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PREFACE

The 11th edition of Biostatistics: A Foundation for the Analysis in the Health Sciences was
prepared to meet the needs of students who may be using the book as a text in a course, and
for professionals who may need a handy desk reference for basic, but widely used, statistical
procedures in their applied work. For undergraduates, several chapters in this edition introduce
concepts to students who are taking a first, generally junior-level or senior-level, course in statis-
tics as part of their pre professional, nursing, or public health education. For beginning graduate
students, both introductory chapters and more advanced topics in the text are suitable for master’s
students in health professions.
The breadth of coverage in the text is much more than may be generally covered in a
one-semester course. This coverage, along with hundreds of practical and specific subject-matter
exercises, allows instructors extensive flexibility in designing a course at various levels. We have
developed some ideas on appropriate topical coverage based on our own use of this text in the
classroom, and we present a matrix below in that regard.
As with previous editions of this book, the 11th edition requires little mathematical knowledge
beyond college algebra. However, as many instructors will attest, it is not uncommon for students
to lack solid proficiency in algebra prior to taking a statistics course. Our experience suggests
that spending some time showing basic, algebraic manipulations of the formulas in the book goes
a long way in quelling fears with mathematics that may easily undermine a statistics course.
We have attempted to maintain an emphasis on practical and intuitive understanding of principles
rather than on abstract concepts, and we therefore maintain a reliance on problem-solving utilizing
examples and practice problems that are drawn largely from the health sciences literature instead
of contrived problems, which makes the text more practical and less abstract. We believe that
this makes the text more interesting for students, and more useful for health professionals who
reference the text while performing their work duties.
There is no doubt that technological sophistication has changed how we teach and how we
apply statistics professionally. The use of hand calculations can be a useful way to develop an
understanding of how formulas work, and they also lead to an appreciation of underlying assump-
tions that need to be considered. However, once basic skills are learned, it is often useful to
explore computer programs for dealing with large and/or real-world problem sets. Additionally,
the reliance on statistical tables, once necessary for finding areas under curves, estimates of prob-
ability, and so on, has largely been replaced by efficient computer algorithms readily available
to students and practitioners. To that end, you will find example outputs from MINITAB, SAS,
SPSS, R, JASP, EXCEL, and others in the text. We do not endorse the use of any particular pro-
gram, but simply note that many are available and both students and professionals will need to
have some facility using the program of their choice. Additionally, we generally only provide out-
puts and explanation regarding programs, not instruction on their use, as there are many books
dedicated to providing stepwise user guides for various programs.

Changes and Updates to This Edition

Many changes and updates have been made to this edition. We have attempted to incorporate
corrections and clarifications that enhance the material presented in hopes of making the text
vii
viii PREFACE

more readable and accessible to the audience. We thank the reviewers of the many editions of
this text for making useful comments and suggestions that have found their way into the new
edition. Of course, there are always ways to improve and enhance, and we welcome comments
and suggestions.
Specific changes to this edition include: (1) a newly rewritten introduction to the scientific
method in Chapter 1; (2) a rearranged and rewritten Chapter 2 that now includes a section on data
visualization and graphing; (3) an introduction to hypothesis testing and controversies surround-
ing p values in Chapter 7; (4) a brief introduction to Poisson regression in Chapter 11; (5) testing
or dependent proportions using McNemar’s Test in Chapter 12; and (6) the use of randomization
procedures, including permutation-based p values and bootstrap confidence intervals, has been
integrated throughout the text.
Other changes have occurred as well. Numerous changes to writing and phrasing have occurred
to enhance clarity throughout the text. Also, by popular demand, we have integrated some R
scripting ideas throughout many chapters for those using that particular software. Finally, for
the benefit of instructors, we have provided some “Instructor-only” problems that will be made
available to adopters of the text to use in their courses. Finally, the statistical tables are readily
available through your instructor. Inasmuch as some professionals and professors still use tables,
we believe it is important to retain access to them, and we continue to provide examples of their use
in the current edition; however, we also show alternatives to tabled probabilities using computer
programs.

Coverage Ideas
In the table below, we provide some suggestions for topical coverage in a variety of contexts, with
“X” indicating those chapters we believe are most relevant for a variety of courses for which we
believe this text is appropriate. As mentioned above, the text is designed to be flexible in order to
accommodate various teaching styles and course presentations. Although the text is designed with
progressive presentation of concepts in mind, certain topics may be skipped or briefly reviewed
so that instructors may focus on concepts most useful for their courses.

Chapters (X: Suggested coverage;

O: Optional coverage)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Undergraduate course for health X X X X X X X X X O O X O O O
sciences students
Graduate course for beginning X X X X X X X X X X O X X X O
health sciences master’s students
Graduate course for graduate health X O O O O X X X X X X X X X X
sciences students who have
completed an introductory
statistics course

Supplements
Several supplements are available for the text on the instructor’s website at www.wiley.com/go/
Daniel/Biostatistics11e. These include:

• Instructor’s Solution Manual, available only to instructors who have adopted the text.
 Preface ix

• Data Sets, over 200 data sets are available to be downloaded in CSV format for ready import-
ing into any basic statistics program.

Acknowledgments
Many reviewers, students, and faculty have made contributions to this text through their careful
review, inquisitive questions, and professional discussion of topics. In particular, we would like
to thank:
• Dr. Sheniz Moonie, University of Nevada, Las Vegas
• Dr. Guogen Shan, University of Nevada, Las Vegas
• Dr. Gian Jhangri, University of Alberta
• Dr. Tina Cunningham, Eastern Virginal Medical School
• Dr. Shakhawat Hossain, University of Winnipeg
• Dr. Milind Phadnis, University of Kansas Medical Center
• Dr. David Anderson, Xavier University of Louisiana
• Dr. Derek Webb, Bemidji State University
• Dr. Keiji Oda, Loma Linda University
• Dr. David Zietler, Grand Valley State University
• Dr. Genady Grabarnik, St. John’s University
• Dr. Al Bartolucci, University of Alabama at Birmingham
• Dr. Hwanseok Choi, University of Southern Mississippi
• Dr. Mark Kelley, University of Pittsburgh at Bradford
• Dr. Wan Tang, Tulane University
• Dr. Phil Gona, University of Massachusetts, Boston
• Dr. Jill Smith, University of California, Riverside
• Dr. Ronnie Brown, University of Baltimore
• Dr. Apoorv Goel, Indiana University-Purdue University Indianapolis
• Dr. Daniel Yorgov, Indiana University-Purdue University Fort Wayne
There are three additional acknowledgments that must be made to important contributors of
the text. Dr. John. P. Holcomb of Cleveland State University updated many of the examples and
exercises found in the text. Dr. Edward Danial of Morgan State University provided an extensive
accuracy review of the 9th edition of the text, and his valuable comments added greatly to the
later editions of the book. Dr. Jodi B. A. McKibben of the Uniformed Services University of the
Health Sciences provided an extensive accuracy review of the 10th edition of the book, and we
remain grateful for her contributions and comments.
We wish to acknowledge the cooperation of Minitab, Inc. for making available to the authors
over many years and editions of the book the latest versions of their software.
Thanks are due to Professors Geoffrey Churchill and Brian Schott of Georgia State University,
who wrote computer programs for generating some of the Appendix tables, and to Professor
Lillian Lin, who read and commented on the logistic regression material in earlier editions of the
x PREFACE

book. Additionally, Dr. James T. Wassell provided useful assistance with some of the survival
analysis methods presented in earlier editions of the text.
We are grateful to the many researchers in the health sciences field who publish their results
and hence make available data that provide valuable practice to the students of biostatistics.

Final Note
I am eternally grateful that I have had the opportunity to work with Dr. Wayne Daniel on several
editions of this text. I was invited by Wayne to work with him in various capacities beginning with
the 8th edition. Since that time, I have had the pleasure to get to know Wayne and to appreciate his
high standards and expectations. Unfortunately, Wayne was not able to participate in this edition.
I am honored that he has entrusted me to carry forward his legacy.

Chad L. Cross
Las Vegas, Nevada
CONTENTS

PREFACE vii

1 INTRODUCTION TO BIOSTATISTICS 1
1.1 Introduction, 2
1.2 Basic Concepts and Definitions, 2
1.3 Measurement and Measurement Scales, 5
1.4 Sampling and Statistical Inference, 7
Exercises, 12
1.5 The Scientific Method, 13
Exercises, 15
1.6 Computers and Technology, 15
1.7 Summary, 16
Review Questions and Exercises, 16
References, 17

2 DESCRIPTIVE STATISTICS 18
2.1 Introduction, 19
2.2 The Ordered Array, 19
2.3 Frequency Tables, 21
Exercises, 25
2.4 Measures of Central Tendency, 29
2.5 Measures of Dispersion, 34
Exercises, 41
2.6 Visualizing Data, 43
Exercises, 51
2.7 Summary, 51
Summary of Formulas for Chapter 2, 51
Review Questions and Exercises, 53
References, 56

3 SOME BASIC PROBABILITY CONCEPTS 57

3.1 Introduction, 57
3.2 Two Views of Probability: Objective and Subjective, 58
3.3 Elementary Properties of Probability, 60

xiii
xiv CONTENTS

3.4 Calculating the Probability of an Event, 61

Exercises, 68
3.5 Bayes’ Theorem, Screening Tests, Sensitivity, Specificity, and Predictive
Value Positive and Negative, 69
Exercises, 73
3.6 Summary, 74
Summary of Formulas for Chapter 3, 75
Review Questions and Exercises, 76
References, 79

4 PROBABILITY DISTRIBUTIONS 80
4.1 Introduction, 81
4.2 Probability Distributions of Discrete Variables, 81
Exercises, 86
4.3 The Binomial Distribution, 87
Exercises, 95
4.4 The Poisson Distribution, 96
Exercises, 100
4.5 Continuous Probability Distributions, 101
4.6 The Normal Distribution, 103
Exercises, 109
4.7 Normal Distribution Applications, 109
Exercises, 113
4.8 Summary, 114
Summary of Formulas for Chapter 4, 114
Review Questions and Exercises, 115
References, 117

5 SOME IMPORTANT SAMPLING DISTRIBUTIONS 119

5.1 Introduction, 119
5.2 Sampling Distributions, 120
5.3 Distribution of the Sample Mean, 121
Exercises, 128
5.4 Distribution of the Difference Between Two Sample Means, 129
Exercises, 133
5.5 Distribution of the Sample Proportion, 134
Exercises, 136
5.6 Distribution of the Difference Between Two Sample
Proportions, 137
Exercises, 139
5.7 Summary, 139
Summary of Formulas for Chapter 5, 140
Review Questions and Exercises, 140
References, 141
 Contents xv

6 ESTIMATION 143
6.1 Introduction, 144
6.2 Confidence Interval for a Population Mean, 147
Exercises, 152
6.3 The t Distribution, 153
Exercises, 157
6.4 Confidence Interval for the Difference Between Two Population
Means, 158
Exercises, 164
6.5 Confidence Interval for a Population Proportion, 165
Exercises, 166
6.6 Confidence Interval for the Difference Between Two Population
Proportions, 167
Exercises, 168
6.7 Determination of Sample Size for Estimating Means, 169
Exercises, 171
6.8 Determination of Sample Size for Estimating Proportions, 171
Exercises, 172
6.9 The Chi-Square Distribution and the Confidence Interval for the Variance
of a Normally Distributed Population, 173
Exercises, 177
6.10 The F-Distribution and the Confidence Interval for the Ratio of the
Variances of Two Normally Distributed Populations, 177
Exercises, 180
6.11 Summary, 181
Summary of Formulas for Chapter 6, 182
Review Questions and Exercises, 183
References, 186

7 HYPOTHESIS TESTING 189

7.1 Introduction, 190
7.2 Hypothesis Testing: A Single Population Mean, 200
Exercises, 211
7.3 Hypothesis Testing: The Difference Between Two Population
Means, 213
Exercises, 221
7.4 Paired Comparisons, 224
Exercises, 229
7.5 Hypothesis Testing: A Single Population Proportion, 232
Exercises, 234
7.6 Hypothesis Testing: The Difference Between Two Population
Proportions, 235
Exercises, 236
xvi CONTENTS

7.7 Hypothesis Testing: A Single Population Variance, 238

Exercises, 240
7.8 Hypothesis Testing: The Ratio of Two Population Variances, 241
Exercises, 244
7.9 The Type II Error and the Power of a Test, 245
Exercises, 249
7.10 Determining Sample Size to Control Type II Errors, 249
Exercises, 251
7.11 Summary, 251
Summary of Formulas for Chapter 7, 252
Review Questions and Exercises, 254
References, 264

8 ANALYSIS OF VARIANCE 267

8.1 Introduction, 268
8.2 The Completely Randomized Design, 271
Exercises, 289
8.3 The Randomized Complete Block Design, 294
Exercises, 301
8.4 The Repeated Measures Design, 305
Exercises, 313
8.5 The Factorial Experiment, 315
Exercises, 326
8.6 Summary, 329
Summary of Formulas for Chapter 8, 329
Review Questions and Exercises, 331
References, 350

9 SIMPLE LINEAR REGRESSION AND CORRELATION 354

9.1 Introduction, 355
9.2 The Regression Model, 355
9.3 The Sample Regression Equation, 357
Exercises, 364
9.4 Evaluating the Regression Equation, 366
Exercises, 380
9.5 Using the Regression Equation, 380
Exercises, 384
9.6 The Correlation Model, 384
9.7 The Correlation Coefficient, 386
Exercises, 394
9.8 Some Precautions, 397
9.9 Summary, 398
Summary of Formulas for Chapter 9, 399
Review Questions and Exercises, 401
References, 413
 Contents xvii

10 MULTIPLE REGRESSION AND CORRELATION 416

10.1 Introduction, 417
10.2 The Multiple Linear Regression Model, 417
10.3 Obtaining the Multiple Regression Equation, 418
Exercises, 423
10.4 Evaluating the Multiple Regression Equation, 427
Exercises, 433
10.5 Using the Multiple Regression Equation, 433
Exercises, 435
10.6 The Multiple Correlation Model, 435
Exercises, 443
10.7 Summary, 446
Summary of Formulas for Chapter 10, 447
Review Questions and Exercises, 448
References, 454

11 REGRESSION ANALYSIS: SOME ADDITIONAL TECHNIQUES 455

11.1 Introduction, 455
11.2 Qualitative Independent Variables, 459
Exercises, 472
11.3 Variable Selection Procedures, 474
Exercises, 478
11.4 Logistic Regression, 485
Exercises, 495
11.5 Poisson Regression, 497
Exercises, 503
11.6 Summary, 504
Summary of Formulas for Chapter 11, 505
Review Questions and Exercises, 506
References, 517

12 ThE CHI-SQUARE DISTRIBUTION AND THE ANALYSIS OF FREQUENCIES 519

12.1 Introduction, 520
12.2 The Mathematical Properties of the Chi-Square Distribution, 520
12.3 Tests of Goodness-of-Fit, 523
Exercises, 533
12.4 Tests of Independence, 535
Exercises, 544
12.5 Tests of Homogeneity, 545
Exercises, 551
12.6 The Fisher’s Exact Test, 552
Exercises, 557
12.7 Relative Risk, Odds Ratio, and the Mantel–Haenszel Statistic, 557
Exercises, 567
12.8 Summary, 569
xviii CONTENTS

Summary of Formulas for Chapter 12, 570

Review Questions and Exercises, 571
References, 576

13 NONPARAMETRIC AND DISTRIBUTION-FREE STATISTICS 579

13.1 Introduction, 580
13.2 Measurement Scales, 581
13.3 The Sign Test, 581
Exercises, 588
13.4 The Wilcoxon Signed-Rank Test for Location, 589
Exercises, 593
13.5 The Median Test, 594
Exercises, 596
13.6 The Mann–Whitney Test, 597
Exercises, 602
13.7 The Kolmogorov–Smirnov Goodness-of-Fit Test, 604
Exercises, 610
13.8 The Kruskal–Wallis One-Way Analysis of Variance by Ranks, 610
Exercises, 615
13.9 The Friedman Two-Way Analysis of Variance by Ranks, 618
Exercises, 622
13.10 The Spearman Rank Correlation Coefficient, 623
Exercises, 629
13.11 Nonparametric Regression Analysis, 631
Exercises, 634
13.12 Summary, 634
Summary of Formulas for Chapter 13, 635
Review Questions and Exercises, 636
References, 644

14 SURVIVAL ANALYSIS 646

14.1 Introduction, 647
14.2 Time-to-Event Data and Censoring, 647
14.3 The Kaplan–Meier Procedure, 651
Exercises, 656
14.4 Comparing Survival Curves, 658
Exercises, 661
14.5 Cox Regression: The Proportional Hazards Model, 663
Exercises, 666
14.6 Summary, 667
Summary of Formulas for Chapter 14, 667
Review Questions and Exercises, 668
References, 669
 Contents xix

15 VITAL STATISTICS 671

15.1 Introduction, 671
15.2 Death Rates and Ratios, 672
Exercises, 677
15.3 Measures of Fertility, 679
Exercises, 681
15.4 Measures of Morbidity, 682
Exercises, 683
15.5 Summary, 683
Summary of Formulas for Chapter 15, 684
Review Questions and Exercises, 685
References, 686

INDEX 689

The following supplements are available through your instructor

APPENDIX: STATISTICAL TABLES
ANSWERS TO SELECTED PROBLEMS
Introduction to Biostatistics
1
C H A PTER O VERV IEW
This chapter is intended to provide an overview of the basic statistical concepts and
definitions used throughout the textbook. A course in statistics requires the student to
learn new and specific terminology. Therefore, this chapter lays the foundation neces-
sary for understanding basic statistical terms and concepts and the role that statisticians
play in promoting scientific discovery.

TO PI C S
1.1 Introduction
1.2 Basic Concepts and Definitions
1.3 Measurement and Measurement Scales
1.4 Sampling and Statistical Inference
1.5 The Scientific Method
1.6 Computers and Technology
1.7 Summary

LEARNING OUTCOMES
After studying this chapter, the student will

1. understand the basic concepts and terminology of biostatistics, including types of

variables, measurement, and measurement scales.
2. be able to select a simple random sample and other scientific samples from a
population of subjects.
3. understand the processes involved in the scientific method.
4. appreciate the advantages of using computers in the statistical analysis of data
generated by studies and experiments conducted by researchers in the health
sciences.

1
2 INTRODUCTION TO BIOSTATISTICS

1.1 Introduction
We are frequently reminded of the fact that we are living in the information age. Appropri-
ately, then, this book is about information—how it is obtained, how it is analyzed, and how it is
interpreted. The information about which we are concerned we call data, and the data are available
to us in the form of numbers or in other non numerical forms that can be analyzed.
The objectives of this book are twofold: (1) to teach the student to organize and summarize
data and (2) to teach the student how to reach decisions about a large body of data by examin-
ing only a small part of it. The concepts and methods necessary for achieving the first objective
are presented under the heading of descriptive statistics, and the second objective is reached
through the study of what is called inferential statistics. This chapter discusses descriptive statis-
tics. Chapters 2 through 5 discuss topics that form the foundation of statistical inference, and most
of the remainder of the book deals with inferential statistics.
Because this volume is designed for persons preparing for or already pursuing a career in the
health field, the illustrative material and exercises reflect the problems and activities that these
persons are likely to encounter in the performance of their duties.

1.2 Basic Concepts and Definitions

Like all fields of learning, statistics has its own vocabulary. Some of the words and phrases
encountered in the study of statistics will be new to those not previously exposed to the subject.
Other terms, though appearing to be familiar, may have specialized meanings that are differ-
ent from the meanings that we are accustomed to associating with these terms. The following are
some common terms that we will use extensively in this book; others will be added as we progress
through the material.

Data
The raw material of statistics is data. For our purposes, we may define data as numbers. The two
kinds of numbers that we use in statistics are numbers that result from the taking—in the usual
sense of the term—of a measurement, and those that result from the process of counting. For
example, when a nurse weighs a patient or takes a patient’s temperature, a measurement, con-
sisting of a number such as 150 pounds or 100 degrees Fahrenheit, is obtained. Quite a different
type of number is obtained when a hospital administrator counts the number of patients—perhaps
20—discharged from the hospital on a given day. Each of the three numbers is a datum, and the
three taken together are data. Data can also be understood to be non numerical, and may include
things such as text or other qualitative items. However, we will focus our interests in this text
largely on numerical data and their associated analyses.

Statistics
The meaning of statistics is implicit in the previous section. More concretely, however, we may
say that statistics is a field of study concerned with (1) the collection, organization, summariza-
tion, and analysis of data and (2) the drawing of inferences about a body of data when only a
part of the data is observed.
The person who performs these statistical activities must be prepared to interpret and to com-
municate the results to someone else as the situation demands. Simply put, we may say that
data are numbers, numbers contain information, and the purpose of statistics is to investigate and
evaluate the nature and meaning of this information.
 1.2 Basic Concepts and Definitions 3

Sources of Data
The performance of statistical activities is motivated by the need to answer a question. For
example, clinicians may want answers to questions regarding the relative merits of competing
treatment procedures. Administrators may want answers to questions regarding such areas of
concern as employee morale or facility utilization. When we determine that the appropriate
approach to seeking an answer to a question will require the use of statistics, we begin to search
for suitable data to serve as the raw material for our investigation. Such data are usually available
from one or more of the following sources:
1. Routinely kept records. It is difficult to imagine any type of organization that does
not keep records of day-to-day transactions of its activities. Hospital medical records, for
example, contain immense amounts of information on patients, while hospital accounting
records contain a wealth of data on the facility’s business activities. When the need for data
arises, we should look for them first among routinely kept records.
2. Surveys. If the data needed to answer a question are not available from routinely kept
records, the logical source may be a survey. Suppose, for example, that the administrator of
a clinic wishes to obtain information regarding the mode of transportation used by patients
to visit the clinic. If admission forms do not contain a question on mode of transportation,
we may conduct a survey among patients to obtain this information.
3. Experiments. Frequently, the data needed to answer a question are available only as
the result of an experiment. A nurse may wish to know which of several strategies is best
for maximizing patient compliance. The nurse might conduct an experiment in which the
different strategies of motivating compliance are tried with different patients. Subsequent
evaluation of the responses to the different strategies might enable the nurse to decide which
is most effective.
4. External sources. The data needed to answer a question may already exist in the form
of published reports, commercially available data banks, or the research literature. In other
words, we may find that someone else has already asked the same question, and the answer
obtained may be applicable to our present situation.

Biostatistics
The tools of statistics are employed in many fields—business, education, psychology, agriculture,
and economics, to mention only a few. When the data analyzed are derived from the biological
sciences and medicine, we use the term biostatistics to distinguish this particular application of
statistical tools and concepts. This area of application is the concern of this book.

Variable
If, as we observe a characteristic, we find that it takes on different values in different persons,
places, or things, we label the characteristic a variable. We do this for the simple reason that the
characteristic is not the same when observed in different possessors of it. Some examples of
variables include diastolic blood pressure, heart rate, the heights of adult males, the weights
of preschool children, and the ages of patients seen in a dental clinic.

Quantitative Variables
A quantitative variable is one that can be measured in the usual sense. We can, for example, obtain
measurements on the heights of adult males, the weights of preschool children, and the ages of
4 INTRODUCTION TO BIOSTATISTICS

patients seen in a dental clinic. These are examples of quantitative variables. Measurements made
on quantitative variables convey information regarding amount.

Qualitative Variables
Some characteristics are not capable of being measured in the sense that height, weight, and age
are measured. Many characteristics can be categorized only, as, for example, when an ill person
is given a medical diagnosis, a person is designated as belonging to an ethnic group, or a person,
place, or object is said to possess or not to possess some characteristic of interest. In such cases,
measuring consists of categorizing. We refer to variables of this kind as qualitative variables.
Measurements made on qualitative variables convey information regarding an attribute.
Although, in the case of qualitative variables, measurement in the usual sense of the word is not
achieved, we can count the number of persons, places, or things belonging to various categories.
A hospital administrator, for example, can count the number of patients admitted during a day
under each of the various admitting diagnoses. These counts, or frequencies as they are called,
are the numbers that we manipulate when our analysis involves qualitative variables.

Random Variable
Whenever we determine the height, weight, or age of an individual, the result is frequently referred
to as a value of the respective variable. When the values obtained arise as a result of chance factors,
so that they cannot be exactly predicted in advance, the variable is called a random variable. An
example of a random variable is adult height. When a child is born, we cannot predict exactly his
or her height at maturity. Attained adult height is the result of numerous genetic and environmental
factors. Values resulting from measurement procedures are often referred to as observations or
measurements.

Discrete Random Variable

Variables may be characterized further as to whether they are discrete or continuous. Since math-
ematically rigorous definitions of discrete and continuous variables are beyond the level of this
book, we offer, instead, nonrigorous definitions and give an example of each.
A discrete variable is characterized by gaps or interruptions in the values that it can assume.
These gaps or interruptions indicate the absence of values between particular values that the vari-
able can assume. Some examples illustrate the point. The number of daily admissions to a general
hospital is a discrete random variable since the number of admissions each day must be repre-
sented by a whole number, such as 0, 1, 2, or 3. The number of admissions on a given day cannot
be a number such as 1.5, 2.997, or 3.333. The number of decayed, missing, or filled teeth per
child in an elementary school is another example of a discrete variable.

Continuous Random Variable

A continuous random variable does not possess the gaps or interruptions characteristic of a dis-
crete random variable. A continuous random variable can assume any value within a specified
relevant interval of values assumed by the variable. Examples of continuous variables include the
various measurements that can be made on individuals such as height, weight, and skull circum-
ference. No matter how close together the observed heights of two people, for example, we can,
theoretically, find another person whose height falls somewhere in between.
 1.3 Measurement and Measurement Scales 5

Because of the limitations of available measuring instruments, however, observations on vari-

ables that are inherently continuous are recorded as if they were discrete. Height, for example,
is usually recorded to the nearest one-quarter, one-half, or whole inch, whereas, with a perfect
measuring device, such a measurement could be made as precise as desired. Therefore, in a non-
technical sense, continuity is limited only by our ability to precisely measure it.

Population
The average person thinks of a population as a collection of entities, usually people. A population
or collection of entities may, however, consist of animals, machines, places, or cells. For our
purposes, we define a population of entities as the largest collection of entities for which we have
an interest at a particular time. If we take a measurement of some variable on each of the entities
in a population, we generate a population of values of that variable. We may, therefore, define a
population of values as the largest collection of values of a random variable for which we have
an interest at a particular time. If, for example, we are interested in the weights of all the children
enrolled in a certain county elementary school system, our population consists of all these weights.
If our interest lies only in the weights of first-grade students in the system, we have a different
population—weights of first-grade students enrolled in the school system. Hence, populations
are determined or defined by our sphere of interest. Populations may be finite or infinite. If a
population of values consists of a fixed number of these values, the population is said to be finite.
If, on the other hand, a population consists of an endless succession of values, the population is
an infinite one. An exact value calculated from a population is referred to as a parameter.

Sample
A sample may be defined simply as a part of a population. Suppose our population consists of
the weights of all the elementary school children enrolled in a certain county school system. If
we collect for analysis the weights of only a fraction of these children, we have only a part of our
population of weights, that is, we have a sample. An estimated value calculated from a sample is
referred to as a statistic.

1.3 Measurement and Measurement Scales

In the preceding discussion, we used the word measurement several times in its usual sense,
and presumably the reader clearly understood the intended meaning. The word measurement,
however, may be given a more scientific definition. In fact, there is a whole body of scientific
literature devoted to the subject of measurement. Part of this literature is concerned also with the
nature of the numbers that result from measurements. Authorities on the subject of measurement
speak of measurement scales that result in the categorization of measurements according to their
nature. In this section, we define measurement and the four resulting measurement scales. A more
detailed discussion of the subject is to be found in the writings of Stevens (1,2).

Measurement
This may be defined as the assignment of numbers to objects or events according to a set of rules.
The various measurement scales result from the fact that measurement may be carried out under
different sets of rules.
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advanced on all sides from the plantations, and nothing but a small
open space divided the people from each other, Sir George directed
them to halt, and, after thanking them for what they had done, he
requested them to rest themselves on the grass till refreshments
could be brought from the Hermitage, after partaking of which they
had best move homewards, as it seemed in vain to attempt anything
more till next day. He then took leave of them, and hurried home to
the Hermitage, from whence a number of people were soon seen
returning with the promised refreshments.
Having finished what was set before them, and sufficiently rested
themselves, most of them departed, having first declared their
readiness to turn out the moment they were wanted. But when his
friends proposed to David Williams his returning home, he resolutely
refused, declaring his determination to continue his search the whole
night; and the poor man’s distress seemed so great, that a number of
the people agreed to accompany him. Robert, on being applied to,
furnished them, from the Hermitage, with a quantity of torches and
lanterns; and the people themselves, having got others from the
cottages in the neighbourhood, divided into bands, and, fixing on
John Maxwell’s house for intelligence to be sent to, parted in
different ways on their search.
At first all were extremely active, and no place the least suspicious
was passed by; but as the night advanced their exertions evidently
flagged, and many of them began to whisper to each other that it was
in vain to expect doing any good in the midst of darkness; and, as the
idea gained ground, the people gradually separated from each other,
and returned to their homes, promising to be ready early in the
morning to renew the search.
“An’ now, David,” said John Maxwell, “let’s be gaun on.”
“No to my house,” cried David;—“not to my ain house. I canna face
Matty, and them no found yet.”
“Aweel, then,” said John, “suppose ye gang hame wi’ me, and fling
yersel down for a wee; an’ then we’ll be ready to start again at gray
daylight.”
“An’ what will Matty think in the meantime?” answered David.
“But gang on, gang on, however,” he added, “an’ I’se follow ye.”
 John Maxwell, glad that he had got him this length, now led the
way, occasionally making a remark to David, which was very briefly
answered, so that John, seeing him in that mood, gave up speaking
to him, till, coming at length to a bad step, and warning David of it,
to which he got no answer, he hastily turned round and found that he
was gone. He immediately went back, calling to David as loud as he
could, but all to no purpose. It then occurred to him that David had
probably changed his mind, and had gone homewards; and, at any
rate, if he had taken another direction, that it was in vain for him to
attempt following him, the light he carried being now nearly burnt
out. He therefore made the best of his way to his own house.
In the meantime, poor David Williams, who could neither endure
the thought of going to his own house nor to his brother-in-law’s,
and had purposely given him the slip, continued to wander up and
down without well knowing where he was, or where he was going to,
when he suddenly found himself, on coming out of the wood, close to
the cottage inhabited by a widow named Elie Anderson.
“I wad gie the world for a drink o’ water,” said he to himself; “but
the puir creature will hae lain down lang syne, an’ I’m sweer to
disturb her;” and as he said this, he listened at the door, and tried to
see in at the window, but he could neither see nor hear anything, and
was turning to go away, when he thought he saw something like the
reflection of a light from a hole in the wall, on a tree which was
opposite. It was too high for him to get at it without something to
stand upon; but after searching about, he got part of an old hen-
coop, and placing it to the side of the house, he mounted quietly on
it. He now applied his eye to the hole where the light came through,
and the first sight which met his horrified gaze was the body of his
eldest daughter, lying on a table quite dead,—a large incision down
her breast, and another across it!
David Williams could not tell how he forced his way into the
house; but he remembered bolts and bars crashing before him,—his
seizing Elie Anderson, and dashing her from him with all his might;
and that he was standing gazing on his murdered child when two
young ones put out their hands from beneath the bed-clothes.
“There’s faither,” said the one.
“Oh, faither, faither,” said the other, “but I’m glad ye’re come, for
Nanny’s been crying sair, sair, an’ she’s a’ bluiding.”
 David pressed them to his heart in a perfect agony, then catching
them up in his arms, he rushed like a maniac from the place, and
soon afterwards burst into John Maxwell’s cottage,—his face pale, his
eye wild, and gasping for breath.
“God be praised,” cried John Maxwell, “the bairns are found! But
where’s Nanny?”
Poor David tried to speak, but could not articulate a word.
“Maybe ye couldna carry them a’?” said John; “but tell me whaur
Nanny is, and I’se set out for her momently.”
“Ye needna, John, ye needna,” said David; “it’s ower late, it’s ower
late!”
“How sae? how sae?” cried John; “surely naething mischancy has
happened to the lassie?”
“John,” said David, “grasping his hand, she’s murdered—my
bairn’s murdered, John!”
“Gude preserve us a’,” cried John; “an’ wha’s dune it?”
“Elie Anderson,” answered David; “the poor innocent lies yonder a’
cut to bits;” and the unhappy man broke into a passion of tears.
John Maxwell darted off to Saunders Wilson’s. “Rise, Saunders!”
cried he, thundering at the door; “haste ye and rise!”
“What’s the matter now?” said Saunders.
“Elie Anderson’s murdered David’s Nanny; sae haste ye, rise, and
yoke your cart, that we may tak her to the towbuith.”
Up jumped Saunders Wilson, and up jumped his wife and his
weans, and in a few minutes the story was spread like wildfire. Many
a man had lain down so weary with the long search they had made,
that nothing they thought would have tempted them to rise again;
but now they and their families sprung from their beds, and hurried,
many of them only half-dressed, to John Maxwell’s, scarcely
believing that the story could be true. Amongst the first came
Geordie Turnbull, who proposed that a number of them should set
off immediately, without waiting till Saunders Wilson was ready, as
Elie Anderson might abscond in the meantime; and away he went,
followed by about a dozen of the most active. They soon reached her
habitation, where they found the door open and a light burning.
 “Ay, ay,” said Geordie, “she’s aff, nae doubt, but we’ll get her yet.
Na, faith,” cried he, entering, “she’s here still; but, gudesake, what a
sight’s this!” continued he, gazing on the slaughtered child. The
others now entered, and seemed filled with horror at what they saw.
“Haste ye,” cried Geordie, “and fling a sheet or something ower
her, that we mayna lose our wits a’thegither. And now, ye wretch,”
turning to Elie Anderson, “your life shall answer for this infernal
deed. Here,” continued he, “bring ropes and tie her, and whenever
Saunders comes up, we’ll off wi’ her to the towbuith.”
Ropes were soon got, and she was tied roughly enough, and then
thrown carelessly into the cart; but notwithstanding the pain
occasioned by her thigh-bone being broken by the force with which
David Williams dashed her to the ground, she answered not one
word to all their threats and reproaches, till the cart coming on some
very uneven ground, occasioned her such exquisite pain, that, losing
all command over herself, she broke out into such a torrent of abuse
against those who surrounded her, that Geordie Turnbull would have
killed her on the spot, had they not prevented him by main force.
Shortly afterwards they arrived at the prison; and having delivered
her to the jailor, with many strict charges to keep her safe, they
immediately returned to assist in the search for the bodies of the
other children, who, they had no doubt, would be found in or about
her house.
When they arrived there, they found an immense crowd
assembled, for the story had spread everywhere; and all who had lost
children, accompanied by their friends and neighbours and
acquaintances, had repaired to the spot, and had already commenced
digging and searching all round. After working in this way for a long
while, without any discovery being made, it was at length proposed
to give up the search and return home, when Robin Galt, who was a
mason, and who had been repeatedly pacing the ground from the
kitchen to the pig-sty, and from the pig-sty to the kitchen, said,
“Frien’s, I’ve been considering, and I canna help thinking that there
maun be a space no discovered atween the sty and the kitchen, an’
I’m unco fond to hae that ascertained.”
“We’ll sune settle that,” says Geordie Turnbull. “Whereabouts
should it be?”
 “Just there, I think,” says Robin.
Geordie immediately drove a stone or two out, so that he could get
his hand in.
“Does onybody see my hand frae the kitchen?” asked he.
“No a bit o’t,” was the answer.
“Nor frae the sty?”
“Nor frae that either.”
“Then there maun be a space, sure enough,” cried Geordie,
drawing out one stone after another, till he had made a large hole in
the wall. “An’ now,” said he, “gie me a light;” and he shoved in a
lantern, and looked into the place. “The Lord preserve us a’!” cried
he, starting back.
“What is’t—what is’t?” cried the people, pressing forward on all
sides.
“Look an’ see!—look an’ see!” he answered; “they’re a there—a’ the
murdered weans are there, lying in a raw!”
The wall was torn down in a moment; and, as he had said, the
bodies of the poor innocents were found laid side by side together.
Those who entered first gazed on the horrid scene without speaking,
and then proceeded to carry out the bodies, and to lay them on the
green before the house. It was then that the grief of the unhappy
parents broke forth; and their cries and lamentations, as they
recognised their murdered little ones, roused the passions of the
crowd to absolute frenzy.
“Hanging’s ower gude for her,” cried one.
“Let’s rive her to coupens,” exclaimed another.
A universal shout was the answer; and immediately the greater
part of them set off for the prison, their numbers increasing as they
ran, and all burning with fury against the unhappy author of so much
misery.
The wretched woman was at this moment sitting with an old crony
who had been admitted to see her, and to whom she was confessing
what had influenced her in acting as she had done.
“Ye ken,” said she, “I haena jist been mysel since a rascal that had
a grudge at me put aboot a story of my having made awa wi’ John
Anderson, wi’ the help o’ arsenic. I was ta’en up and examined aboot
it, and afterwards tried for it, and though I was acquitted, the
neebours aye looked on me wi’ an evil eye, and avoided me. This
drave me to drinking and other bad courses, and it ended in my
leaving that part of the kintra, and coming here. But the thing
rankled in my mind, and many a time hae I sat thinkin’ on it, till I
scarcely kent where I was, or what I was doing. Weel, ae day, as I was
sitting at the roadside, near the Hermitage, and very low about it, I
heard a voice say, ‘Are you thinking on John Anderson, Elie? Ay,
woman,’ said Charlotte Beaumont, for it was her, ‘what a shame in
you to poison your own gudeman!’ and she pointed her finger, and
hissed at me. When I heard that,” continued Elie, “the whole blood in
my body seemed to flee up to my face, an’ my very een were like to
start frae my head; an’ I believe I wad hae killed her on the spot,
hadna ane o’ Sir George’s servants come up at the time; sae I sat
mysel doun again, an’ after a lang while, I reasoned mysel, as I
thought, into the notion that I shouldna mind what a bairn said; but
I hadna forgotten’t for a’ that.
“Weel, ae day that I met wi’ her near the wood, I tell’t her that it
wasna right in her to speak yon gate, an’ didna mean to say ony mair,
hadna the lassie gane on ten times waur nor she had done before,
and sae angered me, that I gied her a wee bit shake, and then she
threatened me wi’ what her faither wad do, and misca’ed me sae sair,
that I struck her, and my passion being ance up, I gaed on striking
her till I killed her outright. I didna ken for a while that she was
dead; but when I found that it was really sae, I had sense enough left
to row her in my apron, an’ to tak her hame wi’ me; an’ when I had
barred the door, I laid her body on a chair, and sat down on my
knees beside it, an’ grat an’ wrung my hands a’ night lang.
“Then I began to think what would be done to me if it was found
out; an’ thought o’ pittin’ her into a cunning place, which the man
who had the house before me, and who was a great poacher, had
contrived to hide his game in; and when that was done, I was a
thought easier, though I couldna forgie mysel for what I had done,
till it cam into my head that it had been the means o’ saving her frae
sin, and frae haein’ muckle to answer for; an’ this thought made me
unco happy. At last I began to think that it would be right to save
mair o’ them, and that it would atone for a’ my former sins; an’ this
took sic a hold o’ me, that I was aye on the watch to get some ane or
ither o’ them by themselves, to dedicate them to their Maker, by
marking their bodies wi’ the holy cross:—but oh!” she groaned, “if I
hae been wrang in a’ this!”
The sound of the people rushing towards the prison was now
distinctly heard; and both at once seemed to apprehend their object.
“Is there no way of escape, Elie,” asked her friend, wringing her
hands.
Elie pointed to her broken thigh, and shook her head. “Besides,”
said she, “I know my hour is come.”
The mob had now reached the prison, and immediately burst open
the doors. Ascending to the room where Elie was confined, they
seized her by the hair, and dragged her furiously downstairs. They
then hurried her to the river, and, with the bitterest curses, plunged
her into the stream; but their intention was not so soon
accomplished as they had expected; and one of the party having
exclaimed that a witch would not drown, it was suggested, and
unanimously agreed to, to burn her. A fire was instantly lighted by
the waterside, and when they thought it was sufficiently kindled, they
threw her into the midst of it. For some time her wet clothes
protected her, but when the fire began to scorch her, she made a
strong exertion, and rolled herself off. She was immediately seized
and thrown on again; but having again succeeded in rolling herself
off, the mob became furious, and called for more wood for the fire;
and by stirring it on all hands, they raised it into a tremendous blaze.
Some of the most active now hastened to lay hold of the poor wretch,
and to toss her into it; but in their hurry one of them having trod on
her broken limb, caused her such excessive pain, that when Geordie
Turnbull stooped to assist in lifting her head, she suddenly caught
him by the thumb with her teeth, and held him so fast, that he found
it impossible to extricate it. She was therefore laid down again, and
in many ways tried to force open her mouth, but without other effect
than increasing Geordie’s agony; till at length one of them seizing a
pointed stick from the fire, and thrusting it into an aperture
occasioned by the loss of some of her teeth, the pressure of its sharp
point against the roof of her mouth, and the smoke setting her
coughing, forced her to relax her hold, when the man’s thumb was
got out of her grasp terribly lacerated. Immediately thereafter she
was tossed in the midst of the flames, and forcibly held there by
means of long prongs; and the fire soon reaching the vital parts, the
poor wretch’s screams and imprecations became so horrifying, that
one of the bystanders, unable to bear it any longer, threw a large
stone at her head, which, hitting her on the temples, deprived her of
sense and motion.
Their vengeance satisfied, the people immediately dispersed,
having first pledged themselves to the strictest secrecy. Most of them
returned home, but a few went back to Elie Anderson’s, whose house,
and everything belonging to her, had been set on fire by the furious
multitude. They then retired, leaving a few men to watch the remains
of the children, till coffins could be procured for them. “Never in a’
my days,” said John Maxwell, when speaking of it afterwards, “did I
weary for daylight as I did that night. When the smoke smothered
the fire, and it was quite dark, we didna mind sae muckle; but when a
rafter or a bit o’ the roof fell in, and a bleeze raise, then the firelight
shining on the ghastly faces of the puir wee innocents a’ laid in a row,
—it was mair than we could weel stand; and it was mony a day or I
was my ainsel again.”
 Chapter III.
Next morning the parents met, and it being agreed that all their
little ones should be interred in one grave, and that the funeral
should take place on the following day, the necessary preparations
were accordingly made. In the meantime, Matty went over to her
brother John Maxwell, to tell him, if possible, to persuade David
Williams not to attend the funeral, as she was sure he could not
stand it. “He hadna closed his ee,” she said, “since that terrible night,
and had neither ate nor drank, but had just wandered up and down
between the house and the fields, moaning as if his heart would
break.” John Maxwell promised to speak to David, but when he did
so, he found him so determined on attending, that it was needless to
say any more on the subject.
On the morning of the funeral, David Williams appeared very
composed; and John Maxwell was saying to some of the neighbours
that he thought he would be quite able to attend, when word was
brought that Geordie Turnbull had died that morning of lock-jaw,
brought on, it was supposed, as much from the idea of his having
been bitten by a witch, or one that was not canny, as from the injury
done to him.
This news made an evident impression on David Williams, and he
became so restless and uneasy, and felt himself so unwell, that he at
one time declared he would not go to the funeral; but getting
afterwards somewhat more composed, he joined the melancholy
procession, and conducted himself with firmness and propriety from
the time of their setting out till all the coffins were lowered into the
grave. But the first spadeful of earth was scarcely thrown in, when
the people were startled by his breaking into a long and loud laugh;—
“There she’s!—there she’s!” he exclaimed; and, darting through the
astonished multitude, he made with all his speed to the gate of the
churchyard.
“Oh! stop him,—will naebody stop him?” cried his distracted wife;
and immediately a number of his friends and acquaintances set off
after him, the remainder of the people crowding to the churchyard
wall, whence there was an extensive view over the surrounding
country. But quickly as those ran who followed him, David Williams
kept far a-head of them, terror lending him wings,—till at length, on
slackening his pace, William Russel, who was the only one near,
gained on him, and endeavoured, by calling in a kind and soothing
manner, to prevail on him to return. This only made him increase his
speed, and William would have been thrown behind farther than
ever, had he not taken a short cut, which brought him very near him.
“Thank God, he will get him now!” cried the people in the
churchyard; when David Williams, turning suddenly to the right,
made with the utmost speed towards a rising ground, at the end of
which was a freestone quarry of great depth. At this sight a cry of
horror arose from the crowd, and most fervently did they pray that
he might yet be overtaken; and great was their joy when they saw
that, by the most wonderful exertion, William Russel had got up so
near as to stretch out his arm to catch him; but at that instant his
foot slipped, and ere he could recover himself, the unhappy man,
who had now gained the summit, loudly shouting, sprung into the
air.
“God preserve us!” cried the people, covering their eyes that they
might not see a fellow-creature dashed in pieces; “it is all over!”
“Then help me to lift his poor wife,” said Isabel Lawson. “And now
stan’ back, and gie her a’ the air, that she may draw her breath.”
“She’s drawn her last breath already, I’m doubting,” said Janet
Ogilvie, an old skilful woman; and her fears were found to be too
true.
“An’ what will become o’ the poor orphans?” said Isabel.
She had scarcely spoken, when Sir George Beaumont advanced,
and, taking one of the children in each hand, he motioned the people
to return towards the grave.
“The puir bairns are provided for now,” whispered one to another,
as they followed to witness the completion of the mournful
ceremony. It was hastily finished in silence, and Sir George having
said a few words to his steward, and committed the orphans to his
care, set out on his way to the Hermitage, the assembled multitude
all standing uncovered as he passed, to mark their respect for his
goodness and humanity.
 As might have been expected, the late unhappy occurrences greatly
affected Lady Beaumont’s health, and Sir George determined to quit
the Hermitage for a time; and directions were accordingly given to
prepare for their immediate removal. While this was doing, the
friend who had been with Elie Anderson in the prison happened to
call at the Hermitage, and the servants crowded about her, eager to
learn what had induced Elie to commit such crimes. When she had
repeated what Elie had said, a young woman, one of the servants,
exclaimed, “I know who’s been the cause of this; for if Bet,”——and
she suddenly checked herself.
“That must mean Betsy Pringle,” said Robert, who was her
sweetheart, and indeed engaged to her; “so you will please let us hear
what you have to say against her, or own that you’re a slanderer.”
“I have no wish to make mischief,” said the servant; “and as what I
said came out without much thought, I would rather say no more;
but I’ll not be called a slanderer neither.”
“Then say what you have to say,” cried Robert; “it’s the only way to
settle the matter.”
“Well, then,” said she, “since I must do it, I shall. Soon after I came
here, I was one day walking with the bairns and Betsy Pringle, when
we met a woman rather oddly dressed, and who had something
queer in her manner, and, when she had left us, I asked Betsy who it
was. ‘Why,’ said Betsy, ‘I don’t know a great deal about her, as she
comes from another part of the country; but if what a friend of mine
told me lately is true, this Elie Anderson, as they call her, should
have been hanged.’
“‘Hanged!’ cried Miss Charlotte; ‘and why should she be hanged,
Betsy?’
“‘Never you mind, Miss Charlotte,’ said Betsy, ‘I’m speaking to
Fanny here.’
“‘You can tell me some other time,’ said I.
“‘Nonsense,’ cried Betsy, ‘what can a bairn know about it? Weel,’
continued she, ‘it was believed that she had made away with John
Anderson, her gudeman.’
“‘What’s a gudeman, Betsy?’ asked Miss Charlotte.
“‘A husband,’ answered she.
 “‘And what’s making away with him, Betsy?’
“‘What need you care?’ said Betsy.
“‘You may just as well tell me,’ said Miss Charlotte; ‘or I’ll ask Elie
Anderson herself all about it, the first time I meet her.’
“‘That would be a good joke,’ said Betsy, laughing; ‘how Elie
Anderson would look to hear a bairn like you speaking about a
gudeman, and making away with him; however,’ she continued, ‘that
means killing him.’
“‘Killing him!’ exclaimed Miss Charlotte. ‘Oh, the wretch; and how
did she kill him, Betsy?’
“‘You must ask no more questions, miss,’ said Betsy, and the
subject dropped.
“‘Betsy,’ said I to her afterwards, you should not have mentioned
these things before the children; do you forget how noticing they
are?’
“‘Oh, so they are,’ said Betsy, ‘but only for the moment; and I’ll
wager Miss Charlotte has forgotten it all already.’
“But, poor thing,” Fanny added, “she remembered it but too well.”
“I’ll not believe this,” cried Robert.
“Let Betsy be called, then,” said the housekeeper, “and we’ll soon
get at the truth.” Betsy came, was questioned by the housekeeper,
and acknowledged the fact.
“Then,” said Robert, “you have murdered my master’s daughter,
and you and I can never be more to one another than we are at this
moment;” and he hastily left the room.
Betsy gazed after him for an instant, and then fell on the floor. She
was immediately raised up and conveyed to bed, but recovering soon
after, and expressing a wish to sleep, her attendant left her. The
unhappy woman, feeling herself unable to face her mistress after
what had happened, immediately got up, and, jumping from the
window, fled from the Hermitage. The first accounts they had of her
were contained in a letter from herself to Lady Beaumont, written on
her death-bed, wherein she described the miserable life she had led
since quitting the Hermitage, and entreating her ladyship’s
forgiveness for the unhappiness which she had occasioned.
 “Let what has happened,” said Lady Beaumont, “be a warning to
those who have the charge of them, to beware of what they say
before children;—a sentiment which Sir George considered as so just
and important, that he had it engraven on the stone which covered
the little innocents, that their fate and its cause might be had in
everlasting remembrance.”—“The Odd Volume.”
 AN ORKNEY WEDDING.

By John Malcolm.
To me more dear, congenial to my heart,
One native charm, than all the gloss of art.—Goldsmith.

Gentle reader! you, I doubt not, have seen many strange sights,
and have passed through a variety of eventful scenes. Perhaps you
have visited the Thames Tunnel, and there threaded your way under
ground and under water, or you may have witnessed Mr Green’s
balloon ascent, and seen him take an airing on horseback among the
clouds.
Perhaps, too, you have been an observer of human life in all its
varieties and extremes: one night figuring away at Almack’s with
aristocratic beauty, and the next footing it with a band of gipsies in
Epping Forest. But, pray tell me, have you ever seen an Orkney
Wedding? If not, as I have just received an invitation to one,
inclusive of a friend, you shall, if it so please you, accompany me to
that scene of rural hospitality.
In conformity with the custom of the country, I have sent off to the
young couple a pair of fowls and a leg of mutton, to play their parts
upon the festive board; and as every family contributes in like
manner, a general pic-nic is formed, which considerably diminishes
the expense incident to the occasion; although, as the festivities are
frequently kept up for three or four days by a numerous assemblage
of rural beauty and fashion, the young people must contrive to live
upon love, if they can, during the first year of their union, having
little else left upon which to subsist, except the fragments of the
mighty feast.
 Well, then, away we go, and about noon approach the scene of
festivity,—a country-seat built in the cottage style, thatched with
straw, and flanked with a barn and a well-filled corn-yard, enclosed
with a turf-dyke.
The wedding company are now seen making their way towards the
place of rendezvous; and the young women, arrayed in white robes of
emblematic purity, exhibit a most edifying example of economy.
With their upper garments carried to a height to which the fashion of
short petticoats never reached even at Paris, they trip it away
barefooted through the mud, until they reach the banks of a purling
stream, about a quarter of a mile distant from the wedding-house.
Here their feet, having been previously kissed by the crystal waters,
and covered with cotton stockings, which in whiteness would fain vie
with the skin they enviously conceal, are inserted into shoes, in
whose mirror of glossy black the enamoured youth obtains a peep of
his own charms, while stooping down to adjust their ties into a love-
knot.
Immediately in front of the outer-door, or principal entrance of the
house, and answering the double purpose of shelter and ornament,
stands a broad square pile, composed of the most varied materials,
needless to be enumerated, and vulgarly denominated a midden,
around the base of which some half-dozen of pigs are acting the part
of miners, in search of its hidden treasures. It is separated from the
house by a sheet of water, tinged with the fairest hues of heaven and
earth, viz., blue and green, and over which we pass by a bridge of
stepping-stones.
And now, my friend, before entering the house, it may be as well to
consider what character you are to personate during the
entertainment; for the good people in these islands, like their
neighbours of the mainland of Scotland, take that friendly interest in
other people’s affairs, which the thankless world very unkindly
denominates impertinent curiosity.
If I pass you off as a lawyer, you will immediately be overwhelmed
with statements of their quarrels and grievances; for they are main
fond of law, and will expend the hard-earned savings of years in
litigation, although the subject-matter of dispute should happen to
be only a goose. You must not, therefore, belong to the bar, since, in
the present case, consultations would produce no fees.
 I think I shall therefore confer upon you the degree of M.D., which
will do as well for the occasion as if you had obtained it by purchase
at the University of Aberdeen; although I am not sure that it also
may not subject you to some trouble in the way of medical advice.
And now having safely passed over the puddle, and tapped gently
at the door, our arrival is immediately announced by a grand musical
chorus, produced by the barking of curs, the cackling of geese, the
quacking of ducks, and the grunting and squeaking of pigs. After this
preliminary salutation, we are received by the bridegroom, and
ushered, with many kind welcomes, into the principal hall, through a
half open door, at one end of which we are refreshed with a picture of
rural felicity, namely, some sleek-looking cows, ruminating in
philosophical tranquillity on the subject of diet.
In the middle of the hall is a large blazing turf fire, the smoke of
which escapes in part through an aperture in the roof, while the
remainder expands in the manner of a pavilion over the heads of the
guests.
A door at the other end of the hall opens into the withdrawing-
room, the principal furniture of which consists of two large chests
filled with oat and barley meal and home-made cheeses, a concealed
bed, and a chest of drawers. Both rooms have floors inlaid with
earth, and roofs of a dark soot colour, from which drops of a
corresponding hue occasionally fall upon the bridal robes of the
ladies, with all the fine effect arising from contrast, and ornamental
on the principle of the patch upon the cheek of beauty.
Separated from the dwelling-house only by a puddle dotted with
stepping-stones stands the barn, which, from its length and breadth,
is admirably adapted for the purposes of a ball-room.
Upon entering the withdrawing-room, which the good people with
admirable modesty call the ben, we take our seats among the elders
and chiefs of the people, and drink to the health of the young couple
in a glass of delicious Hollands, which, unlike Macbeth’s “Amen,”
does not stick in our throats, although we are well aware that it never
paid duty, but was slily smuggled over sea in a Dutch lugger, and
safely stowed, during some dark night, in the caves of the more
remote islands.
 The clergyman having now arrived, the company assembled, and
the ceremony of marriage being about to take place, the parties to be
united walk in, accompanied by the best man and the bride’s maid,—
those important functionaries, whose business it is to pull off the
gloves from the right hands of their constituents, as soon as the order
is given to “join hands,”—but this they find to be no easy matter, for
at that eventful part of the ceremony their efforts are long baffled,
owing to the tightness of the gloves. While they are tugging away to
no purpose, the bridegroom looks chagrined, and the bride is
covered with blushes; and when at last the operation is
accomplished, and perseverance crowned with success, the confusion
of the scene seems to have infected the parson, who thus blunders
through the ceremony:
“Bridegroom,” quoth he, “do you take the woman whom you now
hold by the hand, to be your lawful married husband?”
To which interrogation the bridegroom having nodded in the
affirmative, the parson perceives his mistake, and calls out, “Wife, I
mean.” “Wife, I mean,” echoes the bridegroom; and the whole
company are in a titter.
But, thank heaven, the affair is got over at last; and the bride being
well saluted, a large rich cake is broken over her head, the fragments
of which are the subject of a scramble among the bystanders, by
whom they are picked up as precious relics, having power to produce
love-dreams.
And now the married pair, followed by the whole company, set off
to church, to be kirked, as the phrase is. A performer on the violin
(not quite a Rossini) heads the procession, and plays a variety of
appropriate airs, until he reaches the church-door. As soon as the
party have entered and taken their seats, the parish-clerk, in a truly
impressive and orthodox tone of voice, reads a certain portion of
Scripture, wherein wives are enjoined to be obedient to their
husbands. The service is concluded with a psalm, and the whole
party march back, headed as before by the musician.
Upon returning from church, the company partake of a cold
collation, called the hansel, which is distributed to each and all by
the bride’s mother, who for the time obtains the elegant designation
of hansel-wife. The refreshments consist of cheese, old and new, cut
down in large slices, or rather junks, and placed upon oat and barley
cakes,—some of the former being about an inch thick, and called
snoddies.
These delicate viands are washed down with copious libations of
new ale, which is handed about in a large wooden vessel, having
three handles, and ycleped a three-lugged cog.[18] The etherial
beverage is seasoned with pepper, ginger, and nutmeg, and
thickened with eggs and pieces of toasted biscuit.
18. Also called the Bride’s cog.—Ed.
These preliminaries being concluded, the company return to the
barn, where the music strikes up, and the dancing commences with
what is called the Bride’s Reel; after which, two or three young men
take possession of the floor, which they do not resign until they have
danced with every woman present; they then give place to others,
who pass through the same ordeal, and so on. The dance then
becomes more varied and general. Old men and young ones, maids,
matrons, and grandmothers, mingle in its mazes. And, oh! what
movements are there,—what freaks of the “fantastic toe,”—what
goodly figures and glorious gambols in a dance;—compared to which
the waltz is but the shadow of joy, and the quadrille the feeble effort
of Mirth upon her last legs.
Casting an eye, however, upon the various performers, I cannot
but observe that the old people seem to have monopolised all the airs
and graces; for, while the young maidens slide through the reel in the
most quiet and unostentatious way, and then keep bobbing opposite
to their partners in all the monotony of the back-step, their more
gifted grandmothers figure away in quite another style. With a length
of waist which our modern belles do not wish to possess, and an
underfigure, which they cannot if they would, even with the aid of
pads, but which is nevertheless the true court-shape, rendering the
hoop unnecessary, and which is moreover increased by the swinging
appendages of huge scarlet pockets, stuffed with bread and cheese,
behold them sideling up to their partners in a kind of echellon
movement, spreading out their petticoats like sails, and then, as if
seized with a sudden fit of bashfulness, making a hasty retreat
rearwards. Back they go at a round trot; and seldom do they stop
until their career of retiring modesty ends in a somersault over the
sitters along the sides of the room.
 The old men, in like manner, possess similar advantages over the
young ones; the latter being sadly inferior to their seniors in address
and attitudes. Nor is this much to be wondered at, the young
gentlemen having passed most of their summer vacations at Davis’
Straits, where their society consisted chiefly of bears; whereas the old
ones are men of the world, having in early life entered the Company’s
service (I do not mean that of the East Indies, but of Hudson’s Bay),
where their manners must no doubt have been highly polished by
their intercourse with the Squaws, and all the beauty and fashion of
that interesting country.
Such of them as have sojourned there are called north-westers,
and are distinguished by that modest assurance, and perfect ease and
self-possession, only to be acquired by mixing frequently and freely
with the best society. Indeed, one would suppose that their manners
were formed upon the model of the old French school; and queues
are in general use among them—not, however, those of the small
pigtail kind, but ones which in shape and size strongly resemble the
Boulogne sausage.
And now, amidst these ancients, I recognise my old and very
worthy friend, Mr James Houston, kirk-officer and sexton of the
parish, of whom a few words, perhaps, may not be unacceptable.
His degree of longitude may be about five feet from the earth, and
in latitude he may extend at an average to about three. His
countenance, which is swarthy, and fully as broad as it is long,
although not altogether the model which an Italian painter would
select for his Apollo, would yet be considered handsome among the
Esquimaux; or, as James calls them, the Huskinese. His hair, which
(notwithstanding an age at which Time generally saves us the
expense of the powder-tax) is jet black, is of a length and strength
that would not shrink from comparison with that of a horse’s tail,
and hangs down over his broad shoulders in a fine and generous
flow. The coat which he wears upon this, as upon all other occasions,
is cut upon the model of the spencer; its colour, a “heavenly blue,”
varied by numerous dark spots, like clouds in a summer sky; while
his nether bulk is embraced by a pair of tight buckskin
“unmentionables.”
Extending from the bosom down to the knee he wears a leather
apron. This part of his dress is never dispensed with, except at
church; and though I have not been able to ascertain its precise
purpose with perfect certainty, I am inclined to think it is used as a
perpetual pinafore, to preserve his garments from the pollution of
soup and grease-drops at table.
The principal materials of his dress are, moreover, prepared for
use by his own hands: Mr Houston being at once sole proprietor and
operative of a small manufactory, consisting of a single loom; when
not employed at which, or in spreading the couch of rest in the
churchyard, he enjoys a kind of perpetual otium cum dignitate.
His chief moveables, in addition to the loom, consist of three
Shetland ponies and a small Orkney plough, by the united aid of
which he is enabled to scratch up the surface of a small estate, which
supplies him with grain sufficient for home consumption, but not for
exportation.
His peculiar and more shining accomplishments consist in the art
of mimicking the dance of every man and woman in the parish,
which he does with a curious felicity, and in executing short pieces of
music on that sweetest of lyres, the Jew’s harp.
Like most of his profession, he is a humorist; and though he has
long “walked hand-in-hand with death,” nobody enjoys life with a
keener relish at the festive board or the midnight ball, which he finds
delightful relaxations from his grave occupations during the day;
and yet even these latter afford him a rare and consolatory joy denied
to other men,—I mean that of meeting with his old friends, after they
have been long dead, and of welcoming, with a grin of recognition,
the skulls of his early associates, as he playfully pats them with his
spade, and tosses them into the light of day.
But it is in his capacity of kirk-officer that Mr Houston appears to
the greatest advantage, while ushering the clergyman to the pulpit,
and marching before him with an air truly magnificent, and an
erectness of carriage somewhat beyond the perpendicular, he
performs his important function of opening and shutting the door of
the pulpit, and takes his seat under an almost overwhelming sense of
dignity, being for the time a kind of lord high constable, with whom
is entrusted the execution of the law. And that he does not bear the
sword in vain is known to their cost, by all the litigious and
churchgoing dogs of the parish; for no sooner do they begin to growl
and tear each other, with loud yells, which they generally do, so as to