control applied to a measurement
process, evaluation of binary measurement systems, sample size determination and
allocation in metrology experiments, and an introduction to Bayesian analysis in
metrology.
Throughout this book, R-Code is provided alongside many of the examples to
give the reader an important tool that can be used to perform uncertainty analyses. R
is an open-source programming language whose popularity stems primarily from the
number of packages that are available for a wide range of statistical methods,
including Monte Carlo sampling, linear and nonlinear regression, ANOVA, and
more. R can be downloaded from the Comprehensive R Archive Network (CRAN)
at www.r-project.org and it is available for Windows, Unix-Like, and Mac operating
systems.
The Sandia Uncertainty Calculator (SUNCAL) is also being made available as
open-source software. It was developed by the Primary Standards Lab at Sandia to
perform propagation of uncertainty analyses and other statistical techniques in
metrology. It computes uncertainties using both the GUM and Monte Carlo
methods. Partial derivatives are solved symbolically to provide the analytical for-
mulas used in the calculations. The calculator can handle units conversion and
unlimited input variables and uncertainty components. In addition to uncertainty
propagation, SUNCAL provides calculations for curve fitting uncertainty, analysis
of variance, and false accept/reject risk. SUNCAL was written in Python, a
multipurpose language popular among engineers because of its ability to perform
data analysis along with tasks such as communicating with measurement equipment,
interfacing with databases, and accessing the internet. SUNCAL can be used through
a graphical user interface available for Windows and Mac, or as an importable
Preface ix

Python package for programmers. It is released under the GNU General Public
License, with source code and executables available at https://sandiapsl.github.io.
Appendix A covers common acronyms and abbreviations used in metrology,
followed in Appendix B by guidelines for valid measurements. Appendix C includes
a traceability chain and uncertainty budget case study, presented in more detail than
those in the body of the book. Appendix D includes a quick reference for the GUM
propagation of uncertainty technique and a table of references for common topics in
metrology. Finally, Appendix E provides information regarding the installation of R
software and existing R packages used in metrology.
The acknowledgments are given to those from the Primary Standards Laboratory
and the Statistical Sciences Department who have contributed their expertise and
case studies in this collaborative effort. Our former and present colleagues in this
work include Stuart Kupferman, Tom Wunsch, Bud Burns, Lisa Bunting Baca, Greg
Guidarelli, Andrew Mackrory, David Sanchez, Edward O0
Brien, Jesse Whitehead,
Mark Benner, Meghan Shilling, Donavon Gerty, Stefan Cular, Harold Parks, Eliz-
abeth Auden, Ricky Sandoval, Otis Solomon, Roger Burton, Hy Tran, Raegan
Johnson, Allie Wichhart, Andrew Wofford, Lauren Wilson, and Dan Campbell.
Special thanks to David Walsh for providing the lead probe case study and to Elbara
Ziade for providing the CMM case study. Finally, this book would not have been
possible without the support of Justin Newcomer and Adele Doser, Managers of the
Statistical Sciences Department, Meaghan Carpenter, Senior Manager of the Primary
Standards Lab, and Marcey Hoover, Director of Quality Assurance at Sandia.
Albuquerque, NM, USA Stephen Crowder
Albuquerque, NM, USA Collin Delker
Albuquerque, NM, USA Eric Forrest
Albuquerque, NM, USA Nevin Martin
x Preface

A false balance is an abomination to the
LORD, but a just weight is his delight
Proverbs 11:1

Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Measurement Uncertainty: Why Do We Care? . . . . . . . . . . . . 1
1.2 The History of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Measurement Science and Technological Development . . . . . . 2
1.4 Allegations of Deﬂated Footballs (“Deﬂategate”) . . . . . . . . . . . 3
1.5 Fatality Rates During a Pandemic . . . . . . . . . . . . . . . . . . . . . . 8
1.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.7 Related Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Basic Measurement Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Measurement Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.1 General Measurement Terminology . . . . . . . . . . . . . . 20
2.2.2 Error Approach Terminology . . . . . . . . . . . . . . . . . . 23
2.2.3 Uncertainty Approach Terminology . . . . . . . . . . . . . . 24
2.2.4 Terminology of Calibration . . . . . . . . . . . . . . . . . . . . 28
2.3 Types of Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.1 Physical Measurements . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.2 Electrical Measurements . . . . . . . . . . . . . . . . . . . . . . 30
2.3.3 Other Types of Measurements . . . . . . . . . . . . . . . . . . 30
2.4 Sources of Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.4.1 Evaluating Sources of Uncertainty . . . . . . . . . . . . . . . 33
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.6 Related Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3 The International System of Units, Traceability, and Calibration . . 41
3.1 History of the SI and Base Units . . . . . . . . . . . . . . . . . . . . . . 41
3.1.1 SI Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.1.2 Time: Second (s) . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
xiii

3.1.3 Length: Meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1.4 Mass: Kilogram (kg) . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1.5 Electric Current: Ampere (A) . . . . . . . . . . . . . . . . . . 44
3.1.6 Temperature: Kelvin (K) . . . . . . . . . . . . . . . . . . . . . . 44
3.1.7 Quantity of Substance: Mole (mol) . . . . . . . . . . . . . . 44
3.1.8 Luminous Intensity: Candela (cd) . . . . . . . . . . . . . . . 44
3.2 Derived Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3 Unit Realizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.1 Gauge Block Interferometer . . . . . . . . . . . . . . . . . . . 46
3.3.2 Josephson Volt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.4 Advancements in Unit Definitions . . . . . . . . . . . . . . . . . . . . . 46
3.4.1 Kibble (Watt) Balance . . . . . . . . . . . . . . . . . . . . . . . 47
3.4.2 Intrinsic Pressure Standard . . . . . . . . . . . . . . . . . . . . 48
3.5 Metrological Traceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.6 Measurement Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.6.1 Certified Reference Materials . . . . . . . . . . . . . . . . . . 49
3.6.2 Check Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.7 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.7.1 The Calibration Cycle . . . . . . . . . . . . . . . . . . . . . . . . 51
3.7.2 Legal Aspects of Calibration . . . . . . . . . . . . . . . . . . . 52
3.7.3 Technical Aspects of Calibration . . . . . . . . . . . . . . . . 52
3.7.4 Calibration Policies and Requirements . . . . . . . . . . . . 53
3.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.9 Related Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4 Introduction to Statistics and Probability . . . . . . . . . . . . . . . . . . . . 59
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2 Types of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.3 Exploratory Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.3.1 Calculating Summary Statistics . . . . . . . . . . . . . . . . . 61
4.3.2 Graphical Displays of Data . . . . . . . . . . . . . . . . . . . . 63
4.4 Probability Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.4.1 Identification of Probability Distributions . . . . . . . . . . 69
4.4.2 Estimating Distribution Parameters . . . . . . . . . . . . . . 75
4.4.3 Assessing Distributional Fit . . . . . . . . . . . . . . . . . . . . 76
4.5 Related Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5 Measurement Uncertainty in Decision Making . . . . . . . . . . . . . . . . 81
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2 Measurement Uncertainty and Risk . . . . . . . . . . . . . . . . . . . . 81
xiv Contents

5.2.1 Measurement Uncertainty and Risk
in Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.2.2 Measurement Uncertainty and Risk in Calibration . . . 93
5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.4 Related Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6 The Measurement Model and Uncertainty . . . . . . . . . . . . . . . . . . . 103
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.2 Uncertainty Analysis Framework . . . . . . . . . . . . . . . . . . . . . . 103
6.2.1 Standard Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . 104
6.2.2 Type A Uncertainty Evaluation . . . . . . . . . . . . . . . . . 104
6.2.3 Type B Uncertainty Evaluation . . . . . . . . . . . . . . . . . 104
6.2.4 Combined Standard Uncertainty . . . . . . . . . . . . . . . . 105
6.2.5 Conﬁdence Level and Expanded Uncertainty . . . . . . . 105
6.3 Direct Measurements and the Basic Measurement Model . . . . . 107
6.3.1 Case Study: Voltage Measurement . . . . . . . . . . . . . . . 109
6.3.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.4 Indirect Measurements and the Indirect Measurement Model . . 114
6.4.1 Case Study: Neutron Yield Measurement . . . . . . . . . . 117
6.4.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.5 Related Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
7 Analytical Methods for the Propagation of Uncertainties . . . . . . . . 131
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.2 Mathematical Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7.3 The Simple Case: First-Order Terms with Uncorrelated
Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.3.1 Measurement Examples . . . . . . . . . . . . . . . . . . . . . . 135
7.4 First-Order Terms with Correlated Inputs . . . . . . . . . . . . . . . . 137
7.4.1 Covariance, Correlation, and Effect on
Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.5 Higher-Order Terms with Uncorrelated Inputs . . . . . . . . . . . . . 142
7.6 Multiple Output Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
7.7 Limitations of the Analytical Approach . . . . . . . . . . . . . . . . . . 146
7.8 Related Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Contents xv

8 Monte Carlo Methods for the Propagation of Uncertainties . . . . . . 153
8.1 Introduction to Monte Carlo Methods . . . . . . . . . . . . . . . . . . . 153
8.1.1 Random Sampling Techniques and Random Number
Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
8.1.2 Generation of Probability Density Functions Using
Random Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
8.1.3 Computational Approaches . . . . . . . . . . . . . . . . . . . . 157
8.2 Standard Monte Carlo for Uncertainty Propagation . . . . . . . . . 159
8.2.1 Monte Carlo Techniques . . . . . . . . . . . . . . . . . . . . . . 159
8.3 Comparison to the GUM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
8.3.1 Quantitative GUM Validity Test . . . . . . . . . . . . . . . . 167
8.4 Monte Carlo Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.4.1 Case Study: Neutron Yield Measurement . . . . . . . . . . 169
8.4.2 Case Study: RC Circuit . . . . . . . . . . . . . . . . . . . . . . . 173
8.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
8.6 Related Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
8.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
9 Design of Experiments in Metrology . . . . . . . . . . . . . . . . . . . . . . . . 181
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
9.2 Factorial Experiments in Metrology . . . . . . . . . . . . . . . . . . . . 181
9.2.1 Deﬁning the Measurand and Objective of the
Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
9.2.2 Selecting Factors to Incorporate in the Experiment . . . 183
9.2.3 Selecting Factor Levels and Design Pattern . . . . . . . . 183
9.2.4 Analysis of CMM Errors via Design of Experiments
(24
Full Factorial) . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
9.2.5 Finite Element Method (FEM) Uncertainty Analysis
via Design of Experiments (27–3
Fractional
Factorial) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
9.2.6 Summary of Factorial DOEx Method . . . . . . . . . . . . . 205
9.3 ANOVA Models in Metrology . . . . . . . . . . . . . . . . . . . . . . . . 206
9.3.1 Random Effects Models . . . . . . . . . . . . . . . . . . . . . . 206
9.3.2 Mixed Effects Models . . . . . . . . . . . . . . . . . . . . . . . . 208
9.3.3 Underlying ANOVA Assumptions . . . . . . . . . . . . . . . 209
9.3.4 Gauge R&R Study (Random Effects Model) . . . . . . . 210
9.3.5 Voltage Standard Uncertainty Analysis (Mixed
Effects Model) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
9.3.6 Summary of ANOVA Method . . . . . . . . . . . . . . . . . . 220
9.4 Related Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
9.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
xvi Contents

10 Determining Uncertainties in Fitted Curves . . . . . . . . . . . . . . . . . . 227
10.1 The Purpose of Fitting Curves to Experimental Data . . . . . . . . 227
10.1.1 Resistance vs. Temperature Data . . . . . . . . . . . . . . . . 228
10.1.2 Considerations When Fitting Models to Data . . . . . . . 229
10.2 Methods for Fitting Curves to Experimental Data . . . . . . . . . . 230
10.2.1 Linear Least Squares . . . . . . . . . . . . . . . . . . . . . . . . 231
10.2.2 Uncertainty in Fitting Parameters . . . . . . . . . . . . . . . . 231
10.2.3 Weighted Least Squares: Non-constant u(y) . . . . . . . . 233
10.2.4 Weighted Least Squares: Uncertainty in Both x
and y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
10.3 Uncertainty of a Regression Line . . . . . . . . . . . . . . . . . . . . . . 234
10.3.1 Uncertainty of Fitting Parameters . . . . . . . . . . . . . . . 235
10.3.2 Conﬁdence Bands . . . . . . . . . . . . . . . . . . . . . . . . . . 235
10.3.3 Prediction Bands . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
10.4 How Good Is the Model? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
10.4.1 Residual Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
10.4.2 Slope Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
10.4.3 Quantitative Residual Analysis . . . . . . . . . . . . . . . . . 239
10.5 Uncertainty in Nonlinear Regression . . . . . . . . . . . . . . . . . . . 241
10.5.1 Nonlinear Least Squares . . . . . . . . . . . . . . . . . . . . . . 241
10.5.2 Orthogonal Distance Regression . . . . . . . . . . . . . . . . 243
10.5.3 Conﬁdence and Prediction Bands in Nonlinear
Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
10.6 Using Monte Carlo for Evaluating Uncertainties in Curve
Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
10.6.1 Monte Carlo Approach . . . . . . . . . . . . . . . . . . . . . . . 245
10.6.2 Markov-Chain Monte Carlo Approach . . . . . . . . . . . . 246
10.7 Case Study: Contact Resistance . . . . . . . . . . . . . . . . . . . . . . . 247
10.8 Drift and Predicting Future Values . . . . . . . . . . . . . . . . . . . . . 249
10.8.1 Uncertainty During Use . . . . . . . . . . . . . . . . . . . . . . 249
10.8.2 Validating Drift Uncertainty . . . . . . . . . . . . . . . . . . . 252
10.9 Calibration Interval Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 258
10.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
10.11 Related Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
10.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
11 Special Topics in Metrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
11.2 Statistical Process Control (SPC) . . . . . . . . . . . . . . . . . . . . . . 267
11.2.1 Case Study: Battery Tester Uncertainty
and Monitoring Via SPC . . . . . . . . . . . . . . . . . . . . . . 269
11.2.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
11.3 Binary Measurement Systems (BMS) . . . . . . . . . . . . . . . . . . . 274
11.3.1 BMS Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
11.3.2 BMS Case Study Introduced . . . . . . . . . . . . . . . . . . . 275
Contents xvii

11.3.3 Evaluation of a BMS . . . . . . . . . . . . . . . . . . . . . . . . 275
11.3.4 Sample Sizes for a BMS Study . . . . . . . . . . . . . . . . . 282
11.4 Measurement System Analysis with Destructive Testing . . . . . 284
11.5 Sample Size and Allocation of Samples in Metrology
Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
11.6 Summary of Sample Size Recommendations . . . . . . . . . . . . . . 291
11.7 Bayesian Analysis in Metrology . . . . . . . . . . . . . . . . . . . . . . . 292
11.8 Related Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
11.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
Appendix A: Acronyms and Abbreviations . . . . . . . . . . . . . . . . . . . . . . 303
Appendix B: Guidelines for Valid Measurements . . . . . . . . . . . . . . . . . . 305
Related Reading: Electrical Measurements . . . . . . . . . . . . . . . . . . . . . 305
Related Reading: Time and Frequency Measurements . . . . . . . . . . . . . 305
Related Reading: Physical Measurements . . . . . . . . . . . . . . . . . . . . . . 306
Related Reading: Temperature Measurement . . . . . . . . . . . . . . . . . . . . 306
Related Reading: Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
Related Reading: General Measurement and Instrumentation
Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
Appendix C: Uncertainty Budget Case Study: CMM Length
Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
Coordinate Measuring Machine (CMM) Measurements . . . . . . . . . . . . 309
Product Acceptance Uncertainty: Dimensional Part Inspection
with a CMM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
Radius of Curvature of a Spherical Mirror . . . . . . . . . . . . . . . . 310
The Measurement Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
Measurement Considerations . . . . . . . . . . . . . . . . . . . . . . . . . 311
ROC Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
Uncertainty Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
Related Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
Appendix D: Uncertainty Quick Reference . . . . . . . . . . . . . . . . . . . . . . . 321
GUM Method for Measurement Uncertainty . . . . . . . . . . . . . . . . . . . . 321
Percentage Points of the t Distribution . . . . . . . . . . . . . . . . . . . . . . . . 322
Guardbanding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
Symmetric Specification Limits . . . . . . . . . . . . . . . . . . . . . . . 323
Asymmetric Specification Limits . . . . . . . . . . . . . . . . . . . . . . 323
One-Sided Specification Limits . . . . . . . . . . . . . . . . . . . . . . . 323
Metrology Reference Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
xviii Contents

Appendix E: R for Metrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
Installation of R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
R Packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
R for Metrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
Contents xix

About the Authors
Stephen Crowder is a Principal Member of Technical Staff in the Statistical
Sciences department at Sandia National Laboratories with over 30 years of experi-
ence working in industrial statistics and metrology. He received his B.S. degree in
Mathematics from Abilene Christian University and his M.S. and Ph.D. in Statistics
from Iowa State University. He has previously done research and published in the
ﬁelds of statistical process control, system reliability, and statistics in metrology.
Collin Delker is a Senior Member of Technical Staff at Sandia National Laborato-
ries, working in the Primary Standards Laboratory. He received his B.S. degree in
Electrical Engineering from Kansas State University and his Ph.D. in Electrical
Engineering, with an emphasis on microelectronics and nanotechnology, from Purdue
University. He specializes in developing techniques for the calibration of microwave
frequency devices in addition to providing software solutions for metrology.
Eric Forrest is a Principal Member of Technical Staff at Sandia National Laborato-
ries, working in the Primary Standards Laboratory where he leads the Radiation and
Optics Project. He received his B.S., M.S., and Ph.D. in Nuclear Science and
Engineering from MIT, where he was a National Nuclear Security Administration
Fellow. His research focused on high-speed optical/infrared imaging and development
of nanoengineered surfaces for enhanced heat transfer in nuclear thermal hydraulics
applications. He specializes in uncertainty analyses for complex experimental
measurements.
Nevin Martin is a Member of Technical Staff in the Statistical Sciences Depart-
ment at Sandia National Laboratories. She received her B.S. degree in Finance from
the University of Arizona and her M.S. degree in Statistics from the University of
New Mexico. She collaborates on a wide range of projects that include work in
statistical computing with R, data visualization and modeling, and uncertainty
quantiﬁcation. She teaches a short course on “Introduction to Statistical Computing
in R” and develops R-Code for the application of statistics in metrology.
xxi

Chapter 1
Introduction
Statistics and metrology, that is, the science of measurement, permeate mod-ern
engineering, society, and culture. This chapter provides a brief historical perspective
on the importance of metrology, along with introducing the core concept of uncer-
tainty: a key element that spans both statistics and metrology. The importance of
uncertainty is demonstrated through two contemporary case studies. First, this
chapter considers how uncertainty may have adversely affected the outcome of
pressure measurements on footballs in a 2015 sports scandal often referred to as
“Deﬂategate.” Second, the importance of an accurate measurement model in
obtaining reliable estimates of case fatality rate during a pandemic is discussed.
1.1 Measurement Uncertainty: Why Do We Care?
Measurements are an important part of everyday life. Measurements drive decision-
making in nearly all aspects of modern society. Do you ever question the validity of
a measurement result? You should, considering that every measurement has uncer-
tainty. Knowledge of this associated uncertainty is necessary for making informed
decisions. Yet, uncertainty analysis and propagation constitute a subject area that
rarely receives proper attention in science and engineering curriculums or in public
discourse.
Uncertainty analysis and propagation are central to metrology, the science
of measurement. And metrology is fundamentally interlinked with statistics.
This textbook helps bridge the gap between statistics, metrology, and uncertainty
analysis, not just for the measurement practitioner, but also for those who utilize
measurement data. In this chapter, a brief historical backdrop is provided, along
with two introductory case studies based on contemporary issues. Case studies
demonstrate the importance of a holistic approach to measurement uncertainty and
highlight several concepts and methods that will be introduced in later chapters.
© Springer Nature Switzerland AG 2020
S. Crowder et al., Introduction to Statistics in Metrology,
https://doi.org/10.1007/978-3-030-53329-8_1
1

1.2 The History of Measurement
The importance of proper measurement and its associated measurement uncertainty
have long been recognized. The ancient Egyptians and ancient Mesopotamians
established the earliest known recorded system of measure while constructing the
pyramids and other architectural feats in the 4th to 3rd millennia BCE (Clarke and
Engelbach 1990). Figure 1.1 shows an example of a cubit rod used by the ancient
Egyptians. The cubit rod was used as a unit of length and represented the length of a
Pharaoh’s forearm. In ancient Israel, a well-established system of measurement was
used to ensure that trade of food items and other goods was carriedout fairly and justly.
Prior to the introduction of a standardized system, some would intentionally offset
weights and measures to try to cheat their neighbors in the sale or trade of goods.
Prior to 500 BCE, the ancient Greeks developed a system of official weights
and measures and employed a method of calibration using reference standards. The
Roman Empire adapted the earlier Hellenic system to create a well-documented,
sophisticated system of measurement that employed standards and calibration in
commerce, trade, and engineering (Smith 1851). However, many of the official
weights and measures varied from region to region. In the third century BCE, the
Greek librarian and scientist Eratosthenes measured the circumference of the Earth
simply by observing the lengths of shadows in two locations. He determined the
circumference to be 250,000 stades. The stade was a unit based on the length of a
typical Greek stadium, but there were several regional variations on the definition of
a stade (Walkup 2005). Unfortunately, because of the different definitions in use at
the time, it may never be known exactly how close Eratosthenes’s measurement
came to the modern accepted circumference of the Earth. Not until many centuries
later did weights and measures become internationally standardized.
1.3 Measurement Science and Technological Development
Throughout history, advances in measurement science and standards have been
a prerequisite for the practical implementation of scientific developments. For
example, the concept of interchangeable parts, which revolutionized manufacturing
and led to numerous other technological advances, could only be implemented
successfully with improvements in measurement science. In the late 1700s and
early 1800s, complex mechanical devices, such as firearms, required careful hand-
Fig. 1.1 A replica of the ancient Egyptian cubit rod. A cubit is a unit of length equivalent to the
distance between the elbow and the tip of the middle finger of the ruling Pharaoh at the time
2 1 Introduction

fitment of parts by experienced gunsmiths. In 1801, when Eli Whitney presented
his concept of interchangeable parts for a musket to the United States War
Department (Hays 1959), a key framework, such as dimensional standards, was
not yet available. Unbeknownst to the War Department, the muskets presented were
specially prepared and individual parts were not standardized or interchangeable
with other muskets of the same type. It took decades to successfully realize the vision
of interchangeable parts for modern manufacturing. In fact, gauge blocks, a type of
dimensional standard introduced in the 1890s by Swedish machinist C.E. Johannson
(Althin 1948), were a key facilitator for modern production and fabrication methods,
enabling the use of interchangeable parts and common tooling for assembly line
manufacturing.
The importance of measurement standardization and measurement traceability
for technological advancement and economic growth was realized early in the
Technological Revolution. In 1875, 17 countries, including the USA, signed
the Metre Convention, which established the International Bureau of Weights
and Measures (BIPM) and defined international standards for mass and length.
Improvements in standards and measurement would continue to drive major revo-
lutions in machining, fabrication, and production of industrial, commercial, and con-
sumer goods throughout the 1900s. The advent of digital computing in the late 1940s,
along with advances in air and space travel throughout the last century, necessitated
improvements in all areas of measurement, with associated reductions in uncertainty.
Despite the agreed-upon importance of a universal system of units and maintenance of
consistent standards, treatment of measurement data and its associated uncertainties
remained relatively ambiguous until the 1990s. To this day, measurement uncertainty is
often misunderstood by engineers and scientists performing measurements.
The criticality of accurate measurements in the marketplace has never been greater.
Measurement inaccuracies in food and fuel purchases alone place billions of consumer
dollars at risk each year. Measurement uncertainties in manufacturing increase the risk
of accepting bad product or rejecting good product, each resulting in lost productivity
and profits. Measurement uncertainties in medical diagnostics can result in both missed
or incorrect diagnoses, with major public health implications. Measurements are the
basis for legal decisions and evidence in trials and form the basis for science-based
policies across the globe. The accuracy of such measurements relies heavily on mea-
surement standardization and measurement traceability and is the forefront of topics
discussed in this handbook. We will demonstrate the importance of measurements, and
their associated uncertainties, with two modern real-world case studies highlighting
important measurement uncertainty concepts detailed in later chapters.
1.4 Allegations of Deflated Footballs (“Deflategate”)
During the 2014 American Football Conference (AFC) Championship Game on
January 18, 2015, between the Indianapolis Colts and the New England Patriots of
the National Football League (NFL), allegations arose regarding the New England
Patriots intentionally deflating their game balls to provide an unfair competitive
1.4 Allegations of Deflated Footballs (“Deflategate”) 3

advantage over the Colts. Measurements of football air pressure at halftime became
the central part of a subsequent NFL investigation and disciplinary hearings. In
addition to becoming a public spectacle, the outcome of the investigations resulted
in major penalties for the New England Patriots and their quarterback, Tom Brady.
The Patriots were ultimately fined $1 million and forced to forfeit a first-round draft
pick in 2016 and a fourth-round draft pick in 2017, with Tom Brady (Fig. 1.2). being
suspended for four games. However, a general lack of understanding of measurement
uncertainty may have led to erroneous conclusions based on the football air
pressure data.
The controversy centered on the following requirement in the NFL rulebook
(Goodell 2014):
The ball shall be made up of an inflated (12½ to 13½ pounds) urethane bladder enclosed in a
pebble grained, leather case (natural tan color) without corrugations of any kind. It shall have
the form of a prolate spheroid and the size and weight shall be: long axis, 11–11¼ inches;
long circumference, 28–28½ inches; short circumference, 21 to 21¼ inches; weight, 14 to
15 ounces.
While the requirement, as written, does not specify proper units, it is interpreted
to mean internal football air pressure shall be between 12.5 pounds per square inch
gauge (psig) and 13.5 psig. Proper and consistent use of units is paramount when
specifying a measurement requirement and when reporting measurement results
(introduced in Chap. 3).
Following an interception by the Colts in the first half, suspicions arose of
underinflated Patriots’ game balls. At halftime, two NFL officials measured air
Fig. 1.2 Tom Brady in
2011 as quarterback of the
New England Patriots.
Untraceable measurements
of football air pressure, with
large uncertainties, were
central to allegations that he
directed the deflation of
footballs prior to the 2014
AFC Championship Game.
Photograph by Jeffrey Beall/
CC-BY-SA-3.0
4 1 Introduction

pressure of eleven Patriots’ game balls. Two pressure gauges, provided by another
official, were used for the measurements. The pressure gauges were not calibrated
and therefore lacked traceability (see Chap. 3). In addition, the pressure gauges were
of unknown origin aside from the fact that one had a Wilson logo, whereas the other
did not (Figs. 1.3 and 1.4).
The officials demonstrated an understanding of measurement variability, and
more specifically, repeatability and reproducibility (see Chap. 2): two measurements
were taken on each game ball, with a different gauge and operator used for each.
However, applying a t-distribution and looking at the t-table (introduced in Chap. 4)
show that taking only two independent measurements (one degree of freedom) are
generally inadequate and greatly increase the expanded measurement uncertainty
(see Chap. 6 and Table 1.1).
We can perform a Type A uncertainty evaluation (see Chaps. 2 and 6) of the game-
day internal football pressure data that was recorded by officials. In general, 20–30
independent measurements are desirable to properly assess repeatability and repro-
ducibility (see Chap. 11). However, this may not always be achievable. When the
sample size is less than 30, the t-distribution is typically used. For a limited sample
size (n ¼ 2), the coverage factor for a 95% level of confidence (see Chaps. 2 and 6)
becomes large (12.7), resulting in a much larger expanded uncertainty for the
Fig. 1.3 Pressure gauges
used by the championship
game officials to measure
internal football air pressure
at halftime. The gauge on
the left is referred to as the
“non-logo gauge” and the
gauge on the right was
referred to as the “logo
gauge” (Exponent 2015)
Fig. 1.4 Pressure gauges
used by the championship
game officials to measure
internal football air pressure
at halftime. Pressure gauges
(model CJ-01) distributed
by Wilson sporting goods
were likely manufactured by
Jiao Hsiung Industry Corp.
(Exponent 2015)

measurement. While some might propose treating the eleven different footballs as the
same sample, there is no expectation that the true value of the air pressure in different
footballs will be the same. Variability between footballs would provide insight into
variability in the fill process, but not necessarily the measurement uncertainty.
Repeatability and reproducibility are only one aspect of measurement uncer-
tainty. Type B evaluations (see Chaps. 2 and 6) must also be applied to capture
elements of the pressure measurement uncertainty such as pressure gauge resolution,
inherent pressure gauge uncertainty, and environmental factors. Use of uncalibrated
measuring and test equipment is not recommended for quality-affecting
measurements and precludes the ability to properly determine total uncertainty.
Nonetheless, uncertainty estimates can be made from manufacturer specification
sheets, although these cannot always be trusted. The pressure gauges used by the
officials did not have associated specification sheets. They were likely both produced
by Hsiung Industry Corp. for Wilson, which does not have a stated accuracy for
these gauges. While the display of the digital gauges read to 0.05 psig, resolution is
rarely indicative of total uncertainty, although it is a contributor. The manufacturer’s
specified uncertainty for similar handheld pressure gauges is 1% of full scale
(20 psig), or no better than 0.20 psig. Without a traceable calibration, this
specification is difficult to prove, and based on performance between gauges
measuring the same football, it is likely worse.
Ultimately, we must combine the uncertainties from the Type A and Type B
evaluations for this direct measurement (see Chap. 6). Without going into detail and
assuming the Type A and Type B uncertainties are uncorrelated, we have for ball #1:
uc ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u2
A þ u2
B
q
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
0:152
þ 0:20
= ffiffi
3
p
2
r
¼ 0:19 psig ð1:1Þ
This combination of terms will be discussed in detail in later chapters. We must still
determine the expanded uncertainty at a desired level of confidence. This is done by
Table 1.1 Game-day data for internal air pressure of eleven different Patriots’ footballs taken at
halftime by officials
Ball
Air pressure, non-logo
gauge (psig)
Air pressure, logo
gauge (psig)
Average air
pressure (psig)
Type A std.
uncertainty (psig)
1 11.50 11.80 11.65 0.15
2 10.85 11.20 11.03 0.18
3 11.15 11.50 11.33 0.18
4 10.70 11.00 10.85 0.15
5 11.10 11.45 11.28 0.18
6 11.60 11.95 11.78 0.18
7 11.85 12.30 12.08 0.23
8 11.10 11.55 11.33 0.23
9 10.95 11.35 11.15 0.20
10 10.50 10.90 10.70 0.20
11 10.90 11.35 11.13 0.23
The measurement repeatability is calculated using a Type A uncertainty analysis
6 1 Introduction

multiplying our uncertainty in Eq. (1.1) by an appropriate coverage factor. The
coverage factor is determined by calculating effective degrees of freedom (see
Chap. 6). The degrees of freedom for the Type A uncertainty is relatively straight-
forward: the number of measurements minus (n-1). Since the gauges were not
calibrated, and the specification sheet for the specific gauges used was not available,
our estimate of the Type B uncertainty could have large variability (say up to 50%).
Therefore, the Type B degrees of freedom will be low, as determined from
Eq. (11.22) (see Chap. 11). Assuming 50% relative uncertainty gives us
two degrees of freedom. Ultimately, we can compute an expanded measurement
uncertainty at a 95% level of confidence for ball #1:
U ¼ t95 νeff
ð Þ uc ¼ 4:3 0:19 psig ¼ 0:81 psig ð1:2Þ
Therefore, the complete measurement result for the internal pressure of ball #1 is
11.7 psig 0.81 psig at a level of confidence of 95% (k ¼ 4.3).
The test uncertainty ratio (TUR, introduced in Chap. 5) provides a means of
determining suitability of the measurement when compared to a given requirement.
We can calculate a TUR for the measurement on ball #1 by comparing the total
measurement uncertainty for football air pressure against the requirement in the
NFL rulebook (13.0 psig 0.5 psig):
TUR ¼
Specification Limit
Total measurement uncertainty
¼
0:5 psig
0:81 psig
¼ 0:62 ð1:3Þ
Typically, a TUR of 4 or greater is required to mitigate false accept and
false reject risk (concepts introduced in Chap. 5). A TUR of 0.62 indicates the
measurement equipment and process is not sufficiently accurate to determine
whether or not the requirement was met. The use of uncalibrated gauges and
this uncertainty analysis tells us that the football pressure data alone was not
adequate to conclusively determine whether the true value fell within or outside
the requirement.
Ideally the referees would have performed a well-designed Gauge RR study
(see Chap. 9) to separate out the individual contributors to measurement uncertainty.
Such a study would have resulted in an analysis of variance (ANOVA) to model
uncertainties due to operators and gauges and a Type A evaluation of uncertainty
with many more degrees of freedom.
The saga of football pressure measurement does not end there, however. In the
subsequent investigation (Wells Jr. et al. 2015), a firm was hired to characterize
the pressure gauges used for the game-day measurements. The firm procured a
“master” pressure gauge, shown in Fig. 1.5, with “NIST traceable calibration”
from an unaccredited vendor in an attempt to calibrate the game-day gauges after
the fact. Any vendor, laboratory, or individual can claim traceability to the National
Institute of Standards and Technology (NIST). However, laboratory accreditation
to a standard such as ISO/IEC 17025, through a reputable accrediting body, is
necessary to demonstrate competence in calibration (concept discussed in Chap. 3).

In addition, the so-called calibration of the handheld game-day pressure
gauges after the fact is not a valid practice (see Chap. 3) and only constitutes a
characterization. There is no way to guarantee that the gauges performed the same on
game-day due to drift and other factors. The uncertainty of the “master” gauge, and
uncertainties in general, was not considered or incorporated. An uncertainty or
tolerance must be assigned to a unit under test (UUT) during a valid calibration.
While other evidence, such as interviews with players, ofﬁcials, and equipment
personnel, along with text message conversations ultimately weighed on the out-
come of the investigation and sanctions by the NFL, the centerpiece of the case
was untraceable measurements of internal football air pressure using equipment with
an unacceptably low test uncertainty ratio. As seen in this example, concepts of
measurement uncertainty, uncertainty propagation, calibration, and traceability
have important implications in sports and legal investigations but are unfortunately
not always applied properly. Decisions made on measurement data are only as good
as the uncertainties that come with it.
1.5 Fatality Rates During a Pandemic
An infectious disease is spreading around the globe, with dire predictions of
lethality. Shortly after the World Health Organization (WHO) announces a
Phase 6 pandemic alert and the USA declares a Public Health Emergency, fatality
Fig. 1.5 “Calibrated” master gauge experiment. Traceability was based on calibration provided
from an unaccredited laboratory (Exponent 2015)
8 1 Introduction

rate estimates are as high as 5.1%. The U.S. Centers for Disease Control and
Prevention (CDC) is releasing supplies from the Strategic National Stockpile.
School closures and community level social distancing are being implemented in
certain areas of the USA. The CDC is recommending that colleges suspend classes
through the Fall. Certain countries have instituted travel restrictions and quarantine
requirements. Panic buying of food items and consumer goods is rampant.
This is not 2020. This is 2009, and the Swine Flu pandemic, caused by a novel
strain of the H1N1 influenza virus (H1N1/09), is underway. Despite initial reports of
fatality rates up to 5.1%, with an estimate of 0.6% across all countries considered
(Vaillant et al. 2009), the final estimated fatality rate for the 2009 pandemic was
0.02% (Simonsen et al. 2013; Baldo et al. 2016). The difference in preliminary and
final estimated fatality rate represents a 30-fold decrease. Given the extraordinary
importance of predicted fatality rate in determining appropriate response to a
spreading pandemic at national, regional, and local levels, how could the initial
estimates have been so far off? The answer is because of measurement uncertainty
and sampling bias.
Underestimation of fatality rate in the initial stages of a pandemic may prevent
government leaders and policymakers from implementing appropriate mitigation
and quarantine strategies, leading to millions of excess deaths. Overestimation of
fatality rate can lead to panic, unnecessary quarantines at national, regional, and
local levels, along with irreversible damage to the economy and the livelihoods
of millions of people. Proper estimation of fatality rate during a pandemic, along
with calculation and communication of associated uncertainties and measurement
limitations, is critical for proper decision-making. Yet we see limited attention given
to these important aspects of the problem.
Determination of fatality rate due to a disease represents an indirect measurement
(introduced in Chap. 6). Even with the most accurate measurements of input
parameters, uncertainty in the measurement model itself frequently can lead to
grossly inaccurate estimates of a measurand (see Chap. 2). Here we will begin by
formulating a simple measurement model (“Model 1”) for fatality rate that was
used in initial estimates for H1N1:
CFR ¼
Ndeaths
Ncases
100: ð1:4Þ
Here the CFR is the “case fatality rate” in percent. CFR is crucial for predicting
clinical outcomes in patients infected with a disease and estimating disease burden
on society. The term is somewhat of a misnomer, as it does not constitute a rate,
although the numerator and denominator are usually derived over some time period.
Per the U.S. CDC, the CFR is (Dicker et al. 2012):
The proportion of persons with a particular condition (e.g., patients) who die from that
condition. The denominator is the number of persons with the condition; the numerator is the
number of cause-specific deaths among those persons.
Ndeaths and Ncases represent the number of deaths from disease X and the number
of cases of disease X, respectively. Simple enough? This represents the measurement
1.5 Fatality Rates During a Pandemic 9

model and is effectively the model used by Vaillant et al. (2009) for initial CFR
estimates of H1N1/09 infections during the Swine Flu pandemic.
The standard combined uncertainty (introduced in Chap. 6) for the CFR based on
this model will be
uCFR ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
100
Ncases
2
u2
Ndeaths
þ
100 Ndeaths
Ncases
2
u2
Ncases
s
: ð1:5Þ
Taking the data for the USA, Vaillant computed a CFR of 0.6% based on
Ndeaths ¼ 211 and Ncases ¼ 37,246, where the number of deaths and cases
were taken from data reported in CDC bulletins up to July 16, 2009. While no
uncertainties are provided, we can look at the effects of relative uncertainties of
inputs to determine if this could lead to the gross error in the initial estimate.
An uncertainty of 25% in each input parameter yields a standard uncertainty in
CFR of 0.20% (~0.40% at k ¼ 2). Does the true value for fatality rate fall in
this interval? Probably not, based on later revised estimates. What are we missing?
The error could be in the model itself. While for developed countries with
adequate testing capability, the term in the numerator should be somewhat
representative of the reality, the term in the denominator may not be. Ncases is
typically derived from the confirmed positive case count (via a positive result from
diagnostic testing for disease X). Can you think of any problems with this approach?
For a rapidly spreading disease, if CFR is calculated using aggregate numbers at
a single point in time, estimates can be misleading due to the non-negligible
number of infected patients whose outcome (death or survival) is unknown
(Ghani et al. 2005). In addition, for a disease such as influenza, where a number of
cases are mild, or even asymptomatic, the measurement model in Eq. (1.4) is not
adequate in determining true fatality rate. The true number of cases will likely
be significantly higher, even orders of magnitude higher, skewing the fatality
rate. This effectively represents a selection bias (or sampling bias), whereby only
the sickest patients are tested for disease X, thereby artificially increasing the
fatality rate.
Even with adjustment and more complex models, CFR estimates can be
misleading, especially early in an epidemic or pandemic. Using the number of
individuals infected in Mexico by late April, WHO estimated a CFR of 0.4%
(range: 0.3–1.8%) for H1N1/09 (Fraser et al. 2009). These estimates are still an
order-of-magnitude higher than final estimates due to a significant undercount of
the true number of infections.
Later estimates by the U.S. CDC (Reed et al. 2009; Shrestha et al. 2011) and in
other countries (Kamigaki and Oshitani 2009; Baldo et al. 2016; Simonsen et al.
2013) incorporated a measurement model more akin to the following:
CFR ¼
Ndeaths
a Ncases
100 ð1:6Þ
10 1 Introduction

where a is a multiplier that adjusts the reported number of cases to more adequately
estimate the actual number of cases. This model (which we will call “Model 2”) is
illustrated in Fig. 1.6.
Specifically, for determining number of deaths and number of H1N1/09 cases in
the USA, Reed et al. (2009) and Shrestha et al. (2011) used a more complex model,
relying on the number of hospitalizations from select hospitals (across 60 counties)
participating in the CDC Emerging Infections Program (EIP) surveillance as a more
reliable estimator:
CFR ¼
c1 c2
P
60
i¼1
ndeaths,i

c3 c4 c5
P
60
i¼1
nhospitalizations,i
ð1:7Þ
In this expression,
P
60
i¼1
ndeaths,i ¼ the number of reported fatalities from H1N1/09 over
the 60 counties sampled, including deaths outside of hospitals,
P
60
i¼1
nhospitalizations,i ¼ the
number of reported hospitalizations from H1N1/09 over the 60 counties sampled, c1 ¼
a factor to correct for underestimate of deaths, c2 ¼ a factor to extrapolate the number of
sampled deaths to a national estimate, c3 ¼ a factor to correct for underestimate of
hospitalizations, c4 ¼ a factor to extrapolate the number of sampled hospitalizations to a
Symptomac Cases
Confirmed Posive Cases
(via tesng)
Cases Requiring
Hospitalizaon
Deaths
Asymptomac Cases
Denominator,
Disease X
Fatality Rate
(Model 2)
Denominator,
Disease X
Fatality Rate
(Model 1)
Extrapolaon
Fig. 1.6 Illustration depicting different measurement model inputs for fatality rate of disease X.
Failure to account for unreported cases can lead to significant overestimates of fatality rate.
However, extrapolation is required to estimate unreported case count and leads to large
uncertainties. Adapted from Reed et al. (2009), Shrestha et al. (2011), and Verity et al. (2020)
1.5 Fatality Rates During a Pandemic 11

Another Random Document on
Scribd Without Any Related Topics

In March, 1648, he found that further action was necessary. He
declared that one-fourth of the houses had been turned into taverns
for the sale of brandy, tobacco and beer, and that they were
detrimental to the welfare of the community; he therefore issued a
set of rules for their regulation. No new tap-houses should be
opened without the unanimous vote of the Director and Council.
Those who had been tapsters could continue as such for four years
at least, but in the meantime, should seek some other means of
livelihood, so as not to be dependent on it. Orders as to closing at
nine o’clock every night and on Sundays were repeated. Tapsters
were to report all fights or disorderly conduct in their places, and
physicians were to report all cases where they were called on to
dress wounds received in such disturbances. This does not
necessarily indicate that New Amsterdam was at this time a
disorderly place, for like New York of the present day, it was a
cosmopolitan city. The population at that time was not over five
hundred souls, and it has been declared that eighteen different
languages were spoken by the inhabitants.
Litschoe’s
Tavern
Some time previous to the year 1648 Daniel Litschoe established an
inn on what is now Pearl Street in the outskirts of the town, which
became the resort of the country people coming in from Long Island.
Litschoe came out to New Amsterdam with the earliest settlers as
ensign in the military service of the Dutch. He was with Stuyvesant
at Beverwyck and on his order hauled down the lord’s colors. He also
went out with Stuyvesant in the expedition against the Swedes on
the Delaware as lieutenant.
The tavern seems to have been a good-sized building, for it is
spoken of as “the great house,” but this is to be taken as in
comparison with its neighbors. It had at least a quarter of an acre of
ground attached to it, and stood back some little distance from the
street. A part of the lot is now covered by No. 125 Pearl Street. In
the spring of 1651, Litschoe leased this house to Andries Jochemsen,

who kept it as a tavern or ale house for many years and had lots of
trouble with the authorities. He would tap on Sundays and after nine
o’clock, and his house was the resort of disorderly persons. After
keeping tavern for some years in a house which he had built just
outside the city wall, Litschoe purchased a lot inside the wall
between it and the house he had resided in some years before, and
here he, and after his death in 1662, his wife, Annetje, kept a tavern
for many years.
When Sir Henry Moody came from Virginia in 1660 to exchange
ratifications of the treaty to regulate commerce between that colony
and New Netherland he was received with all the usual diplomatic
honors. Two members of the council, under escort of halberdiers,
were sent “to compliment him in his lodgings,” and Moody,
appearing in the fort, presented his credentials. He resided a
considerable time at the house of Daniel Litschoe and when he left
the city he failed to settle his score, for which his library left at the
house was sold. More people came into the city over the river road
from the Long Island ferry than from any other direction, and
Litschoe’s tavern near the city gate was an inviting resting place. It
was one of the stations where fire-buckets were kept for use in
cases of emergency.

WATER GATE, FOOT OF WALL STREET
The city wall, above mentioned, was a line of palisades straight
across the island along the northerly side of the present Wall Street,
passing through the present Trinity Churchyard. On the inside of the
palisades was an embankment and a ditch. It was built in the year
1653, when England and Holland were at war and New Amsterdam
was threatened by the New England colonists. Through this line of
defence there were two gates, the land-gate at the present junction
of Broadway and Wall Street and the water-gate at the river road or
present Pearl Street.
Peter
Cock’s
Troubles to
Obtain a
Wife
Peter Cock added much to the piquancy of the gossip of the taverns
and the town when, in 1653, probably no longer a soldier, he
brought suit against Annetje Cornelissen Van Vorst, claiming the

fulfillment of a promise of marriage. The case occupied the time and
attention of the Court of Burgomasters and Schepens at a great
many sessions, statements and counter-statements being presented
to the Court, who, considering the case too large for them, sent it,
with the papers, to the Director and Council for their decision. It was
sent back to the Court of Burgomasters and Schepens, with a
recommendation to appoint a committee to examine the papers and
report. The final decision, pronounced May 18, 1654, was that the
promise was a binding contract. From this decision Annetje
appealed, but it was confirmed. In some way Annetje obtained a
release, at any rate, she married November 11, 1656, Claes Jansen
Van Purmerendt, a tobacco planter of Paulus Hook. Peter consoled
himself with another Annetje, for on June 13, 1657, he married
Annetje Dirks, of Amsterdam.
In 1661 Annetje Cock was a widow and in control of the tavern
which Peter Cock had left. She asked permission to build a new
house on the southeast corner of the lot, which request was refused,
as it would be too near the fort. Her husband had contracted for the
building of a house on the lot, which she claimed was voided by his
death, and wished to make a new contract with others, but the court
decided that the old contract was binding. A new house was built
which was kept by her as a tavern for many years.
A Dutch
Tavern
The taverns of New Amsterdam were probably modeled somewhat
after those of Holland, for the Dutch were a people who stuck to the
customs of the fatherland. The description of a Dutch tavern, from
the journal of one of our citizens who visited a part of the
Netherlands where customs have not changed for centuries is here
given.
“It was the business of the good vrow or her maid to show up the
traveller, and open the doors in the smooth partition of the box
which was to receive his weary limbs for the night, and which
otherwise he might not be able to discover, and after he crept into it,

to come back again and blow out the candle, and in the morning to
draw the curtains of the windows at the hour he fixed to rise. There
was generally one room in which all the guests were received, and
where there was a pleasant reunion in the evening, and all the
visitors ate, drank and smoked. It had, in one corner, a closet,
which, when opened (and, honestly, it was not unfrequently
opened), disclosed sundry decanters, glasses and black bottles; and,
on one side of the room, a rack in which were suspended by their
bowls a score or two of very long pipes, each one inscribed with the
name of a neighbor or owner. This was the room of Mynheer the
landlord. He had no care beyond this; mevrow was the head of the
house; she attended to all the wants of the guests, and gave them
the information which they might desire. She was always on the spot
as when, with a ‘wet te rusten,’ like a good mother, she bade you
good night, and when, with a ‘hoo-y-reis,’ like an old friend, she
bade you good-by.”
In the contract for building the ferry house on the Long Island side
of the East River for Egbert Van Borsum in 1655, provision was
made for bedsteads to be built in the walls as described above. Thus
an apartment could be made to accommodate several travellers at
night and yet, in day time, present a neat appearance and be used
as a public room. Provision was also made for the closet or pantry,
for it was a source of profit.
A few years later the Ferry Tavern of Van Borsum had acquired such
a reputation, to which the culinary art of Annetje, his wife, greatly
contributed, that it became the resort of the best citizens when they
wished for something extra good, and of the officials of government,
as we find that a bill rendered by Van Borsum in February, 1658, for
wine and liquor furnished the Director and other officers was
ordered to be paid.
A Grand
Dinner
When, in 1658, Captain Beaulieu wished to give a fine dinner to his
friends, he did not go to the tavern of the Worshipful Burgomaster

Martin Crigier nor to that of Lieutenant Litschoe, who entertained
the English Ambassador a few years later, nor yet to the popular
tavern of Metje Wessels; but was influenced, for some good reason,
to go to the house of Egbert Van Borsum, the Ferry Tavern on the
Long Island side of the river. Here the Captain and his thirteen
friends sat down to a dinner for which Van Borsum, if the record is
correct, charged him three hundred and ten florins, or at the rate of
nine dollars per plate; and it appears that it was worth the price, for
although Beaulieu was sued by Van Borsum for the bill, his defence
was that he was to pay only one-half of the expense, the other half
to be paid by a few of the other guests. No complaint was made that
the amount charged was excessive. Annetje Van Borsum testified
before the Court that she made the arrangement and bargain with
Beaulieu alone and looked to him for payment. The Court took this
view and gave a verdict against Beaulieu for the full amount.
Annetje Van Borsum must certainly have been a fine cook, and the
dinner must have been served with some expensive accessories, of
the nature of which we can hardly surmise. It serves to show that
New Amsterdam, even at this early period, was not entirely devoid
of expensive luxuries (for such must have been the case). After the
death of Egbert Van Borsum, his widow, Annetje, continued the
business for several years, she herself managing the tavern, and her
son, Hermanus, attending to the ferry. In her declining years she
retired to the city of New Amsterdam where she died at a green old
age.
In 1655 Solomon Peterson La Chair, a gentleman of the legal
profession, made his appearance in New Amsterdam, and, as there
was not a promising prospect in that line of business, he rented the
house of Teunis Kray, on the Graft, and petitioned the Burgomasters
and Schepens for permission to keep it as a tavern, which could be
managed by his wife in his absence on legal business, and would be
of great assistance to him in gaining a livelihood. Permission was
granted. He afterwards bought the house of Kray, agreeing to pay
for it in instalments; but as Kray had formerly sued him for the rent
he had now to sue him for the very first instalment; and he never

succeeded in paying for it, the money, even when he had it ready, as
he says, slipping through his fingers. He did not pay anyone he
owed until forced to. He used every means which his learning in the
law and his own ingenuity could devise to avoid paying his just
debts. He was impecunious and improvident and constantly in
trouble; yet he was a man of considerable learning and ability, as
evinced by his register of business as a notary, a volume of some
three hundred pages, which was discovered in the county clerk’s
office some years ago. He obtained a license to practice as a notary
in 1661. La Chair, defaulting in payment, Kray came again in
possession of the house he had sold, and La Chair moved to a house
in Hough Street, where he continued to keep a tavern until his
death, a few years later. There was much discussion in the little
town on political matters, and La Chair, as a man versed in the law,
could probably attract many to his house, where, no doubt, such
subjects were thoroughly discussed.
November 26, 1656, a petition was presented to the Burgomasters
and Schepens from Metje Wessels, requesting permission “to follow
the trade of an eating house and to bring in and tap out wine and
beer,” which was granted.
Metje
Wessels’
Tavern
Metje Wessels’ house was situated on The Water, which was what is
now the north side of Pearl Street, between Whitehall and Broad
Streets, in the busiest part of the little city, and not far from the City
Hall. It became a noted place for Burgomasters’ dinners, and was a
popular place for festivities of all kinds, characteristic of the taverns
of this period. The Burgomasters and Schepens of New Amsterdam
had discovered the toothsome terrapin, for which their successors,
the aldermen of New York City, were, years ago, known to be
particularly partial, and their dinners at the widow’s tavern were no
doubt supplied with this delicious viand. Van der Donck, writing in
1656, says: “Some persons prepare delicious dishes from the water

terrapin which is luscious food.” Here men went on the arrival of a
ship, to meet the skipper and hear the news from the fatherland or
from other foreign ports. Here were discussed the tidings from up
the river, where many young men were making adventurous
excursions among the Indians, in the far-off northern wilderness, in
the profitable business of gathering furs. The trade in furs, the
Indian troubles, the military expeditions, the Dominie’s sermons and
the Director-General’s proclamations,—these, and a great many
more, both public and personal matters—were talked over. It was a
sort of business and social exchange where were gathered and
distributed news and gossip of all kinds.
“THEY HAD DISCOVERED THE TOOTHSOME TERRAPIN”

Dutch
Festivities
The Dutch of New Amsterdam had a large capacity for enjoyment
and in their holiday season of Christmas and New Year, gave
themselves up to every kind of festivity and sport that the place
could afford. We find from records that some of these were firing of
guns, beating of drums, dancing, playing of tick-tack, bowling,
playing of ninepins, sleighing parties or wagon rides, etc. The
taverns and taprooms were full of life and there were likewise many
family festivities and amusements, where the tables were loaded
with all the good things to eat and drink that were obtainable. Not
only was it the season of the delight and enjoyment of the young
and gay, but the older and graver citizens joined in the sports with
enthusiasm and encouragement. Even the Burgomasters and
Schepens, with the other officials, when the season of festivity
approached, closed the public offices temporarily. “Whereas,” it is
recorded, “the winter festivals are at hand, it is found good, that
between this date and three weeks after Christmas the ordinary
meetings of the Court shall be dispensed with.”
Gathered together to celebrate one of the anniversaries of the
festive season, the flickering lights from oil lamps and tallow
candles, reflected from the whitewashed walls of Madame Wessels’
assembly room, shone on as happy and gay hearted a gathering as
is found in the magnificent and brilliantly lighted halls of our present
grand city. They shone on “fair women and brave men.”
Notwithstanding the humorous caricatures of Washington Irving, the
women were comely and the men were a sturdy and adventurous
lot. Here was the government official, with his sword at his side.
Here was the prosperous trader or merchant in his silk or velvet
breeches and coat flowered with silver lace, with gold or silver
buttons, lace neck cloth and silk stockings. He also wore a sword.
The common burgher in his homespun breeches and Kersey coat
also took a part. Handsome dresses, displayed on female forms were
not numerous but there were some that indicated the success and
prosperity of the heads of the families represented by the wearers.

Gowns of thick embroidered silk and petticoats of cloth and quilted
silk graced the festive dance.
May-day was also celebrated with great spirit and on this occasion
the people were accorded by the city magistrates the greatest
license. It was announced that “any damage which may come from
the general rejoicing within the city on May-day shall be made
known to the Burgomasters at the City Hall immediately thereafter
when means shall be taken to furnish reparation.”
But Governor Stuyvesant had no sympathy for such “unprofitable
customs,” and such “unnecessary waste of powder.” He forbade on
New Year and May-days, the firing of guns, the beating of drums or
the planting of May-poles, and ordered that at these times there
shall not be “any wines, brandy-wines or beer dealt out.” It is
supposed that this ordinance was not strictly enforced and that its
restrictions were little observed.
Stuyvesant also, in February, 1658, forbade the farmers and their
servants to “ride the goose” at the feast of Bacchus and Shrovetide,
which brought a protest from the Burgomasters and Schepens, who
felt aggrieved that the Director General and Council should have
done so without their knowledge and consent. “Riding the goose,” or
“pulling the goose,” was a cruel sport, but it was not the fate of the
goose that moved the tender heart of Stuyvesant. He says in
response to the protest that “in their time it has never been
practiced here, and yet, notwithstanding the same may in some
place of the fatherland be tolerated and looked at through the
fingers, it is altogether unprofitable, unnecessary and criminal for
subjects and neighbors to celebrate such pagan and Popish feasts,
and to practice such evil customs.” He then gives the Burgomasters
and Schepens a sound scolding for their presumption, and informs
them “that the institution of a little bench of Justice under the title of
Schout, Burgomasters and Commissioners does in no wise interfere
with or diminish aught of the power and authority of the Director
General and Councellors in the enacting of any ordinance or making

any particular interdict, especially such as tend to the glory of God
and the best interests of the Inhabitants.”

II
New York and the Pirates
The
English in
New York
When the English captured New Amsterdam, the heart of the British
soldier was no doubt cheered and gladdened by the sight of the Sign
of Saint George and the Dragon, which was boldly hung out in front
of the house looking out on the river on the west side of the present
Pearl Street just above Maiden Lane, kept by James Webb, from
London. It was a stone house which had been built more than
fifteen years before by Sander Leendertsen (Alexander Lindsay),
upon the site of the present 211 Pearl Street. When in March, 1665,
the citizens were called upon to state how many soldiers they could
lodge, the entry is made in the records that “The Man of the Knight
of St. George will take one,” which undoubtedly refers to the
landlord of this house. Webb, in 1665, married Margaret Radel, a
widow, and probably kept the house for some years. It was on the
road leading to the Long Island ferry, a favorite location for taverns.
Although Colonel Nicolls, the first deputy Governor for his Royal
Highness, James, Duke of York, is said to have filled his purse from
the proceeds of land grants and by compelling the holders of old
grants to pay him for confirmation, and to have been active in
adding to his profits in many other ways, and, although he was
given despotic power, yet his rule was characterized by so much
leniency and moderation, compared with the paternal, though
arbitrary, rule of Peter Stuyvesant, that he became as popular with
the inhabitants as, under the circumstances, could be expected.
When, at the end of four years, he solicited and obtained his recall,
a grand dinner was given him at the house of Cornelis Steenwyck,

one of the most prominent Dutch merchants of the city, and two
militia companies, the Dutch officers of which had received their
commissions from him, escorted him to the ship which was to bear
him to England.
“THE MAN OF THE KNIGHT OF ST. GEORGE”
The English officials were naturally desirous of introducing English
ways and customs. Moved by this spirit, Governor Nicolls, to
encourage the English sport of horse-racing, established a race-
course at Hempstead, Long Island, which was continued and kept up
by his successors, who issued proclamations, directed to the
justices, that races should be held in the month of May.

New York, when it came into the hands of the English, was
thoroughly Dutch, and the Englishman was not pleased by the ways
and customs of the Dutch in tavern life, so different from the
English. In a tavern conducted in the Dutch way, where the landlord
and all the attendants spoke the Dutch language, the government
officials and the English officers did not feel that ease and comfort
that they would in a truly English inn.
The prominent Dutch taverns continued to flourish, but in the course
of time, there was a gradual change, produced by the English
influence. The Dutch tavern keeper differed much from the inn-
keeper of England, and the newcomers, assuming the airs of
conquerors, accustomed to the warm welcome of an English inn,
chafed under the restrains which they found or fancied, and many
broils occurred between the landlords and their Dutch countrymen
on one side and the English soldiers and sailors on the other.
The
Governor
Builds a
Tavern
Although previous to this time and some years subsequent, the
records of public business transacted at taverns are numerous, for a
long time after the English came into control, there is no indication
that the taverns were thus much used by the English officials. The
want of a tavern truly English, that would satisfy the officers of the
government, may have been the cause which led Governor Lovelace
to build, in 1672, on his own account, an inn or ordinary right next
to the City Hall, and to ask the magistrates for permission to connect
the upper story of the house with the City Hall by a door opening
into the Court’s Chambers. The proposition was agreed to by the
magistrates, leaving it to the governor to pay what he thought fit for
“the vacant strooke of ground” lying between the buildings and “not
to cut off the entrance into the prison doore or common gaol.”
This door connecting the City Hall and the tavern was meant to
serve, in its way, a very useful purpose, but lacking reliable data in

reference to the part it played in facilitating communication between
the tavern taproom and the halls of justice, we leave each reader to
supply the deficiency by his own opinions on the subject.
Tavern
Regulation
s
It was a uniform custom in the English colonies to make provision
for the care of strangers and to regulate by law the taverns and the
sale of strong drink. By the duke’s laws, which were enacted, or
rather accepted, by representatives of the people at the Hempstead
convention, in 1665, inn-keepers were not allowed to charge “above
eight pence a meal with small beer,” and were required to always
have on hand a supply of “strong and wholesome” malted liquor.
In January, 1676, it was ordered that “all persons who keep publick
houses shall sell beere as well as wyn and other liquors and keep
lodgings for strangers.” It was proposed to the governor by the
mayor and aldermen that six houses be appointed to sell “all sorts of
wine, brandy and rum and lodgings,” and eight to “sell beere, syder,
mum and rum and to provide for strangers as the law directs,” that
two of “the wine houses be ordinaryes, and four of the beere-
houses.” Prices were fixed at which the tapsters should sell. French
wines and Madeira were from one and three pence to two shillings
per quart; brandy at six pence and rum at three pence per gill; beer
and cider were three and four pence per quart. In the ordinary at
the wine house the meal was one shilling and in that at the beer
house it was eight pence; lodging at the wine house was four pence
per night, and at the beer house it was three pence. Thus a sharp
distinction was drawn between the two classes of houses and there
was in all probability as great a difference in their keepers.
First
Merchants’
Exchange
Broad Street had become a desirable place of residence and many
citizens of the better class made it their home. The canal or ditch

through the middle of it, from the present Exchange Place to the
river, would never have been there if New York had not been
originally a Dutch town. Across the canal, near the river, between
the present Stone and Bridge Streets, was a bridge. This was a
favorite lounging place for idlers, where, leaning over the railing of
the bridge, they could watch the ebb and flow of the tide and the
various small boats which went a little way up the canal to discharge
their cargoes of oysters, fish and country produce brought over from
Long Island or other nearby points. It was the center of probably
more stir and activity than any other place in the little city. Here the
merchants had become accustomed to meet for trade and the
transaction of business of various kinds. This induced Governor
Lovelace, March 24, 1669-70, to issue an order establishing a sort of
business exchange. This order specified that the meeting of the
merchants should be between the hours of eleven and twelve on
Friday mornings, at present near the bridge, and the mayor was
directed to take care that they should not be disturbed. The time of
meeting and dispersing was to be announced by the ringing of a
bell. It was the beginning of the merchants’ exchange. This
continued to be the meeting place of the merchants, and near this
spot a building called the Exchange was subsequently built.
Not far away, on the present northwesterly corner of Broad and Pearl
Streets, stood the tavern of James Matthews, who, besides keeping
a tavern, was a merchant and a man of considerable means. The
meeting place for merchants being almost in front of his door his
house was a very convenient place for them to retire to, to
consummate their bargains over a social glass. In 1678 and in 1685
he was one of the farmers of the excise. He died in the latter part of
the year 1685, or early in 1686, and his widow continued to keep
the house for about two years, when she also died. The executors of
her estate petitioned, in March, 1688, for an abatement of £20
excise money.
In September, 1676, Abraham Corbett, “driven with his family from
his home eastward of New England,” petitioned for a license to distill

strong liquors, which was granted him. He became a lieutenant in
the militia in 1684; and was one of the farmers of the excise in
1688, which indicates that he was a man of respectability and
deserving of public confidence. He was also a tavern keeper. When
Samuel Leete, clerk of the Court of Mayor and Aldermen, and an
Alderman of the city, died in 1679, he left to Abraham Corbett, “all
my household goods in part payment of what I owe him for meat
and drink.” By Governor Dongan’s Charter of 1686, Abraham Corbett
was appointed an Assistant Alderman. In 1680 he purchased for
sixty pounds sterling a house and lot on the east side of Broadway,
two or three doors south of the present Exchange Place, and some
years later on this lot he erected a fine tavern, which he called the
“Royal Oak,” where he spent his declining years in its management.
Considering the position which Corbett held in the esteem of the
people there is no doubt that his house received the patronage of
the best class of the community.
In these early days there were no parks, but the open country was
near at hand with all the charms of nature. Just south of the present
Trinity Churchyard was the Governor’s Garden. A large gateway led
to it and to a charming spot—a piece of elevated ground covered
with natural forest—called the “Locust Trees,” which was a resort for
those who enjoyed the open air, where they could look out on the
broad expanse of the Hudson. It was not then covered with that
panorama of moving craft which it now presents. It was the same
majestic river as now, but its surface was unbroken except by a
lonely canoe or a small sail or two lazily drifting up or down the
stream, with the green shores of Staten Island and Pavonia in the
distance.
The road along the East River, beyond the “water gate,” had a
number of dwellings on its upper side. On the way to the ferry a
road joined it called the “Maadge poadge,” or Maiden Lane, and a
little way further another, the present John Street, led up to
Vandercliff’s Orchard, which is said to have been a place of public

resort, owned and kept by Dirck Vandercliff, who was also a
merchant, and in 1687 was an assistant alderman.
A singular incident occurred at this place in 1682. James Graham,
who was an alderman of the city in 1681, recorder in 1683, and
afterwards attorney-general, had, according to evidence, expressed
a desire to make the acquaintance of Captain Baxter, an English
officer recently arrived in the Province, and accordingly a party of
several friends, including Graham and Baxter, met at the tavern of
Dirck Vandercliff in “The Orchard,” to spend a social afternoon and
evening. About nine o’clock, as the company was about to break up,
Graham, after paying the reckoning, was called aside by Baxter, but
not out of the sight of the company. Those present saw Baxter act
as if to kiss Graham, when the latter called out that he had been
stabbed. He had been struck with a knife under the collar bone, the
wound being about four inches deep. Baxter was arrested and
bound over to await his trial in case of Graham’s death, but the
wound did not prove to be mortal.
Wolfert
Webber’s
Tavern
On the hillside at the present Chatham Square, near the Collect or
fresh water pond and the sparkling stream that fed it with the purest
water on Manhattan Island, in a charming retreat, then considered
far beyond the city wall, stood the tavern of Wolfert Webber, built in
the time of the Dutch, and for a long time the farthest outlying
dwelling on the eastern side. We find in the record that in 1655, a
daughter of Wolfert Webber, tavernkeeper, had been returned to him
from her captivity among the Indians. Notwithstanding the danger
from attacks of the Indians, Webber continued to keep this house,
and it was probably patronized by people who wished to enjoy the
pleasures of the quiet and beautiful spot where it was located. In the
marshes or swamps to the northwest, called the Kripple Bush, the
sportsman could, in season, find woodcock in abundance, or he
could enjoy the more gentle sport of angling in the Collect. Although

the eastern side of the Collect was very attractive, the western side,
at one time, was the residence of the very poorest class of people,
and, on account of the stagnant water of the nearby swamps,
considered very unhealthy.
When the Dutch were in possession of the city for the second time
and called it New Orange, Wolfert Webber was made a magistrate
for the Outside People, or those beyond the Fresh Water, and under
the English he was appointed by the Dongan Charter of 1686 an
assistant alderman. He represented the Out Ward as assistant
Alderman in 1688, 1689, 1706 and 1707, and was still keeping the
tavern at this same place. In April, 1715, “enjoying yet good health,
but being ancient,” he made his will, and died a year or two after.
In 1660, on account of the repeated attacks of the Indians on the
outside settlements, an order was issued requiring the abandonment
of isolated habitations, and the gathering of the people in hamlets or
villages for mutual protection. In response to this order there came a
petition from those living beyond the fresh water stream asking that
their houses might be permitted to remain, and that encouragement
be held out to others to build near them so as to form a village. This
request was granted and a village was established near the bowery
of Governor Stuyvesant. A tavern, a blacksmith shop and a few other
buildings formed the settlement to which was added shortly after a
small church, erected by the governor on a part of his farm. To this
farm or bowery Stuyvesant retired when the English had relieved
him of the cares of office. The road leading to this village became
known as the Bowery Road or Lane.
For a time this was the end of the road, but when the English came
into possession of the city, they soon sought to open communication
with the New England colonies by land and with the recently made
settlement of New Harlem. A road was laid out which, in time, was
extended through the whole length of the island to King’s Bridge,
and became the highway of travel for all going to the north or east.
The Two-
Mile Tavern

The tavern which had been set up at the village, as travel increased
became known as the two-mile stopping place, and is said to have
been a famous place of resort. Its situation was admirable, for the
purpose, and it was, no doubt, visited by those making excursions of
pleasure from the city, especially sleighing parties. At this time and
for a great many years this was the only road of any great length on
which such a sport could be enjoyed. For a long time the tavern was
occupied by Adriaen Cornelissen, who was farmer and tavern-keeper.
He was living here in 1674, when the Dutch for the second time
were in possession of New Amsterdam, which they then called New
Orange, and was appointed one of the schepens or magistrates for
the outside people or those beyond the wall. Under the English rule
he was Assistant Alderman in 1684 and in 1687. In 1689 he was
made a captain of militia, his commission bearing date, December
16th of that year.
When, in 1690, commissioners came down from the New England
colonies to confer with those of New York and deliberate on proper
steps to be taken against the French and Indians, they declined to
enter the city on account of the prevalence of small-pox, and
Governor Leisler fixed upon this house as the place of meeting,
describing it as a good, neat house, about two miles from the city,
and kept by Captain Arian Cornelis. Here the commissioners met on
the 1st of May, 1690.
John Clapp
Tavern-
Keeper
A few years later the landlord of this tavern was John Clapp, the
maker and publisher of the first almanac by a resident of New York
City, which he says was “the product of my many spare Minnits.” It
was not the first printed in New York, for Bradford had, for several
years, printed Leed’s Almanac. Clapp claims to have been the first
person in New York to set up a hackney coach, and announces in his
almanac that “about two miles without the City of New York, at the
place called the Bowery, any Gentlemen Travellers that are strangers

to the City, may have very good Entertainment, for themselves and
Horses, where there is also a Hackney Coach and good Saddle
Horses to be hired.” He was a promoter of social festivities, which
well became him as a genial landlord. In the Almanac, under June, is
found the following:
“The 24th of this month is celebrated the Feast of St. John Baptist,
in commemoration of which (and to keep up a happy union and
lasting friendship by the sweet harmony of good society), a feast is
held by the Johns of this city, at John Clapp’s in the Bowery, where
any Gentleman whose Christian name is John may find a hearty
wellcome to joyn in consort with his namesakes.” He notes that John
Clapp’s in the Bowery, two miles from the postoffice, is generally the
baiting place where gentlemen take leave of their Friends going on a
long journey, “where a parting glass or two of generous Wine,
If well apply’d, makes the dull Horses feel,
One Spur i’ th’ Head is worth two in the heel.”
Seven miles from Clapp’s was the half way house, nine miles further
was King’s Bridge, and from King’s Bridge to Old Shute’s, at East
Chester, was six miles.
Excepting that of the governor, it is doubtful if there was a single
equipage for pleasure in the City of New York at this time, and the
ease with which a sled or sleigh could be constructed, which would
smoothly and silently glide over the snow, made sleigh-riding a great
sport during the period when it could be enjoyed. That John Clapp’s
house, at the two mile station, was a great place of resort at such
times, is no mere supposition. We have the testimony of Madam
Sarah Knight, who was in New York in 1704, that this was so. She
had come from Boston to New York on horseback, and the quaint
and humorous way in which she has told the story of her travels has
made her little book a gem for the antiquarian. She says of the New
Yorkers: “Their diversion in the winter is riding sleys about three
miles out of town, where they have houses of entertainment at a

place called the Bowery.” On an excursion with Mr. Burroughs, she
says that she believes that she met that day as many as fifty or sixty
“sleys,” which, she says, “fly with great swiftness, and some are so
furious that they’ll turn out of the path for none but a Loden cart,”
which surely indicates the enthusiasm with which the sport was
enjoyed, and John Clapp, at such times, was, no doubt, a very busy
man.
John Clapp seems to have received an education which made him a
prominent man among the settlers. In the time of Governor Leisler
he was a resident of Flushing, when, “at a town meeting upon Long
Island where divers of the freeholders of the Towns of Hamsted,
Jamaica, Flushing and Newtown wer mett and assembled, to consult
on the lamentable state and condition that Theire Maj’ties liege
subjects lay under; by the severe oppressions and Tyranical
usurpations of Jacob Leisler and his accomplices, it was desired by
the freeholders aforesaid that Capt. John Clapp should write an
humble letter to Their Maj’ties Secr’ty of Stat in all there behalves
and signify to there Maj’ties in what a sad condition we are all in.—
Nov. 7th, 1690.” This is followed by a long letter.
He was clerk of the New York Assembly, in session in New York
during the year 1692. He was also a tavern keeper at that time, and
must have been a man to win the esteem and good will of those
who became his guests. Lucas Santen, who was at one time
collector of the port of New York, and a member of Governor
Dongan’s Council, when he died, in 1692, left “to my landlord,
Captain John Clapp, £40 to buy him a mourning ring, in
consideration of the trouble I have given him.” The next year Clapp
succeeded Cornelissen as landlord of the tavern in the Bowery
village. Here all the travel to the north and east passed his door and
we can hardly believe that any traveler would, without stopping,
pass the door of such a genial and jovial landlord as we are
convinced was John Clapp, and we have reason to believe that his
house was a favorite resort for the people in the city. He was
undoubtedly residing here in 1703, and at some time between this

date and 1710 removed to Rye, in Westchester county, for in the
latter year John Clapp made returns of the names of men from 16 to
60 in the County of Westchester, and he was interested there in
large grants of land.
Towards the close of the seventeenth century there were two
features in the local history of New York City which attract attention.
For many years before the close of the century it was regarded by
the maritime countries of Europe as a protecting port for pirates,
and the political disturbances which resulted in the execution of
Jacob Leisler and Jacob Minhorne continued to divide the community
into two contending factions composed of many bitter partisans.
Trade With
Pirates
Respected merchants from New York sent out ships to the coast of
Africa for slaves, loaded with liquors, arms, ammunition and other
articles, just such as would be desired by pirates, which they
exchanged at tremendous advance in prices for the plunder of these
robbers of the seas, and returned to New York with slaves and the
valuable goods they had thus obtained. One successful voyage was
often sufficient to make the owners of the vessel wealthy, and they
claimed that they were doing nothing wrong; that they had a perfect
right to buy goods of any kind wherever they could purchase them
to the best advantage. With some this trade in the plunder of pirates
was, no doubt, incidental, but it was profitable, although they ran
the risk of being the victims of pirates themselves.
Pirates came into port and were received not only in a friendly
manner, but were even honored by unusual attentions from the
governor, who was apparently interested in their ventures.
William Mason went out of the harbor of New York in 1689 with a
commission as a privateer. He turned pirate, made war on East India
commerce, and reaped a rich harvest of gold and East India goods,
with which he filled his ship. When the ship returned under the
command of Edward Coats, she put in on the east end of Long

Island, where Coats and his crew found a friendly reception, and
learning that they might be favorably received in New York, came
into this port. Coats and his crew, by making valuable presents to
the Governor and his family, and also to members of the Council,
were unmolested. The ship was presented to the Governor, who sold
it for £800. Coats said that his exemption from prosecution cost him
£1,800.
Captain Thomas Tew, who was known as a pirate, and had been the
subject of complaint from the East India Company, came to New
York in November, 1694, and was received by Governor Fletcher on
terms of intimate companionship; was invited to his table, and rode
by his side in his coach and six. He gave elegant presents to the
Governor and his family, and left with a commission as privateer
against the French, agreeing to discharge his cargo in this port. He
went directly to his former field of activity and made his name still
more notorious by his depredations upon the East India commerce.
Bellomont’
s
Difficulties
About this time, John Hoare came to New York and received the
usual commission from Governor Fletcher to act against the French.
He openly avowed that his destination was for the African coast and
recruited for that purpose. From the sequel we can not avoid the
conclusion that there was some kind of an understanding with some
of the merchants of New York, for after he had been absent about a
year they sent out the ship Fortune to Madagascar, loaded with
goods suitable for pirates, where she was met by Hoare’s ship, filled
with valuable plunder. The goods were transferred to the Fortune,
and with a part of Hoare’s crew she returned to New York. At this
time Governor Fletcher, whose dealings with pirates had been
brought to the attention of the British government, had been
superseded by the Earl of Bellomont, whose instructions were to put
a stop to this illegal trade. The cargo of the Fortune, when she
arrived in New York, was secretly gotten ashore in the night, and

stored. By order of Bellomont the goods were seized and officers
were about to remove them, when a large number of merchants
interfered to prevent them from doing it, using violence and locking
the officers in the house, who, after three hours, were only released
by the appearance of the lieutenant-governor and three files of men.
The ship Fortune was forfeited.
Frederick Phillipse, one of the Governor’s Council, and reported the
richest man in New York, expected a ship from Madagascar and to
prevent her arrival in the port of New York with goods that might
subject her to forfeiture, sent out his son Adolphus, on a vessel
ostensibly bound for Virginia, which laid off the port until the
expected vessel arrived, when the East India goods on board were
transferred to her and carried to the Delaware, leaving the

Madagascar ship to enter with only slaves as her cargo. The East
India goods were sent to Hamburg, where they were seized.
“AS GENUINE PIRATES AS EVER SAILED THE SEA”
In taverns of medium and even in some of the better class, could
have been met at this period men who had taken part in captures on
the African coast, and who, over their mugs of ale, entertained their
companions with stories of their adventures, modified somewhat as
suggested by prudence. They were not men of swarthy complexion
and ferocious features, with knife and pistol in belt, as pictured by
the imagination of writers of tales of the sea, yet they were,
nevertheless, as genuine pirates as ever sailed the sea.
For some time, in the latter part of the year 1694, Thomas Tew, the
notorious pirate, was a well known and picturesque figure on the

streets and in the taverns of New York, where he spent money
lavishly, ordering brandy, ale and other beverages for whoever would
drink with him. He was a man about forty years of age, of slight
figure and dark complexion; richly and strikingly dressed. He wore a
blue cap with a band of cloth of silver, and a blue jacket bordered
with gold lace and ornamented with large pearl buttons. Loose
trunks of white linen extended to his knees, where they were joined
by curiously worked stockings. From his neck hung a rich chain of
gold, and in his belt, curiously knit, he carried a dagger, its hilt set
with the rarest gems.
The exciting events of the Leisler period had left in the body politic a
festering sore that would not heal. The Leislerians believed that the
execution of Jacob Leisler and his son-in-law, Jacob Minhorne, had
been nothing less than murder, and their relatives and friends were
active in England in endeavors to revive the honor of their names
and to reverse the attainder of their estates. In this situation of
affairs it can readily be seen that there was much uneasiness and
excitement in the community, and the taverns were the centers of all
this boiling and agitated disturbance in the mercantile and political
life of New York.

CAPTAIN TEW
The bitter opposition which Bellomont received from the merchants
and the wealthiest of the people of New York compelled him to look
to the Leislerians for support and to appoint to office members of
that party. He seems besides to have been moved to take this step
from a conviction that great injustice had been done. A few extracts
from his letters will tend to show the situation as he viewed it.
From a letter of the Earl of Bellomont to the Board of Trade, dated
September 21, 1698:
“The Jacobite party in this towne have a clubb commonly every
Saturday (which was Colonel Fletcher’s clubb day). Last Saturday
was seaven night, there mett twenty seaven of them, their

ringleaders are Colonel Bayard, Colonel Minviele, both of the
Councill, Mr. Nicolls, late of the Councill, and Wilson, late Sheriff of
this towne; there is so great a rancor and inveterancy in these
people that I think it by no means proper for me to leave this
province till I have your Lordship’s orders upon the representations I
made to your Lordships by the Richmond Frigatt, and since by Mr.
Weaver; for I do verily believe if I should goe from hence, the
people would fall together by the ears, besides, should I goe away, it
would give the faction great advantage, and would tend very much
to the revenue ceasing, and the measures I have proposed to myself
for the obtaining the continuance of this present revenue would be
thereby frustrated. This the Faction know very well, and therefore
are very free in their wishes that I were gone to my other
governments.”
To Mr. Popple, Secretary of the Board of Trade, he writes:
“This day another instance happen’d of the brutishness of some of
the people here. The Master of the ship that carries this packet, was
with me last Tuesday and promised to call on me on Thursday for
the King’s packetts, but it seems intended to disappoint me and
leave my letters behind and begon his voyage. I refer you for an
account of this man’s behavior to the inclosed certificate and
warrant, only this I must tell you, I sent yesterday the Commissioner
of the Customes Mr. Hungerford to pray him to come to me and
receive the King’s packetts, and he swore he would not for all the
Governours in Christendom, and he would not be Post Boy to carry
letters for any body; which refusal of his made me send a warrant to
bring him by force. The angry merchants of this town had without
doubt encouraged this man to be thus insolent, or he durst not have
refused to carry the letters, after promising me faithfully, he would
call for and carry them. This is another specimen of the rage and
malice of these people, who I am satisfied nothing but fear keeps
from rebelling against the Government; unlawful trade and Arabian
gold brought in by Pirat ships from the Red Sea are the things they
thirst after.”

On October 18, 1700, he wrote to Secretary Vernon, as follows:
“The Lords of the Councill of Trade direct me to make an experiment
in working some navall Stores here, with the soldiers. I cannot go
about it with such Officers who I believe would rather traverse me in
such a design than further it; and would I fear stir up a mutiny
among the sould’rs, if I should propose to ’em the working of Navall
Stores for the King. I am not for breaking those Lieut’s, but
exchanging them for honest, good Lieut’s in some of the Regiments
in England. My first Lieut’s name is Peter Matthews, bred up from a
child with Coll. Fletcher ’tis at his house that the angry people of
this Town have a Club and hold their cabals; my second Lieut’s is
John Buckley; there is also another Lieut, in Maj’r Ingoldesby’s
Company whose name is Matthew Shank, a most sad drunken sott,
and under no good character for manhood. I desire also he may be
exchanged for a better man from England.”
Colonel Fletcher, on his return to England, asked for an examination,
which was accorded him by the Lords of Trade. Plausible
explanations were made of his conduct, but they were not
convincing, and the Lords of Trade recommended that the charges
be referred to the Attorney-General for further action. The King,
however, seems to have interposed, as there is no evidence of
further proceedings against him. Of his subsequent career nothing is
known.

III
The Coffee House
An Exciting
Election
In September, 1701, a very exciting election took place in the city.
Thomas Noell, the mayor, was commissioned and sworn into office
on the 14th day of October, 1701. The returns of the election for
aldermen and assistant aldermen, which gave the Leislerians a
majority in the board, were contested in some of the wards and a
scrutiny was ordered by the mayor, who appointed committees,
composed of members of both parties, to examine the votes in the
contested wards. Some of the Leislerians, who were appointed on
these committees, refused to serve, claiming that it was irregular;
nevertheless, the scrutiny was completed, and those declared
elected, after much excitement and disturbance, finally took their
seats at the board. Among those who were declared elected was
John Hutchins, landlord of the Coffee House or King’s Arms, situated
on the west side of Broadway, next above Trinity Churchyard, where
the Trinity Building now stands. He had represented the West Ward
as alderman in 1697. In 1698 he was returned as elected, but his
election was contested, and his opponent, Robert Walters, was
declared elected. He was now again alderman of the West Ward. He
had come out with Governor Sloughter as a lieutenant in the regular
service and had since then, for the most part of the time, made his
residence in New York City. He was one of the signers of a petition
stating grievances at New York in 1692 and 1693, during Fletcher’s
rule. In this paper it is stated that Lieut. John Hutchins was
imprisoned at Albany and sent to New York, and coming before
Governor Fletcher, was suspended and kept out of his pay, because
he had favored the cause of Leisler, and had endeavored to

Welcome to our website – the ideal destination for book lovers and
knowledge seekers. With a mission to inspire endlessly, we offer a
vast collection of books, ranging from classic literary works to
specialized publications, self-development books, and children's
literature. Each book is a new journey of discovery, expanding
knowledge and enriching the soul of the reade
Our website is not just a platform for buying books, but a bridge
connecting readers to the timeless values of culture and wisdom. With
an elegant, user-friendly interface and an intelligent search system,
we are committed to providing a quick and convenient shopping
experience. Additionally, our special promotions and home delivery
services ensure that you save time and fully enjoy the joy of reading.
Let us accompany you on the journey of exploring knowledge and
personal growth!
textbookfull.com

Introduction to Statistics in Metrology Stephen Crowder

More Related Content

Similar to Introduction to Statistics in Metrology Stephen Crowder (20)

Recently uploaded (20)

Introduction to Statistics in Metrology Stephen Crowder