Applied Statistical Inference with MINITAB Sally Lesik

Visit ebookfinal.com to download the full version and
explore more ebooks or textbooks
Applied Statistical Inference with MINITAB Sally
Lesik
_____ Click the link below to download _____
https://ebookfinal.com/download/applied-statistical-
inference-with-minitab-sally-lesik/
Explore and download more ebooks or textbook at ebookfinal.com

Here are some recommended products that we believe you will be
interested in. You can click the link to download.
Statistical Inference Vijay K. Rohatgi
https://ebookfinal.com/download/statistical-inference-vijay-k-rohatgi/
Statistical Inference 2nd Edition George Casella
https://ebookfinal.com/download/statistical-inference-2nd-edition-
george-casella/
Introductory Statistical Inference 1st Edition Nitis
Mukhopadhyay
https://ebookfinal.com/download/introductory-statistical-
inference-1st-edition-nitis-mukhopadhyay/
Probability and Statistical Inference 2nd Edition Robert
Bartoszy■ski
https://ebookfinal.com/download/probability-and-statistical-
inference-2nd-edition-robert-bartoszynski/

Statistical Models and Causal Inference A Dialogue with
the Social Sciences 1st Edition David A. Freedman
https://ebookfinal.com/download/statistical-models-and-causal-
inference-a-dialogue-with-the-social-sciences-1st-edition-david-a-
freedman/
Essentials of Statistical Inference 1st edition Edition G.
A. Young
https://ebookfinal.com/download/essentials-of-statistical-
inference-1st-edition-edition-g-a-young/
GARCH Models Structure Statistical Inference and Financial
Applications Christian Francq
https://ebookfinal.com/download/garch-models-structure-statistical-
inference-and-financial-applications-christian-francq/
Statistical Physics Optimization Inference and Message
Passing Algorithms 1st Edition Florent Krzakala
https://ebookfinal.com/download/statistical-physics-optimization-
inference-and-message-passing-algorithms-1st-edition-florent-krzakala/
Constrained Statistical Inference Inequality Order and
Shape Restrictions 1st Edition Mervyn J. Silvapulle
https://ebookfinal.com/download/constrained-statistical-inference-
inequality-order-and-shape-restrictions-1st-edition-mervyn-j-
silvapulle/

Applied Statistical Inference with MINITAB Sally Lesik
Digital Instant Download
Author(s): Sally Lesik
ISBN(s): 9781420065848, 142006584X
Edition: Har/Cdr
File Details: PDF, 14.83 MB
Year: 2009
Language: english

Applied Statistical Inference
with MINITAB®
C6583_C000.indd 1 11/20/09 11:11:47 AM
© 2010 by Taylor & Francis Group, LLC

C6583_C000.indd 2 11/20/09 11:11:48 AM

STATISTICS: Textbooks and Monographs
D. B. Owen
Founding Editor, 1972–1991
Editors
N. Balakrishnan
McMaster University
William R. Schucany
Southern Methodist University
Editorial Board
Thomas B. Barker
Rochester Institute of Technology
Paul R. Garvey
The MITRE Corporation
Subir Ghosh
University of California, Riverside
David E. A. Giles
University of Victoria
Arjun K. Gupta
Bowling Green State
University
Nicholas Jewell
University of California, Berkeley
Sastry G. Pantula
North Carolina State
University
Daryl S. Paulson
Biosciences Laboratories, Inc.
Aman Ullah
University of California,
Riverside
Brian E. White
The MITRE Corporation
C6583_C000.indd 3 11/20/09 11:11:48 AM

STATISTICS: Textbooks and Monographs
Recent Titles
Nonparametric Statistical Inference, Fourth Edition, Revised and Expanded, Jean Dickinson Gibbons and
Subhabrata Chakraborti
Computer-Aided Econometrics, edited by David E.A. Giles
The EM Algorithm and Related Statistical Models, edited by Michiko Watanabe and
Kazunori Yamaguchi
Multivariate Statistical Analysis, Second Edition, Revised and Expanded, Narayan C. Giri
Computational Methods in Statistics and Econometrics, Hisashi Tanizaki
Applied Sequential Methodologies: Real-World Examples with DataAnalysis, edited by
Nitis Mukhopadhyay, Sujay Datta, and Saibal Chattopadhyay
Handbook of Beta Distribution and Its Applications, edited by Arjun K. Gupta and
Saralees Nadarajah
Item Response Theory: Parameter Estimation Techniques, Second Edition, edited by Frank B. Baker
and Seock-Ho Kim
Statistical Methods in Computer Security, edited by William W. S. Chen
Elementary Statistical Quality Control, Second Edition, John T. Burr
Data Analysis of Asymmetric Structures, Takayuki Saito and Hiroshi Yadohisa
Mathematical Statistics with Applications, Asha Seth Kapadia, Wenyaw Chan, and Lemuel Moyé
Advances on Models, Characterizations and Applications, N. Balakrishnan, I. G. Bairamov, and
O. L. Gebizlioglu
Survey Sampling: Theory and Methods, Second Edition, Arijit Chaudhuri and Horst Stenger
Statistical Design of Experiments with Engineering Applications, Kamel Rekab and
Muzaffar Shaikh
Quality by Experimental Design, Third Edition, Thomas B. Barker
Handbook of Parallel Computing and Statistics, Erricos John Kontoghiorghes
Statistical Inference Based on Divergence Measures, Leandro Pardo
A Kalman Filter Primer, Randy Eubank
Introductory Statistical Inference, Nitis Mukhopadhyay
Handbook of Statistical Distributions with Applications, K. Krishnamoorthy
A Course on Queueing Models, Joti Lal Jain, Sri Gopal Mohanty, and Walter Böhm
Univariate and Multivariate General Linear Models: Theory and Applications with SAS,
Second Edition, Kevin Kim and Neil Timm
Randomization Tests, Fourth Edition, Eugene S. Edgington and Patrick Onghena
Design and Analysis of Experiments: Classical and Regression Approaches with SAS,
Leonard C. Onyiah
Analytical Methods for Risk Management: A Systems Engineering Perspective,
Paul R. Garvey
Confidence Intervals in Generalized Regression Models, Esa Uusipaikka
Introduction to Spatial Econometrics, James LeSage and R. Kelley Pace
Acceptance Sampling in Quality Control, Edward G. Schilling and Dean V. Neubauer
Applied Statistical Inference with MINITAB, Sally A. Lesik
C6583_C000.indd 4 11/20/09 11:11:48 AM

Sally A. Lesik
Central Connecticut State University
New Britain, Connecticut, U.S.A.
Applied Statistical Inference
with MINITAB®
C6583_C000.indd 5 11/20/09 11:11:48 AM

CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Version Date: 20110725
International Standard Book Number-13: 978-1-4200-6584-8 (eBook - PDF)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts
have been made to publish reliable data and information, but the author and publisher cannot assume
responsibility for the validity of all materials or the consequences of their use. The authors and publishers
have attempted to trace the copyright holders of all material reproduced in this publication and apologize to
copyright holders if permission to publish in this form has not been obtained. If any copyright material has
not been acknowledged please write and let us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit-
ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented,
including photocopying, microfilming, and recording, or in any information storage or retrieval system,
without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.
com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood
Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and
registration for a variety of users. For organizations that have been granted a photocopy license by the CCC,
a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used
only for identification and explanation without intent to infringe.
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com

Dedication
To DHK … for all the laughter and the joy.
To NNK … for believing.
C6583_C000e.indd 7 11/19/09 4:50:14 PM

C6583_C000e.indd 8 11/19/09 4:50:14 PM

ix
Contents
Preface.
................................................................................................................... xiii
Acknowledgments..............................................................................................xvii
1 Introduction......................................................................................................1
1.1 What This Book Is About.
..............................................................................1
1.1.1 Graphical Displays of Data................................................................2
1.1.2 Descriptive Representations of Data................................................2
1.1.3 Basic Statistical Inference.
..................................................................3
1.1.4 Regression Analysis...........................................................................3
1.1.5 Analysis of Variance...........................................................................3
1.2 Types of Studies..............................................................................................4
1.3 What Is Statistics?...........................................................................................5
1.4 Types of Variables...........................................................................................6
1.5 Classification of Variables..............................................................................7
1.6 Entering Data into MINITAB®......................................................................9
Exercises..................................................................................................................12
2 Graphing Variables.......................................................................................15
2.1 Introduction...................................................................................................15
2.2 Histograms....................................................................................................15
2.3 Using MINITAB to Create Histograms.....................................................17
2.4 Stem-and-Leaf Plots.
.....................................................................................18
2.5 Using MINITAB to Create a Stem-and-Leaf Plot.....................................23
2.6 Bar Charts......................................................................................................24
2.7 Using MINITAB to Create a Bar Chart......................................................24
2.8 Box Plots.........................................................................................................25
2.9 Using MINITAB to Create Box Plots..........................................................30
2.10 Scatter Plots.
...................................................................................................31
2.11 Using MINITAB to Create Scatter Plots.
....................................................35
2.12 Marginal Plots...............................................................................................39
2.13 Using MINITAB to Create Marginal Plots................................................39
Exercises..................................................................................................................39
3 Descriptive Representations of Data and Random Variables..............49
3.1 Introduction...................................................................................................49
3.2 Descriptive Statistics ...................................................................................49
3.3 Measures of Center.......................................................................................50
3.4 Measures of Spread......................................................................................54
3.5 Using MINITAB to Calculate Descriptive Statistics................................58
C6583_C000toc.indd 9 11/19/09 4:51:15 PM

x Contents
3.6 Random Variables and Their Distributions.............................................. 61
3.7 Sampling Distributions................................................................................63
Exercises.................................................................................................................. 74
4 Basic Statistical Inference............................................................................83
4.1 Introduction...................................................................................................83
4.2 Confidence Intervals.
....................................................................................83
4.3
Using MINITAB to Calculate Confidence Intervals for a
Population Mean...........................................................................................89
4.4
Hypothesis Testing: A One-Sample t-Test for a Population Mean........91
4.5 Using MINITAB for a One-Sample t-Test..................................................97
4.6 Power Analysis for a One-Sample t-Test................................................. 103
4.7
Using MINITAB for a Power Analysis for a One-Sample t-Test.......... 104
4.8
Confidence Interval for the Difference between Two Means............... 110
4.9
Using MINITAB to Calculate a Confidence Interval for the
Difference between Two Means............................................................... 112
4.10 Testing the Difference between Two Means........................................... 115
4.11
Using MINITAB to Test the Difference between Two Means.............. 118
4.12 Using MINITAB to Create an Interval Plot............................................. 119
4.13
Using MINITAB for a Power Analysis for a Two-Sample t-Test.......... 121
4.14
Confidence Intervals and Hypothesis Tests for Proportions...............127
4.15 Using MINITAB for a One-Sample Proportion...................................... 131
4.16 Power Analysis for a One-Sample Proportion.......................................133
4.17 Differences between Two Proportions....................................................135
4.18
Using MINITAB for Two-Sample Proportion Confidence
Intervals and Hypothesis Tests.
................................................................ 139
4.19 Power Analysis for a Two-Sample Proportion....................................... 141
Exercises................................................................................................................ 144
Reference ..............................................................................................................154
5 Simple Linear Regression..........................................................................155
5.1 Introduction.................................................................................................155
5.2 Simple Linear Regression Model..............................................................156
5.3 Model Assumptions................................................................................... 163
5.4 Finding the Equation of the Line of Best Fit...........................................164
5.5 Using MINITAB for Simple Linear Regression...................................... 167
5.6 Regression Inference.................................................................................. 171
5.7 Inferences about the Population Regression Parameters......................172
5.8 Using MINITAB to Test the Population Slope Parameter..................... 175
5.9
Confidence Intervals for the Mean Response for a Specific Value
of the Predictor Variable............................................................................177
5.10
Prediction Intervals for a Response for a Specific Value of the
Predictor Variable....................................................................................... 178
5.11
Using MINITAB to Find Confidence and Prediction Intervals.
...........180
Exercises................................................................................................................190
C6583_C000toc.indd 10 11/19/09 4:51:15 PM
© 2010 by Taylor Francis Group, LLC

Contents xi
6 More on Simple Linear Regression.
.........................................................193
6.1
Introduction................................................................................................. 193
6.2
Coefficient of Determination.
.................................................................... 193
6.3
Using MINITAB to Find the Coefficient of Determination.................. 195
6.4
Sample Coefficient of Correlation.
............................................................ 196
6.5
Correlation Inference.
.................................................................................200
6.6
Using MINITAB for Correlation Analysis..............................................204
6.7
Assessing Linear Regression Model Assumptions...............................204
6.8
Using MINITAB to Create Exploratory Plots of Residuals...................206
6.9
Formal Test of the Normality Assumption............................................. 217
6.10
Using MINITAB for the Ryan–Joiner Test............................................... 219
6.11
Assessing Outliers...................................................................................... 219
6.12
Assessing Outliers: Leverage Values.......................................................221
6.13
Using MINITAB to Calculate Leverage Values......................................222
6.14
Assessing Outliers: Internally Studentized Residuals..........................225
6.15
Using MINITAB to Calculate Internally Studentized Residuals.........226
6.16
Assessing Outliers: Cook’s Distances......................................................228
6.17
Using MINITAB to Find Cook’s Distances.............................................228
6.18
How to Deal with Outliers........................................................................229
Exercises................................................................................................................231
References.
.............................................................................................................238
7 Multiple Regression Analysis.
..................................................................239
7.1 Introduction.................................................................................................239
7.2 Basics of Multiple Regression Analysis...................................................239
7.3 Using MINITAB to Create a Matrix Plot.................................................242
7.4 Using MINITAB for Multiple Regression.
...............................................245
7.5 Coefficient of Determination for Multiple Regression..........................248
7.6 Analysis of Variance Table........................................................................248
7.7 Testing Individual Population Regression Parameters.........................253
7.8 Using MINITAB to Test Individual Regression Parameters.
................256
7.9 Multicollinearity.........................................................................................257
7.10 Variance Inflation Factors..........................................................................258
7.11 Using MINITAB to Calculate Variance Inflation Factors...................... 261
7.12 Multiple Regression Model Assumptions...............................................264
7.13
Using MINITAB to Check Multiple
Regression Model Assumptions...............................................................264
7.14 Quadratic and Higher-Order Predictor Variables.................................268
7.15 Using MINITAB to Create a Quadratic Variable....................................268
Exercises................................................................................................................273
8 More on Multiple Regression...................................................................277
8.1 Introduction.................................................................................................277
8.2 Using Categorical Predictor Variables.....................................................277
8.3 Using MINITAB for Categorical Predictor Variables............................279
C6583_C000toc.indd 11 11/19/09 4:51:16 PM

xii Contents
8.4 Adjusted R2..................................................................................................284
8.5 Best Subsets Regression.............................................................................289
8.6 Using MINITAB for Best Subsets Regression.........................................296
8.7
Confidence and Prediction Intervals for Multiple Regression.............298
8.8
Using MINITAB to Calculate Confidence and Prediction
Intervals for a Multiple Regression Analysis.
.........................................299
8.9 Assessing Outliers......................................................................................302
Exercises................................................................................................................303
9 Analysis of Variance (ANOVA)................................................................307
9.1 Introduction.................................................................................................307
9.2 Basic Experimental Design.
.......................................................................307
9.3 One-Way ANOVA.......................................................................................309
9.4 Model Assumptions................................................................................... 316
9.5 Assumption of Constant Variance........................................................... 317
9.6 Normality Assumption..............................................................................322
9.7 Using MINITAB for One-Way ANOVAs.................................................323
9.8 Multiple Comparison Techniques............................................................338
9.9 Using MINITAB for Multiple Comparisons...........................................343
9.10 Power Analysis and One-Way ANOVA.
..................................................344
Exercises................................................................................................................348
References.
.............................................................................................................351
10 Other Topics.
.................................................................................................353
10.1
Introduction.................................................................................................353
10.2
Two-Way Analysis of Variance.................................................................353
10.3
Using MINITAB for a Two-Way ANOVA.
...............................................360
10.4
Nonparametric Statistics.
...........................................................................377
10.5
Wilcoxon Signed-Rank Test.......................................................................378
10.6
Using MINITAB for the Wilcoxon Signed-Rank Test............................382
10.7
Kruskal–Wallis Test....................................................................................388
10.8
Using MINITAB for the Kruskal–Wallis Test......................................... 391
10.8
Basic Time Series Analysis........................................................................398
Exercises................................................................................................................ 411
Appendix A.......................................................................................................... 415
Index......................................................................................................................427
C6583_C000toc.indd 12 11/19/09 4:51:16 PM

xiii
xiii
Preface
There are numerous statistics books that are available for readers who are
learning statistics for the first time. What distinguishes this book from many
is that it presents statistics with an emphasis toward applications for readers
who are not experts in statistics, but who want to learn about basic inferen-
tial techniques and be able to implement such techniques in practice using a
statistical software package. One characteristic of this text is that it is written
in such a way that the material is presented in a seamless manner, thus mak-
ing it easier to read and follow. By using a seamless step-by-step approach,
readers are introduced to a topic, presented with the calculations in detail,
provided with how to interpret the findings, and given an illustration of how
to perform the same analysis with a statistical software program. Although
this approach may be somewhat different than is presented in other texts,
readers may find it easier to learn statistics by being exposed to all the calcu-
lations and software details.
This text is written to be beginner-friendly and is oriented toward the prac-
tical use of statistics. The presentation leans less toward the theoretical side of
statistics and is focused more on addressing the expectations of students and
practitioners who are not experts in statistics but who are interested in getting
an appreciation for applying statistical techniques using a statistical software
program. One of the key features of this text is that the mathematical calcula-
tions are presented in step-by-step detail. Presenting such detail on how the
calculations are actually done by hand and the kinds of inferences that can
be made comes from teaching a course on applied inference to undergradu-
ate and graduate students who understood only the most basic statistical con-
cepts, but who plan to use statistics in their senior or master’s theses. Many
beginning readers of statistics tend to struggle when they are not presented
with step-by-step details and are left to fill in the gaps of how a particular
statistic is calculated. Although the prerequisite level of mathematics for this
text is intermediate algebra, many novices still like to see the nuts-and-bolts of
the calculations so they can get a better understanding of the concepts and to
connect with what the software program is actually doing.
Another key feature of this text is that instructions on how to use
the statistical software package MINITAB® are incorporated in detail
immediately following a topic. By presenting the software explanations
immediately following a given topic, this allows the reader to learn about
the topic and then see how to use a statistical package to arrive at the same
conclusions as found when doing the calculations by hand. This style of
presentation comes from watching many beginners become increasingly
frustrated when trying to read through statistics text books where it was
necessary to flip through the pages to try to relate the presentation of the
C6583_C000g.indd 13 11/19/09 4:50:35 PM

xiv Preface
topic with the appropriate software package and commands. A part of
creating a seamless presentation required using only a single statistical
software package, specifically MINITAB. Using only a single software
package provides the reader with the opportunity to focus on the details
of a specific package without having to filter through the commands or
output from other programs.
The audience for this text can come from diverse disciplines. I chose to
write this text to be useful for just about any field of study and especially
for those students who attend colleges and universities that may not offer
discipline-specific statistics courses. By not targeting any specific discipline,
this allowed me to present examples and discussions based on data and sce-
narios that are common to many students in their everyday lives. Perhaps
the biggest challenge in writing this text is that many disciplines have their
own spin on what topics should be presented as well as how they should
be presented. Though such differences in emphasis and presentation across
the various fields can often be seen as a source of tension, it pushed me to
think more deeply about the subject and how to best express the concepts
of applied statistical inference in a general and understandable way. In this
text I tried to present the material as simply as possible without sacrificing
the necessary technical details. Also, given differences in notation and ter-
minology across fields, on many occasions I incorporated the notation and
terminology that is used by MINITAB.
The choice to use MINITAB as the single statistical software program for
this text was an easy one. MINITAB is a very simple and easy to use statisti-
cal package. But yet, MINITAB is also very sophisticated and many fields
such as business and engineering actively use it. The clear menus and infor-
mative dialog boxes make it a natural choice for a text such as this which is
written for a novice with little or no experience using a statistical software
package. The printouts are clear and easy to follow, while still presenting
enough relevant information, and the graphics are excellent.
Like many things in life, good data is hard to find. For the data sets used
in this text, some were intentionally contrived and modified in order to be
manageable enough to illustrate the step-by-step calculations and the infer-
ences that can be made. By using smaller data sets, this allowed for the
mathematical calculations to be done out in their entirety so that readers
can follow through the step-by-step calculations if they wish. Other sets of
data presented are either entire sets of actual data that are available from
the public domain or subsets of data available from the public domain. Each
chapter has a set of homework problems that were created to give the reader
some practice in using the techniques and methods described in the text
with real data.
This text was written to establish the foundation for students to build on
should they decide to study more advanced inferential statistics. Virtually
every type of statistical inference in practice, from beginning to advanced,
relies on confidence intervals, hypothesis testing, validating model
C6583_C000g.indd 14 11/19/09 4:50:35 PM

Preface xv
assumptions, and power analysis. Since this book was written with these
considerations emphasized throughout, it is my hope that readers will be
able to generalize the basic framework of applied inference at just about any
level. The topics covered and the order with which the topics are presented
in this text may not follow most traditional texts. However, I decided to write
a text that was oriented toward the practical use of statistics for those who
may be contemplating using statistics in their own work.
Chapter 1 presents a basic introduction to some common terminology that
one is likely to encounter when learning statistics. Although conventions
and definitions may differ across disciplines, I tried to use more common
definitions and terminology throughout the text while also trying to stay
consistent with notation and terminology that is used in MINITAB.
Chapter 2 presents some basic graphs as well as how to create such graphs
using MINITAB. The presentation of graphs such as the stem-and-leaf plot
and the box plot are aligned with the conventions used in MINITAB. For
instance, the stem-and-leaf plot generated in MINITAB will have an extra col-
umn that includes the cumulative frequencies below and above the median,
and the quartiles for the box plot are calculated by using interpolation.
Chapter 3 presents basic descriptive statistics using both traditional hand-
calculations along with MINITAB. The calculations are done out in detail
to give students the chance to feel more comfortable with the notation and
symbols that are introduced. Although somewhat untraditional, I also intro-
duce random variables and sampling distributions in this chapter as I saw it
as a natural extension of a way to describe variables.
Chapter 4 presents basic statistical inference. I begin by deriving confi-
dence intervals using the t-distribution, and I also emphasize the interpreta-
tion of confidence intervals as students seem to get confused with what a
confidence interval is really estimating. I also begin the discussion about
hypothesis tests by testing a single population mean. I repeatedly elaborate
on how inferences are made with confidence intervals and hypothesis test-
ing by referring back to the sampling distribution of the sample mean. This
chapter also covers basic inferences for proportions. Chapter 4 also provides
a conceptual introduction to power analysis as well as how to use MINITAB
to conduct a power analysis.
Chapter 5 describes simple linear regression. To understand simple linear
regression, one must have a good intuitive feel for what the line of best fit is.
I elaborate on this topic by first presenting how a line for two random points
can be used to express the relationship between two variables. I then show
how the line of best fit is “better” in the sense that it is the single line that
best fits the data. This chapter also provides an introduction to the model
assumptions for simple linear regression and how to make inferences with
the line of best fit.
Chapter 6 provides more detail for simple linear regression by describ-
ing the coefficient of determination, the sample correlation coefficient, and
how to assess model assumptions. One key feature of this chapter is that it
C6583_C000g.indd 15 11/19/09 4:50:35 PM

xvi Preface
introduces the Ryan–Joiner test as a formal test of the normality assumption.
There is also a discussion on how to assess outliers by using leverage values,
studentized residuals, and Cook’s distances.
Chapter 7 provides an introduction to multiple regression analysis. The
ANOVA table and the issue of multicollinearity are introduced. Chapter 8
provides more detail for multiple regression by introducing how to include
categorical predictor variables, how to pick the best model, and how to assess
outliers.
Chapter 9 provides a conceptual introduction to basic experimental design
and the basics of a one-way ANOVA. This chapter introduces Bartlett’s and
Levene’s tests as a formal way to establish the assumption of constant vari-
ance. Multiple comparison techniques are also introduced as well as power
analysis for a one-way ANOVA.
Chapter 10 provides a discussion of a two-way ANOVA in addition to
some basic non-parametric analyses and basic time series analysis. The
calculations for the test statistics for the Wilcoxon signed-rank test and the
Kruskall–Wallis test are worked out in great detail to help the reader gain a
greater understanding of the complexities of these tests.
C6583_C000g.indd 16 11/19/09 4:50:36 PM

xvii
Acknowledgments
There are so many people who contributed to this project over the past few
years. I am particularly grateful to my friend and colleague Frank Bensics,
who graciously agreed to edit many versions of this manuscript. His many
suggestions, comments, and corrections brought a new perspective to the
work. I am also grateful to my friend and colleague Zbigniew Prusak, who
not only provided valuable comments about the content and presentation of
the text, but who also sat in on my class on numerous occasions and provided
valuable feedback about how students struggle when learning statistics.
David Grubbs, Susan Horwitz, and the staff at Taylor Francis were most
helpful. Not only was I encouraged to write the text as I saw fit, I also received
continuous support, patience, and guidance along the way. I would also like
to thank the reviewers for the numerous comments and corrections that help
guide my writing.
Finally, I would like to extend my gratitude and appreciation to my fiends,
family, and colleagues who directly and indirectly contributed to this project.
Correspondence
Although a great amount of effort has gone into making this text clear and
accurate, if you have any suggestions or comments regarding errors, content,
or feel that some clarification is needed, please contact me at lesiks@ccsu.edu.
I am interested in hearing your feedback and comments.
Portions of the input and output contained in this publication/book are printed
with permission of Minitab Inc. All material remains the exclusive property
and copyright of Minitab Inc. All rights reserved.
MINITAB® and all other trademarks and logos for the Company’s products
and services are the exclusive property of Minitab Inc. All other marks
referenced remain the property of their respective owners. See minitab.com
for more information.
C6583_C000h.indd 17 11/20/09 5:29:10 PM

1
1
Introduction
1.1 What This Book Is About
Statistical inference involves collecting and analyzing data in order to answer
a meaningful question of interest. For instance, a researcher in education
may want to know if using computers in an algebra classroom is effective in
helping students build their mathematical skills. A researcher in psychology
may want to know whether children who play violent video games tend to
have more disturbing thoughts than children who do not play violent video
games. In other fields, such as environmental science, researchers may want
to know what factors contribute to global warming by asking questions such
as which makes and models of automobiles emit larger amounts of green-
house gas.
Once a researcher has described a problem he or she wishes to investigate,
he or she will set out to collect or identify a set of data that consists of infor-
mation about a variable or variables of interest. There are two basic types of
data that can be collected, quantitative data and qualitative data.
Quantitative data is numeric in form. The main purpose of collecting quan-
titative data is to describe some phenomenon using numbers. For example,
quantitative data could be collected to assess the effect of advertising on
gross product sales.
On the other hand, qualitative data is categorical in nature and describes
some phenomenon using words. For instance, qualitative data can be used
to describe what the learning environment is like in a given mathematics
classroom by using words to describe the types of interactions between
the students and the teacher and how students appear to be engaged in
learning.
Determining whether to collect quantitative or qualitative data is typi-
cally driven by the characteristic or relationship that is being assessed and
the type of data that is available. The purpose of this book is to introduce
some of the different statistical methods and techniques that can be used
to analyze data in a meaningful way. The methods and techniques that we
will be considering in this book are broadly categorized as follows:
Graphical displays of data
Descriptive representations of data
C6583_C001.indd 1 11/19/09 4:51:39 PM

2 Applied Statistical Inference with MINITAB
Basic statistical inference
Regression analysis
Analysis of variance
1.1.1 Graphical Displays of Data
Graphical displays of data visually describe some of the characteristics of a
set of data by using different types of charts and graphs. The advantage to
using charts and graphs to display data is that a large amount of informa-
tion can be displayed in a concise manner. For example, suppose you are
interested in comparing the fuel efficiency for the following four different
makes and models of vehicles: the Toyota Corolla®, the Honda Civic®, the
Ford Focus®, and the Chevrolet Aveo®. You could obtain the average miles
per gallon for both city and highway driving for each of the models you are
interested in and then graph the comparison between the different brands of
cars by using a bar chart, as illustrated in Figure 1.1.
Notice that Figure 1.1 graphically displays the city and highway miles per
gallon for each of the different makes and models of cars, and thus allows
you to make comparisons between the different cars.
1.1.2 Descriptive Representations of Data
Descriptive representations of data consist of methods and techniques that
can be used to describe and summarize data. For instance, if you have ever
shopped for a new car you may have noticed that the sticker on the window
Car
City/Highway
40
30
20
10
0
MPG
Chart of MPG
City Highway
City Highway
Toyota Corolla Honda Civic Ford Focus Chevrolet Aveo
City Highway City Highway
Figure 1.1
Bar chart comparing city and highway mileage per gallon based on the different brands
of cars.
C6583_C001.indd 2 11/19/09 4:51:40 PM

Introduction 3
of the car provides the average miles per gallon of gasoline for both city and
highway driving. This value describes, on average, the gas mileage that you
can expect from the vehicle. For example, the sticker on the window of the
2007 Ford Focus® suggests that, on average, the vehicle will get 27 miles per
gallon of gasoline driving in the city and 37 miles per gallon driving on the
highway (http:/
/www.fueleconomy.gov/feg/byclass.htm).
1.1.3 Basic Statistical Inference
Basic statistical inference relies on estimating or predicting an unknown char-
acteristic of interest by using available data. For example, suppose that a crimi-
nologist wants to know whether the average yearly crime rate in the United
States has increased over the last year. Because it can be very difficult and time-
consuming to obtain the yearly crime rate for every single community in the
United States, the criminologist may decide to collect a representative sample
of the communities in the United States along with their respective crime rates
for the past 2 years. Then by using the available information obtained from
this representative sample of communities, the criminologist could then try to
make an inference or prediction about whether the crime rate has increased
over the past year for the entire United States.
1.1.4 Regression Analysis
Regression analysis is a statistical technique that consists of developing and
validating models that can be used to describe how one variable is related
to another variable or collection of different variables. For instance, the price
of a house is determined by many factors, such as square footage, lot size,
number of bedrooms, number of bathrooms, and age. Regression analysis
would allow you to develop a model that describes how the price of a house
is related to these factors.
1.1.5 Analysis of Variance
Analysis of variance is a statistical technique that can be used to estimate
whether there are differences in averages between more than two groups
based on some characteristic. For example, suppose you are interested in
determining whether there is a difference in the number of pages you can
print with four different brands of printer toner. One way to assess this could
be to set up an experiment where you have four identical brands of print-
ers and a total of sixteen printer cartridges (four printer cartridges of each
brand). Then you could put the printer cartridges in each of the printers and
count up the total number of pages that each printer printed with the given
cartridge. An analysis of variance could then be used to see if there is a dif-
ference in the average (or mean) number of pages printed across the different
brands of printer cartridges.
C6583_C001.indd 3 11/19/09 4:51:40 PM

Discovering Diverse Content Through
Random Scribd Documents

now, and I can remember that she was a very beautiful and a very
foolish woman. Poor innocent Rupert!”
Rupert came down to dinner ten minutes late, to find that
everybody had gone in. Arriving under cover of the fish, he took the
chair which was left for him by Lady Devene, who always liked him
to sit upon her right hand. Edith, he noted with sorrow, was some
way off, between two of the shooting guests, and three places
removed from Dick, who occupied the end of the table.
“Ach! my dear Rupert,” said Lady Devene, “you are terribly late,
and I could wait no longer, it spoils the cook. Now you shall have no
soup as a punishment. What? Did you go to sleep over that big book
of yours up in the library?”
He made some excuse, and the matter passed off, while he ate, or
pretended to eat his fish in silence. Indeed to him, in his excited
state of mind, this splendid and rather lengthy New Year’s feast
proved the strangest of entertainments. There was a curious air of
unreality about it. Could he, Rupert, after the wonderful and glorious
thing that had happened to him utterly changing the vista of his life,
making it grand and noble as the columns of Karnac beneath the
moon, be the same Rupert who had gone out shooting that
morning? Could the handsome, phlegmatic German lady who sat by
him discoursing on the cooking be the same passion-torn, doom-
haunted woman, who told him how she had crawled upon her knees
after her mocking husband for the prize of her infant’s soul? Nay,
was it she who sat there at all? Was it not another, whom he well
remembered in that seat, the lovely Clara, with her splendid,
unhappy eyes full of the presage of death and destruction; those
eyes that he felt still watched him, he knew not whence, reproaching
him, warning him he knew not of what? Was the gay and beautiful
lady yonder, who laughed and joked with her companions, the same
Edith to whom he had vowed himself not an hour gone? Yes, it must
be so, for there upon her finger gleamed his golden ring, and what
was more, Dick had seen it, for he was watching her hand with a
frown upon his handsome face.

Why, too, Rupert wondered, did another vision thrust itself upon
him at this moment, that of the temple of Abu-Simbel bathed in the
evening lights which turned the waters of the Nile red as though
with blood, and of the smiling and colossal statues of the first
monarch of long ago, whose ring was set upon Edith’s hand in token
of their troth? Of the dark, white-haired figure of old Bakhita also,
who had not crossed his mind for many a day, standing there among
the rocks and calling to him that they would meet again, calling to
Dick and Edith also, something that he could not understand, and
then turning to speak to a shadow behind her.
The meal ended at last, and as was the custom in this house,
everyone, men and women, left the table together to go into the
great hall hung with holly and with mistletoe, where there would be
music, and perhaps dancing to follow, and all might smoke who
wished. Here were some other guests, the village clergyman’s
daughters and two families from the neighbourhood, making a party
of twenty or thirty in all, and here also was Mrs. Ullershaw, who had
dined in her own room, and come down to see the old year out.
Rupert went to sit by his mother, for a kind of shyness kept him
away from Edith. She laid her hand on his, and with a smile that
made her grey and careworn face beautiful, said how happy she
was, after so many lonely years, to be at the birth of one more of
them with him, even though it should prove her last.
“Don’t talk like that, mother,” he answered, “it is painful.”
“Yes, dear,” she replied, in her gentle voice, “but all life is painful,
a long road of renunciation with farewells for milestones. And when
we think ourselves most happy, as I do to-night, then we should
remember these truths more even than at other times. The moment
is all we have, dear; beyond it lies the Will of God, and nothing that
we can call our own.”
Rupert made no answer, for this talk of hers all seemed part of his
fantastic imaginings at the dinner-table, a sad music to which they
were set. Yet he remembered that once before she had spoken to

him of renunciation when, as a lad, he lay sick after the death of
Clara; remembered, too, that from that day to this he had practised
its stern creed, devoting himself to duty and following after faith.
Why, now on this joyous night, the night of his re-birth in honest
love, did his mother again preach to him her stern creed of
renunciation?
At least it was one in which that company did not believe. How
merry they were, as though there were no such things as sorrow,
sickness, and death, or bitter disillusionment, that is worse than
death. Listen! the music began, and see, they were dancing. Dick
was waltzing with Edith, and notwithstanding her hurt shoulder,
seemed to be holding her close enough. They danced beautifully,
like one creature, their bodies moving like a single body. Why should
he mind it when she was his, and his alone? Why should he feel sore
because he whose life had been occupied in stern business had
never found time to learn to dance?
Hark! the sound of the bells from the neighbouring church floated
sweetly, solemnly into the hall, dominating the music. The year was
dying, the new year was at hand. Edith ceased her waltzing and
came towards Rupert, one tall, white figure on that wide expanse of
polished floor, and so graceful were her slow movements that they
put him in mind of a sea-gull floating through the air, or a swan
gliding on the water. To him she came, smiling sweetly, then as the
turret clock boomed out the hour of midnight, whispered in his ear:
“I whom you have made so happy wish you a happy New Year—
with me, Rupert,” and turning, she curtseyed to him ever so little.
In the chorus of general congratulations no one heard her low
speech, though Mrs. Ullershaw noted the curtsey and the look upon
Edith’s face—Rupert’s she could not see, for his back was to her—
and wondered what they meant, not without anxiety. Could it be—
well, if it was, why should the thing trouble her? Yet troubled she
was, without a doubt, so much so that all this scene of gaiety
became distasteful to her, and she watched for an opportunity to rise
and slip away.

Meanwhile Rupert was enraptured, enchanted with delight, so
much so that he could find no answer to Edith’s charming speech,
except to mutter—“Thank you. Thank you.” Words would not come,
and to go down upon his knees before her, which struck him as the
only fitting acknowledgment of that graceful salutation, was clearly
impossible. She smiled at his embarrassment, thinking to herself
how differently the ready-witted Dick, whose side she had just left,
would have dealt with such a situation, then went on quickly:
“Your mother is preparing to leave us, and you will wish to go with
her. So good-night, dearest, for I am tired, and shan’t stop here
long. I shall count the days till we meet in London. Again, good-
night, good-night!” and brushing her hand against his as she passed,
she left him.

CHAPTER VIII.
EDITH’S CRUSHED LILIES
“Rupert,” said his mother, “I want you to give me your arm to my
room, I am going to bed.”
“Certainly,” he answered, “but wait one minute, dear. I have to
take that eight o’clock train to-morrow morning, so I will just say
good-bye to Tabitha, as I shan’t come back again.”
Mrs. Ullershaw breathed more freely. If there were anything in the
wind about Edith he would not be taking the eight o’clock train.
“Go,” she said; “I’ll wait.”
Lady Devene was by herself, since amongst that gay throng of
young people no one took much note of her, seated in a big oak
chair on a little dais at the end of the hall far away from the fire and
hot water coils, for she found the heat oppressive. As he made his
way towards her even the preoccupied Rupert could not help
noticing how imposing she looked in her simple black dress, which
contrasted so markedly with her golden hair and white and massive
face, set up there above them all, elbow on knee and chin on hand,
her blue eyes gazing over their heads at nothingness. In reality, the
miserable woman was greeting the New Year in her own fashion, not
with gaiety and laughter, but with repentance for her sins during that
which was past, and prayers for support during that which was to
come.
“Ach, Rupert!” she said, rousing herself and smiling pleasantly as
she always did at him, “it is kind of you to leave those young people

and their jokes to come to talk with the German frau, for that is
what they call me among themselves, and indeed what I am.”
“I am afraid,” he said, “I have only come to say good-night, or
rather good-bye, for I must go to town to-morrow morning before
you will be down.”
She looked at him sharply.
“So I have driven you away with my tale of troubles. Well, I
thought that I should, and you are wise to leave this house where
there is so much misery, dead and living, for no good thing can
happen in it, no good thing can come out of it—”
“Indeed,” broke in Rupert, “that is not why I am going at all, it is
because—” and he told her of the visit he must pay.
“You do not speak fibs well like the rest of them, Rupert; you have
some other reason, I see it on your face, something to do with that
dreadful Dick, I suppose, or his—ach! what is the English word—his
flame, Edith. What? Has she been playing tricks with you too? If so,
beware of her; I tell you, that woman is dangerous; she will breed
trouble in the world like his lordship.”
Rupert felt very angry, then he looked at that calm, fateful face
which a few hours before he had seen so impassioned, and all his
anger died, and was replaced by a fear which chilled him from head
to heel. He felt that this brooding, lonely woman had insight, born
perhaps of her own continual griefs; that she saw deep into the
heart of things. He who understood her, who sympathised with, even
if he did not entirely adopt her stern religious views, who knew that
prayer and suffering are the parents of true sight, felt sure that this
sight was hers. At least he felt it for a moment, then the unpleasant
conviction passed away, for how could its blackness endure in the
light of the rosy optimism of new-risen and successful love?
“You are morbid,” he said, “and although I am sure you do not
wish to be so, that makes you unjust, makes you pass hard
judgments.”
“Doubtless it is true,” she replied, with a sigh, “and I thank you for
telling me my faults. Yes, Rupert, I am morbid, unjust, a passer of

hard judgments, who must endure hard judgment,” and she bowed
her stately, gold-crowned head as before the appointed stroke of
wrath, then held out her hand and said simply: “Good-bye, Rupert! I
do not suppose that you will often come to see me more—ach! why
should you? Still if you do, you will be welcome, for on you I pass no
hard judgments, and never shall, whatever they say of you.”
So he shook her hand and went away saddened.
Giving his mother his arm, for she was very infirm, Rupert led her
quietly out of a side door and down the long passages to her room,
which was next to his own at the end of the house, for stairs being
difficult to her, she slept on the ground floor, and he at hand to keep
her company.
“Mother,” he said, when he had put her in her chair and stirred the
fire to a blaze, “I have something to tell you.”
She looked up quickly, for her alarm had returned, and said:
“What is it, Rupert?”
“Don’t look frightened, dear,” he replied, “nothing bad, something
very good, very happy. I am engaged to be married to Edith, and I
have come to ask your blessing on me, or rather on both of us, for
she is now a part of me.”
“Oh, Rupert, you have that always,” she answered, sinking back in
her chair; “but I am astonished.”
“Why?” he asked, in a vexed voice, for he had expected a flow of
enthusiasm that would match his own, not this chilly air of
wonderment.
“Because—of course, nobody ever told me so—but I always
understood that it was Dick Learmer whom Edith cared for, that is
why I never thought anything of her little empressé ways with you.”
Again, Rupert was staggered. Dick—always Dick, first from Lady
Devene and now from his mother. What could be the meaning of it?
Then again optimism came to his aid, he who knew full surely that
Dick was nothing to Edith.

“You are mistaken there for once, mother,” he said, with a cheerful
laugh. “I knew from the first what she thought about Dick, for she
spoke very seriously to me of him and his performances in a way she
would never have done if there were anything in this silly idea.”
“Women often do speak seriously of the bad behaviour of the man
of whom they are fond, especially to one whom they think may
influence him for good,” replied his mother, with the wistful smile
which she was wont to wear when thinking of her own deep
affection for a man who had deserved it little.
“Perhaps,” he said. “All I have to say is that if ever there was
anything—and I know there wasn’t—it is as dead as last month’s
moon.”
Mrs. Ullershaw thought to herself that this simile drawn from the
changeful moon, that waxes anew as surely as it wanes, was
scarcely fortunate. But she kept a watch upon her lips.
“I am very glad to hear it,” she said, “and no doubt it was all a
mistake, since, of course, if she had wished it, she might have
married Dick long ago, before you came into her life at all. Well,
dearest, I can only say that I wish you every happiness, and pray
that she may be as good a wife to you as I know you will be
husband to her. She is lovely,” she went on, as though summing up
Edith’s best points, “one of the most graceful and finished women
whom I have ever seen; she is very clever in her own way, too,
though perhaps not in yours; thoughtful and observant. Ambitious
also, and will therefore make an excellent wife for a man with a
career. She is good-tempered and kind, as I know, for we have
always got on well during the years we have lived together. Yes, you
will be considered very fortunate, Rupert.”
“These are her advantages, what are her drawbacks?” he asked
shrewdly, feeling that his mother was keeping something from him,
“though I must say at once that in my eyes she has none.”
“Which is as it should be, Rupert. Well, I will tell you frankly, so
that you may guard against them if I am right. Edith likes pleasure
and the good things of the world, as, after all, is only natural, and

she is extravagant, which perhaps in certain circumstances will not
matter. Again, I hope you will never fall ill, for she is not a good
nurse, not from unkindness, but because she has a constitutional
horror of all ill-health or unsightliness. I have seen her turn white at
meeting a cripple even, and I don’t think that she has ever quite
liked sitting with me since I had that stroke, especially while it
disfigured my face and made the lower eyelid drop.”
“We all have failings which we can’t help,” he answered; “natural
antipathies that are born in us, and I am glad to say I am fairly
sound at present. So I don’t think much of that black list, mother.
Anything to add to it?”
She hesitated, then said:
“Only one thing, dear. It does strike me as curious that such a girl
as Edith should be so attached to men like Dick Learmer and Lord
Devene, for she is fond of them both.”
“Relationship, I suppose; also the latter has been very kind to her,
and doubtless she is grateful.”
“Yes, most kind; indeed, he was her guardian until she came of
age, and has practically supported her for years. But it isn’t
gratitude, it is sympathy between her and him. They are as alike in
character, mentally, I mean, as—as they are in face.”
Rupert laughed, for to compare the blooming Edith with the faded,
wrinkled Devene, or even her quick humour that turned men and
things to mild ridicule, with his savage cynicism which tore them
both to pieces and stamped upon their fragments, seemed absurd.
“I can’t see the slightest resemblance,” he said. “You are
cultivating imagination in your old age, mother.”
She looked up to answer, then thought a moment, and remarked:
“I daresay that you are perfectly right, Rupert, and that these
things are all my fancy; only, my dear boy, try to make her go to
church from time to time, that can’t do any woman harm. Now I
have done with criticisms, and if I have made a few, you must
forgive me; it is only because I find it hard to think that any woman
can be worthy of you, and of course the best of us are not perfect,

except to a lover. On the whole, I think that I may congratulate you,
and I do so from my heart. God bless you both; you, my son, and
Edith, my daughter, for as such I shall regard her. Now, dear, good-
night, I am tired. Ring the bell for the maid, will you?”
He did so, and then by an afterthought said:
“You remember that I have to go away. You will speak to Edith,
won’t you?”
“Of course, my love, when Edith speaks to me,” the old lady
replied, with gentle dignity. “But why, under the circumstances, are
you going?”
At that moment the maid entered the room, so he gave no
answer, only made a few remarks about the manner of his mother’s
journey back to town and kissed her in good-bye.
When the maid had left again Mrs. Ullershaw, as was her custom,
said her prayers, offering up petitions long and earnest for the
welfare of her beloved only son, and that the woman whom he had
chosen might prove a blessing to him. But from those prayers she
could take no comfort, they seemed to fall back upon her head like
dead things, rejected, or unheard, she knew not which. Often she
had thought to herself how happy she would be when Rupert came
to tell her that he had chosen a wife, yet now that he had chosen,
she was not happy.
Oh, she would tell the truth to her own heart since it must never
pass her lips. She did not trust this gay and lovely woman; she
thought her irreligious, worldly, and self-seeking; she believed that
she had engaged herself to Rupert because he was the heir to a
peerage and great wealth, distinguished also; not because she loved
him. Although her son was of it, she hated the stock whence Edith
sprang; as she knew now, from the first Ullershaw, who founded the
great fortunes of the family, in this way or that they had all been
bad, and Edith, she was certain, had not escaped that taint of blood.
Even in Rupert, as the adventure of his youth proved, it was present,
and only by discipline and self-denial had he overcome his nature.
But Edith and self-denial were far apart. Yes; a cold shadow fell

upon her prayers, and it was cast by the beautiful form of Edith—
Edith who held Rupert’s destiny in her hands.
Within a few feet of her Rupert also offered up his petitions, or
rather his paean of thanksgiving and praise for the glory that had
fallen from Heaven upon his mortal head, for the pure and beautiful
love which he had won that should be his lamp through life and in
death his guiding-star.
A while after Rupert had gone, half an hour perhaps, Edith,
noticing that Dick had left the hall, as she thought to see off the last
of the departing guests, took the opportunity to slip away to bed
since she wished for no more of his company that night. Yet she was
not destined to escape it, for as she passed the door of the library
on her way up stairs, that same room in which Rupert had proposed
to her, she found Dick standing there.
“Oh,” he said, “I was looking for you. Just come in and tell me if
this belongs to you. I think you must have left it behind.”
Carelessly, without design or thought, she stepped into the room,
whereon he closed the door, and as though by accident placed
himself between it and her.
“Well, what is it?” she asked, for her curiosity was stirred; she
thought that she might have dropped something during her
interview with Rupert. “Where is it? What have I lost?”
“That’s just what I want to ask you,” he answered, with a scarcely
suppressed sneer. “Is it perhaps what you are pleased to call your
heart?”
“I beg your pardon?” said Edith interrogatively.
“Well, on the whole, you may have reason to do so. Come, Edith,
no secrets between old friends. Why do you wear that ring upon
your finger? It was on Ullershaw’s this morning.”
She reflected a moment, then with characteristic courage came to
the conclusion that she might as well get it over at once. The same
instinct that had prompted her to become engaged to Rupert within

half an hour of having made up her mind to the deed, made her
determine to take the opportunity to break once and for all with her
evil genius, Dick.
“Oh,” she answered calmly, “didn’t I tell you? I meant to in the
hall. Why, for the usual reason that one wears a ring upon that
finger—because I am engaged to him.”
Dick went perfectly white, and his black eyes glowed in his head
like half-extinguished fires.
“You false—”
She held up her hand, and he left the sentence unfinished.
“Don’t speak that which you might regret and I might remember,
Dick; but since you force me to it, listen for a moment to me, and
then let us say good-night, or good-bye, as you wish. I have been
faithful to that old, silly promise, wrung from me as a girl. For you I
have lost opportunity after opportunity, hoping that you would
mend, imploring you to mend, and you, you know well how you
have treated me, and what you are to-day, a discredited man, the
toady of Lord Devene, living on his bounty because you are useful to
him. Yet I clung to you who am a fool, and only this morning I made
up my mind to reject Rupert also. Then you played that trick at the
shooting; you pretended not to see that I was hurt, you pretended
that you did not fire the shot, because you are mean and were afraid
of Rupert. I tell you that as I sat upon the ground there and
understood, in a flash I saw you as you are, and I had done with
you. Compare yourself with him and you too will understand. And
now, move away from that door and let me go.”
“I understand perfectly well that Rupert is the heir to a peerage
and I am not,” he answered, who saw that, being defenceless, his
only safety lay in attack. “You have sold yourself, Edith, sold yourself
to a man you don’t care that for,” and he snapped his fingers. “Oh,
don’t take the trouble to lie to me, you know you don’t, and you
know that I know it too. You have just made a fool of him to suit
yourself, as you can with most men when you please, and though I

don’t like the infernal, pious prig, I tell you I am sorry for him, poor
beggar.”
“Have you done?” asked Edith calmly.
“No, not yet. You sneer at me and turn up your eyes—yes, you—
because I am not a kind of saint fit to go in double harness with this
Rupert, and because, not being the next heir to great rank and
fortune, I haven’t been plastered over with decorations like he has
for shooting savages in the Soudan because, too, as I must live
somehow, I do so out of Devene. Well, my most immaculate Edith,
and how do you live yourself? Who paid for that pretty dress upon
your back, and those pearls? Not Rupert as yet, I suppose? Where
did you get the money from with which you helped me once? I wish
you would tell me, because I have never seen you work, and I would
like to have the secret of plenty for nothing.”
“What is the good of asking questions of which you perfectly well
know the answer, Dick? Of course George has helped me. Why
shouldn’t he, as he can quite well afford to, and is the head of the
family? Now I am going to help myself in the only way a woman
can, by prudent and respectable marriage, entered on, I will tell you
in confidence, with the approval, or rather by the especial wish of
George himself.”
“Good Lord!” said Dick, with a bitter laugh. “What a grudge he
must have against the man to set you on to marry him! Now I am
certain there is something in all that old talk about the saint in his
boyhood and the lovely and lamented Clara. No; just spare me three
minutes longer. It would be a pity to spoil this conversation. Has it
ever occurred to you, most virtuous Edith, that whatever I am—and
I don’t set up for much—it is you who are responsible for me; you
who led me on and threw me off by fits, just as it suited you; you
who for your own worldly reasons never would marry, or even
become openly engaged to me, although you said you loved me—”
“I never said that,” broke in Edith, rousing herself from her
attitude of affected indifference to this tirade. “I never said I loved
you, and for a very good reason, because I don’t, and never did, you

or any other man. I can’t—as yet, but one day perhaps I shall, and
then—I may have said that you attracted me—me, who stand before
you, not my heart, which is quite a different matter, as men like you
should know well enough.”
“Men like me can only judge of emotions by the manner of their
expression. Even when they do not believe what she says, they take
it for granted that a woman means what she does. Well, to return, I
say that you are responsible, you and no other. If you had let me, I
would have married you and changed my ways, but though you
were ‘attracted,’ this you would never do because we should have
been poor. So you sent me off to others, and then, when it amused
you, drew me back again, and thus sank me deeper into the mud,
until you ruined me.”
“Did I not tell you that you are a coward, Dick, though I never
thought that you would prove it out of your own mouth within five
minutes. Only cowards put the burden of their own wrong-doing
upon the heads of others. So far from ruining you, I tried to save
you. You say that I played with you; it is not the truth. The truth is,
that from time to time I associated with you again, hoping against
hope that you might have reformed. Could I have believed that you
meant to turn over a new leaf, I think that I would have risked all
and married you, but, thank God! I was saved from that. And now I
have done with you. Go your way, and let me go mine.”
“Done with me? Not quite, I think, for perhaps the old ‘attraction’
still remains, and with most women that means repulsion from other
men. Let us see now,” and suddenly, without giving her a single hint
of his intention, he caught her in his arms and kissed her
passionately. “There,” he said, as he let her go, “perhaps you will
forgive an old lover—although you are engaged to a new one?”
“Dick,” she said, in a low voice, “listen to me and remember this.
If you touch me like that again, I will go straight to Rupert, and I
think he would kill you. As I am not strong enough to protect myself
from insult, I must find one who is. More, you talk as though I had
been in the habit of allowing you to embrace me, perhaps to pave
the way for demands of blackmail. What are the facts? Eight or nine

years ago, when I made that foolish promise, you kissed me once,
and never again from that hour to this. Dick, you coward! I am
indeed grateful that I never felt more than a passing attraction for
you. Now open that door, or I ring the bell and send for Colonel
Ullershaw.”
So Dick opened it, and without another word she swept past him.
Edith reached her room so thoroughly upset that she did what she
had not done since her mother’s death—sat down and cried. Like
other people, she had her good points, and when she seemed to be
worst, it was not really of her own will, but because circumstances
overwhelmed her. She could not help it if she liked, or, as she put it,
had been “attracted” by Dick, with whom she was brought up, and
whose ingrained natural weakness appealed to that sense of
protection which is so common among women, and finds its last
expression in the joys and fears of motherhood.
Every word she had spoken to him was true. Before she was out
of her teens, overborne by his passionate attack, she had made
some conditional promise that she would marry him at an undefined
date in the future, and it was then for the first and—until this night—
the last time that he had kissed her. She had done her best to keep
him straight, an utterly impossible task, for his ways were
congenitally crooked, and during those periods when he seemed to
mend, had received him back into her favour. Only that day she had
at last convinced herself that he was beyond hope, with the results
which we know. And now he had behaved thus, insulting her in a
dozen directions with the gibes of his bitter tongue, and at last most
grossly by taking advantage of his strength and opportunity to do
what he had done.
The worst of it was that she could not be as angry with him as she
ought, perhaps because she knew that his outrageous talk and
behaviour sprang from the one true and permanent thing in the
fickle constitution of Dick’s character—his love for her. That love,
indeed, was of the most unsatisfactory kind. For instance, it did not
urge him on to honest effort, or suffice to keep him straight, in any
sense. Yet it existed, and must be reckoned with, nor was she upon

whom it was outpoured the person likely to take too harsh a view
even of its excesses. She could ruin Dick if she liked. A word to Lord
Devene, and another to Rupert, would be sufficient to turn him out
to starve upon the world, so that within six months he might be
sought for and found upon the box of a hansom cab, or in the bunk
of a Salvation Army shelter. Yet she knew that she would never
speak those words, and that he knew it also. Alas! even those
insolent kisses of his had angered rather than outraged her; after
them she did not rub her face with her handkerchief as she had
done once that day.
Again, it was not her fault if she shrank from Rupert, whom she
ought to, and theoretically did, adore. It was in her blood, and she
was not mistress of her blood; for all her strength and will she was
but a feather blown by the wind, and as yet she could find no weight
to enable her to stand against that wind. Still, her resolution never
wavered; she had made up her mind to marry Rupert—yes, and to
make him as good a wife as she could be, and marry him she would.
Now there were dangers ahead of her. Someone might have seen
her go into that library with Dick at near one o’clock in the morning.
Dick himself might drop hints; he was capable of it, or worse. She
must take her precautions. For a moment Edith thought, then going
to a table, took a piece of paper and wrote upon it:
1st January. 2 A.M.
To Rupert,—A promise for the New Year, and a
remembrance of the old, from her who loves him best
of all upon the earth.
E.
Then she directed an envelope, and on the top of it wrote that it
was to be delivered to Colonel Ullershaw before he left, and took
from her breast the lilies she had worn, which she was sure he
would know again, purposing to enclose them in the letter, only to
find that in her efforts to free herself from Dick, they had been
crushed to a shapeless mass. Almost did Edith begin to weep again

with vexation, for she could think of nothing else to send, and was
too weary to compose another letter. At this moment she
remembered that these were not all the lilies which the gardener
had sent up to her. In a glass stood the remainder of them. She
went to it, and carefully counted out an equal number of sprays and
leaves, tied them with the same wire, and having thrown those that
were broken into the grate to burn, enclosed them in the envelope.
“He will never know the difference,” she murmured to herself, with
a dreary little smile, “for when they are in love who can tell the false
from the true?”

CHAPTER IX.
RUPERT ACCEPTS A MISSION
The interval between the 1st of January and the 13th of April, the
day of Rupert’s marriage, may be briefly passed over. All the actors
are on the scene, except those who have to arrive out of the
Soudanese desert; their characters and objects are known, and it
remains only to follow the development of the human forces which
have been set in motion to their inevitable end, whatever that may
be.
The choosing of this date, the 13th, which chanced to be a Friday,
was one of the grim little jokes of Lord Devene, from whose house
the marriage was to take place; a public protest against the
prevalence of vulgar superstitions by one who held all such folly in
contempt. To these Rupert, a plain-sailing man who believed his
days to be directed from above, was certainly less open than most,
although even he, by choice, would have avoided anything that
might suggest unpleasant thoughts. Edith, however, neglectful as
she was of any form of religion, still felt such ancient and obscure
influences, and protested, but in vain. The date suited him, said her
cousin. There were reasons why the marriage could not take place
before, and on Saturday, the 14th, he had to go away for a fortnight
to be present in Lancashire at an arbitration which would be lengthy,
and held in situ as to legal matters connected with his coal-mines.
So she yielded, and the invitations were issued for Friday, the 13th
of April.
Meanwhile things went on much as might be expected. Rupert sat
in Edith’s pocket and beamed on her all day, never guessing, poor,

blind man, that at times he bored her almost to madness. Still she
played her part faithfully and well, paying him back word for word
and smile for smile, if not always tenderness for tenderness. Mrs.
Ullershaw, having shaken off her preliminary fears and doubts, was
cheerful in her demeanour, and being happy in the happiness of her
son, proclaimed on every occasion her complete contentment with
the match. Lord Devene appeared pleased also, as indeed he was,
and lost no opportunity of holding up Rupert as a model lover, while
that unfortunate man writhed beneath his sarcasms.
Thus once—it was after one of those Grosvenor Square dinners
which Rupert hated so heartily, he found a chance of pointing a
moral in his best manner. Rupert, as usual, had planted himself by
Edith in a corner of the room, whence, much as she wished it, she
could not escape, making of her and himself the object of the
amused attention of the company.
“Look at them,” said Lord Devene, who had unexpectedly entered,
with a smile and a wave of the hand that made everybody laugh,
especially Dick, who found their aspect absurd.
“Rupert, do get up,” said Edith; “they are laughing at us.”
“Then let them laugh,” he grumbled, as he obeyed, following her
sheepishly to the centre of the room.
While they advanced, some new sally which they could not hear
provoked a fresh outburst of merriment.
“What is it that amuses you?” asked Rupert crossly.
“Ach, Rupert,” said Lady Devene, “they laugh at you because you
do like to sit alone with your betrothed; but I do not laugh, I think it
is quite proper.”
“Tabitha puts it too roughly,” broke in Lord Devene. “We are not
making fun of beauty and valour completing each other so
charmingly in that far corner, we are paying them our tribute of
joyous and respectful admiration. I confess that it delights me, who
am getting old and cynical, to see people so enraptured by mere
companionship. That, my dear Rupert, is what comes of not being
blasé. With the excellent Frenchman, you can say: ‘J’aime

éperdument et pour toujours car je n’ai jamais éparpillé mon cœur;
le parfait amour c’est la couronne de la vertu.’ Now you reap the rich
reward of a youth which I believe to have been immaculate. Happy
is the man who, thrusting aside, or being thrust aside of opportunity,
reserves his first great passion for his wife.”
A renewed titter greeted this very elaborate sarcasm, for so
everyone felt it to be, especially Rupert, who coloured violently. Only
Lady Devene came to his aid and tried to cover his confusion.
“Bah!” she said, “your wit, George, seems to smell of the lamp and
to have a nasty sting in its tail. Why should you mock at these young
people because they are honest enough to show that they are fond
of each other, as they ought to be? Pay no attention and go back to
your corner, my dears, and I will come and sit in front of you; or at
least tell them they should be sorry they cannot say they have not
scattered their hearts about; that is what the French word means,
doesn’t it?”
Then in the amusement that was caused by Lady Devene’s mixed
metaphors and quaint suggestion that with her ample form she
should shelter the confidences of Rupert and Edith from prying eyes,
the joke was turned from them to her, as she meant that it should
be, and finally forgotten. But neither Rupert nor Edith forgot it.
Never again did they sit close together in that Grosvenor Square
drawing-room, even in the fancied absence of Lord Devene, a result
for which Edith, who hated such public demonstrations, was truly
grateful.
For a while after the announcement of the engagement Rupert
and Dick had seen as little of each other as was possible, the former,
because he had not forgiven Dick’s conduct at the shooting party,
which impressed his mind far more than the vague talk about him
and Edith in the past. In this, indeed, he had never believed, and his
nature being utterly unsuspicious, it was now totally forgotten. As for
Dick, he had his own reasons for the avoidance of his successful
rival, whom all men and women united to honour. By degrees,
however, Edith, who lived in perpetual fear of some passionate
outburst from Dick, managed to patch up their differences, at least

to the outward eye, for the abyss between them was too wide to be
ever really bridged. Indeed, her efforts in this direction nearly
resulted in what she most wanted to avoid, an open quarrel.
It came about in this fashion. The opportunity which had been
foreseen arose; the sitting member for that county division in which
Lord Devene lived had retired, and Dick was put up to contest the
seat in the Radical interest against a strong and popular
Conservative candidate. His chances of success were fair, as the
constituency was notoriously fickle, and public feeling just then was
running against the Tories. Also Lord Devene, although as a peer he
could take no active part in the election, was using his great wealth
and interest in every legitimate way to secure his nominee’s return.
When the contest, with the details of which we need not concern
ourselves, drew near its close, Dick himself suggested that it might
help him, and give variety to one of his larger meetings, if Rupert
would come and talk a little about Egypt and the Arabs with whom
he had fought so often. He knew well that although country people
will attend political gatherings and shout on this side or on that
according as they think that their personal advantage lies, all the
best of them are in reality far more interested in exciting stories of
fact from someone whom they respect, than in the polemics of party
politicians.
When the suggestion was made to him, needless to say, Rupert
declined it at once. Theoretically, he was a Liberal; that is to say, like
most good and earnest men he desired the welfare of the people
and the promotion of all measures by which it might be furthered.
But on the other hand, he was no bitter Radical of the stamp of Lord
Devene, who wished to pull down and burn for the sake of the crash
and the flare; and he was, on the other hand, what nowadays is
called an Imperialist, believing in the mission of Britain among the
peoples of the earth, and desiring the consolidation of her empire’s
might because it meant justice, peace, and individual security;
because it freed the slave, paralysed the hands of rapine, and
caused the corn to grow and the child to laugh.

Now Rupert did not consider that these causes would be promoted
by the return of Dick to Parliament, where he would sit as a
mouthpiece of Lord Devene. Then Edith intervened, and dropping
Dick out of the matter, asked him to do this for her sake. She
explained that for family reasons it would be a good thing if Dick
won this seat, as thereby a new career would be open to him who
sadly needed one; also that Dick himself would be most grateful.
The end of it was that Rupert consented, forgetting, or not being
aware, that as an officer on leave he had no business to appear
upon a party platform, a fact of which Dick did not think it necessary
to remind him.
The meeting, which was one of the last of the campaign, took
place in the corn-hall of a small country town, and was crowded by
the supporters of Dick and a large contingent of his opponents. The
candidate himself, who spoke glibly and well enough, for as Edith
and others had often found out, Dick did not lack for readiness, gave
his address, which was cheered by his friends and groaned at by his
foes. It was of the stereotyped order—that is to say, utterly
worthless, a mere collection of the parrot platitudes of the hour by
which the great heart of the people was supposed to be moved, but
for all that, well and forcibly delivered.
Then followed a heavy and long-winded member of Parliament, at
whom, before he had done, the whole room hooted, while some of
the occupants of the back benches began to sing and shuffle their
feet. Next the chairman, a prosperous local manufacturer, rose and
said that he was going to call upon Colonel Ullershaw of the
Egyptian army, Companion of the Bath, member of the Distinguished
Service Order, and of the Turkish Order of the Medjidie (he called it
“Gee-gee,” or something like it), and the possessor of various
medals, to say nothing of his being the relative and present heir of
their most esteemed friend and neighbour, the noble Lord Devene,
and therefore intimately connected with every one of them, to
address them. The gallant Colonel would not make them a political
speech, as they had had enough of politics for that night (at this the
audience enthusiastically shouted, Hear, hear!), but he would tell

them about the wars in Egypt which, although many of them did not
approve of those wars, were still interesting to hear about as at any
rate they paid for them (more hear! hears!). He might well call him
gallant, as they would say also when he told them the following
story, and to the absolute horror of Rupert, who was literally
writhing on a back seat behind this dreadful man, and to the
amusement of Edith sitting at his side, he proceeded to give a
highly-coloured and garbled version of the exploit that did not win
him the Victoria Cross, whereon a voice shouted:
“That’s all true. I was there. I saw the Colonel come in with the
man.” (Renewed and tempestuous cheers.)
There being no help for it, Rupert rose, and was warmly greeted.
He had never given his mind to public speaking, and although his
voice was good and resonant, it cannot be said that at the beginning
his remarks compelled attention. Indeed, after five minutes of them,
Dick and his agent, counting him a failure, began to consult as to
how they could get him down, while Edith felt mortified. Then, as he
wandered on with a long and scientific account of the Egyptian
campaigns, someone shouted: “Stow all that history book, and tell
us about Gordon.”
Instantly Rupert took fire, for Gordon was his favourite hero, the
man whom he had known, loved and revered above all other men.
He began to tell them about Gordon, about his glorious and
desperate enterprise undertaken at the request of the Government,
about his splendid fight against overwhelming odds, whilst sick at
heart he awaited the relief which was sent too late; about that
journey to save him in which he, Rupert, had shared, about the
details of his martyr-death. Then, quite forgetting the occasion and
whom he had come to support, he broke into a really eloquent tirade
against those whom he considered to be responsible for the
desertion of Gordon.
To finish up with, in answer to the suggestion of a voice in the
audience that Gordon was not really dead, he actually quoted some
well-known lines of poetry which he had by heart:

“He will not come again, whatever our need,
He will not come, who is happy, being freed
From the deathly flesh and perishable things,
And lies of statesmen and rewards of kings,”
and then suddenly sat down amidst a tempest of cheers, mingled
with cries of “Shame!” in which the whole room joined.
“Great Heavens!” said Dick fiercely, to his agent, “I believe that
speech will lose us the election.”
“Shouldn’t wonder,” answered the agent grimly. “Whatever did you
get him here for? Better have stuck to the party patter.”
Meanwhile a man, standing on a form, bawled out:
“And is them the beggars as you wishes us to vote for, master?”
Whereon followed what the local paper (luckily for Rupert his
remarks were reported nowhere else) described as “great
confusion,” which culminated in something like a free fight.
In the midst of all this tumult, Dick, who was beside himself with
passion, forced his way to Rupert, and almost shaking his fist in his
face, shouted at him:
“Damn you! You did that on purpose. You’ve lost me the seat, but
sooner or later I’ll be even with you, you canting hypocrite—”
He got no further, for next instant Rupert’s heavy right hand fell
upon his shoulder and forced him to a chair.
“You don’t know what you are saying,” he said; “but speak like
that again, and I’ll throw you off the platform.”
Then Dick, feeling that iron grip still upon his shoulder, was silent.
Here we may close the account of this curious scene, which once
more showed the undesirability of invoking the aid of inexperienced
and too honest persons at party meetings. To Dick the matter was
serious enough, but to Edith’s surprise, Lord Devene, whom she had
thought would be angry, was intensely amused. Indeed, he went so
far as to say that whether Dick got in or not, that one delightful
story was worth the cost of the entire campaign.

When Rupert came to understand what he had done, needless to
say he showed much penitence, and wrote a letter of apology to
Dick, in which he “regretted having spoken the truth about Gordon
in the excitement of the moment,” and gave him leave, if he wished,
“to publish this letter.” Of this kind offer Dick did not avail himself.
Under advice, however, he wrote back, saying sarcastically that the
fault was his, who should have remembered that “distinguished men
of action were rarely adepts at public speaking, and could not be
expected to understand the exigencies of party affairs, which seldom
made it desirable to drag the last veil from Truth, however pure and
beautiful she might be.” He concluded by apologising, in his turn, for
any words that he might have spoken “in the excitement of the
moment.”
Thus, outwardly, at any rate, matters were patched up between
them; still Dick did not forget his promise to be even sooner or later,
or indeed the weight of Rupert’s hand, of which his shoulder showed
traces for many a day.
As for the end of the contest, the Devene money and interest
prevailed at last, Dick being returned triumphantly with a small but
sufficient majority of fifteen votes, reduced to thirteen on a recount.
A few days later he took his seat in the House, where he was
enthusiastically received by his party, to which the winning of this
election was of consequence.
Dick had not very long to wait for his first opportunity of “coming
even” with Rupert. As it chanced, on the 11th of April, two days
before the marriage, he met and fell into conversation with Lord
Southwick in the lobby of the House.
“By the way,” said his lordship, “rather a pity that Ullershaw is just
going to be married; we have got a job that would exactly suit him.”
“What is that?” asked Dick, pricking up his ears.
“Oh! a man is wanted who knows those rascally Arab sheiks who
live about the frontier at Wady-Halfa—secret service mission, to get
round them privately, you know; I can’t tell you the details, not that
I think you would give me away to your people. The officer sent

must be thoroughly acquainted with Arabic, and with the beastly
manners and customs of the natives. Ullershaw’s name came up at
once as the very man, but I said that I was going to his wedding in
two days, so as we couldn’t think of anyone else, the matter was left
over till to-morrow afternoon.”
“When would he have to start?” asked Dick.
“At once, the thing is urgent; on Friday by the Brindisi mail, about
seven o’clock in the evening, and you see he is to be married that
afternoon. It’s a thousand pities, as it would have been a great
chance for him and for us too.”
Dick thought a moment and light came to him.
“My cousin Ullershaw is a curious fellow,” he said, “and I am not
by any means certain that he would let his marriage stand in the
way of duty, if it were put to him like that. How long would this
mission take?”
“Oh! he could be back here in three months, but—er—you know—
it would not be entirely devoid of risk. That’s why we must have
someone whose nerve can be really relied on.”
“Ullershaw likes risks. As you say, it would suit him down to the
ground. Look here, Lord Southwick! why don’t you give him the
chance? It would be kind of you. It’s a shame to take away a fellow’s
opportunities because he commits the crime of getting married, and
matrimonial bliss will generally keep three months. Send for him and
ask him. At any rate, he will appreciate the compliment.”
“Don’t think I should if I had only been married an hour or two,”
said Lord Southwick. “However, the public service must be
considered, so I will hear what my chief says. Where will a wire find
him?”
Dick gave the address, and as an afterthought added that of Lord
Devene in Grosvenor Square, where it occurred to him that Rupert
would very likely be on the following afternoon, suggesting that it
would be wise to send any telegram in duplicate.
“Very well,” said the Under-Secretary, as he made a note of the
addresses. “I will settle it one way or another to-morrow afternoon;

shan’t get the chance before,” and he turned to go.
“One word,” broke in Dick. “I shall take it as a favour if you don’t
mention my name in connection with this matter. Of course I want to
do him a good turn, but there is no knowing how the lady will take
it, and I might get wigged afterwards.”
“All right,” answered Lord Southwick, with a laugh, “I’ll remember.”
“I don’t think that Edith would see spending her honeymoon
amongst the savages of the Soudan,” reflected Dick to himself, with
a crooked little smile, as he made his way into the House. “‘Not
devoid of risk.’ Yes, Rupert’s friend, Gordon, went on a special
mission to the Soudan, and did not come back.”
On the following afternoon about four o’clock, as Rupert was
leaving his mother’s house to see Edith in Grosvenor Square, where
she had taken up her abode, a messenger put a telegram into his
hand, which read:
Come to the War Office at once. Must speak with you
upon very important business. Will wait here till five.
SOUTHWICK.
Wondering what he was wanted for, Rupert told his cabman to
drive to Pall Mall, and within half an hour of the receipt of the
telegram sent in his card. Presently he was shown, not to the Under-
Secretary’s room, but into another, where he found the Secretary of
State, and with him, Lord Southwick.
“Prompt, very prompt, I see, Colonel Ullershaw,” said the former,
“an excellent quality in an officer. Now sit down and I will just go
over the main points of this business. If you undertake it, Lord
Southwick will explain the details afterwards. You know the Wady-
Halfa district and the Shillook Arabs and their headmen, don’t you,
and you can speak Arabic well, can’t you? Also you have had
diplomatic experience, haven’t you?”

“Yes, sir, to all four questions,” answered Rupert.
“Very good. These Shillooks have been giving a lot of trouble,
raiding and killing people about Abu-Simbel and so forth. According
to our reports, which you can see afterwards, they have been stirred
up by a rascal called Ibrahim, the Sheik of the Sweet Wells. Do you
know him?”
“Yes, sir,” replied Rupert, with a little smile, “he threatened to
murder me the other day.”
“I can quite believe it. Now see here. We are advised that several
of these Shillook chiefs, including the one who has the most
influence, are getting tired of the Khalifa and his little ways, and are,
in short, open to treat, if only they can be got at by someone whom
they know and have their palms well-greased. Now, for various
reasons, the Egyptian Government does not wish to send an
embassy to them, or any officer who is at present on the spot. You
see the Khalifa would hear of it at once and might come down on
them. What is wanted is an envoy travelling apparently on his own
business, or if it is feasible, disguised as an Arab, who will slip
through to them quietly and arrange a treaty. I need not say that,
whoever did this satisfactorily, would earn the gratitude of the
Egyptian Government, and would not be overlooked at the proper
time. Now, Colonel Ullershaw, it has occurred to us that you are the
very man for this affair, especially as you would take our complete
confidence with you.”
“I am much honoured,” said Rupert, flushing at the compliment. “I
should like the mission above all things, especially as I understand
these men, one or two of whom are rather friends of mine. Indeed,
the most influential of them accompanied me on a shooting
expedition, and if anyone can move him, I think I can.”
“There would be risks,” put in Lord Southwick meaningly, for under
the circumstances his kind heart misgave him.
“I don’t mind risks, or, at least, I am accustomed to them, my
lord,” said Rupert quietly.

“There is another point,” went on Lord Southwick. “Supposing that
you were to fail—and failure must be contemplated—it might be
needful, as no forward policy has been announced at present, for
those in authority not to take any official notice of the affair, which
would possibly be used as a handle for attack upon them. You
would, therefore, receive no written instructions, and the necessary
money would be handed to you in gold.”
“I quite understand,” answered Rupert, “and so long as I am not
thought the worse of in such an event, or made to suffer for it, it is
all the same to me. Only,” he added, suddenly remembering his
forthcoming marriage, “when should I have to start?”
“By the evening mail to-morrow,” said the Secretary of State, “for
the conditions may change and will not bear delay.”
Rupert’s jaw fell. “I am to be married to-morrow at half-past two,
sir.”
The Secretary of State and Lord Southwick looked at each other;
then the former spoke.
“We know that, Colonel Ullershaw, especially as one of us is to
have the pleasure of attending your wedding. Still, in your own
interests and what we are sure you will consider much more, in
those of your country, we felt it right to give you the first offer of
this delicate and responsible mission. Situated as you are, we do not
urge you to accept it, especially as in the event of your refusal, for
which we shall not in the least blame you, we have another officer
waiting to take your place. At the same time, I tell you candidly that
I do not think you will refuse, because I believe you to be a man
who sets duty above every other earthly consideration. And now,
sorry as I am to hurry you when there is so much to be considered
on both sides, I must ask for your decision, as the other gentleman
must absolutely have twenty-four hours in which to make his
preparations.”
Rupert rose and walked twice up and down the room, while they
watched him—Lord Southwick very uneasily. At the second turn, he
halted opposite to the Secretary of State.

“You used the word duty, sir,” he said, “and therefore I have little
choice in the matter. I accept the mission with which you have been
pleased to honour me.”
Lord Southwick opened his mouth to speak, but the Secretary of
State cut him short.
“As Colonel Ullershaw has accepted, I do not think we need waste
further time in discussion. Colonel Ullershaw, I congratulate you on
the spirit that you have shown, which, as I thought it would, from
your record and the judgment I formed of you at our previous
interview, has led you to place your duty to your Queen and country
before your personal happiness and convenience. I trust—and
indeed I may say I believe—that our arrangement of this afternoon
may prove, not the starting-point, it is true, but a very high step in a
great and distinguished career. Good-day; I wish you all success.
Lord Southwick will join you in his room presently and settle the
details.”
“It seems a little rough,” said Lord Southwick, as the door closed
behind Rupert, “on his marriage day and so forth. Supposing he got
killed, as he very likely will.”
“Many men, as good or better, have come to grief in doing their
duty,” answered his chief, a pompous individual who modelled
himself upon the Spartans, at any rate where other people were
concerned. “He must take his chance like the rest. Give him the
K.C.B. and that sort of thing if he gets through, you know.”
“K.C.B.s aren’t much use to dead men, or their widows either,”
grumbled Lord Southwick. “I rather wish we hadn’t talked to him
about duty; you see, he is a quixotic sort of fellow, and really, as he
isn’t even to have a commission, there can’t be any duty in the
matter. He’s only a kind of volunteer on a second-class, forlorn hope,
to prepare the way by bribes and otherwise for an advance about
which nothing is to be said, with the chance of being repudiated as
having exceeded his instructions if anything goes wrong.”
“Really, Southwick,” said his chief uneasily, “it is a pity all this
didn’t occur to you before you urged his employment—on the

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!
ebookfinal.com

Applied Statistical Inference with MINITAB Sally Lesik

More Related Content

Similar to Applied Statistical Inference with MINITAB Sally Lesik (20)

Recently uploaded (20)

Applied Statistical Inference with MINITAB Sally Lesik