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Biostatistical Methods in Epidemiology 1st Edition
Stephen C. Newman Digital Instant Download
Author(s): Stephen C. Newman, Newman
ISBN(s): 9780471461609, 0471461601
Edition: 1
File Details: PDF, 1.87 MB
Year: 2001
Language: english
Biostatistical Methods
in Epidemiology
Biostatistical Methods
in Epidemiology

STEPHEN C. NEWMAN

A Wiley-Interscience Publication
JOHN WILEY & SONS, INC.
New York • Chichester • Weinheim • Brisbane • Singapore • Toronto
This book is printed on acid-free paper. ∞
Copyright 
c 2001 by John Wiley & Sons, Inc. All rights reserved.

Published simultaneously in Canada.

No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or
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For ordering and customer service, call 1-800-CALL-WILEY.

Library of Congress Cataloging-in-Publication Data:

Newman, Stephen C., 1952–
Biostatistical methods in epidemiology / Stephen C. Newman.
p. cm.—(Wiley series in probability and statistics. Biostatistics section)
Includes bibliographical references and index.
ISBN 0-471-36914-4 (cloth : alk. paper)
1. Epidemiology—Statistical methods. 2. Cohort analysis. I. Title. II. Series.
RA652.2.M3 N49 2001
614.4 07 27—dc21 2001028222
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
To Sandra
 Contents

1. Introduction 1
1.1 Probability, 1
1.2 Parameter Estimation, 21
1.3 Random Sampling, 27

2. Measurement Issues in Epidemiology 31

2.1 Systematic and Random Error, 31
2.2 Measures of Effect, 33
2.3 Confounding, 40
2.4 Collapsibility Approach to Confounding, 46
2.5 Counterfactual Approach to Confounding, 55
2.6 Methods to Control Confounding, 67
2.7 Bias Due to an Unknown Confounder, 69
2.8 Misclassification, 72
2.9 Scope of this Book, 75

3. Binomial Methods for Single Sample Closed Cohort Data 77

3.1 Exact Methods, 77
3.2 Asymptotic Methods, 82

4. Odds Ratio Methods for Unstratified Closed Cohort Data 89

4.1 Asymptotic Unconditional Methods for a Single 2 × 2 Table, 90
4.2 Exact Conditional Methods for a Single 2 × 2 Table, 101
4.3 Asymptotic Conditional Methods for a Single 2 × 2 Table, 106
4.4 Cornfield’s Approximation, 109
4.5 Summary of Examples and Recommendations, 112
4.6 Asymptotic Methods for a Single 2 × I Table, 112

vii
viii CONTENTS

5. Odds Ratio Methods for Stratified Closed Cohort Data 119

5.1 Asymptotic Unconditional Methods for J (2 × 2) Tables, 119
5.2 Asymptotic Conditional Methods for J (2 × 2) Tables, 129
5.3 Mantel–Haenszel Estimate of the Odds Ratio, 132
5.4 Weighted Least Squares Methods for J (2 × 2) Tables, 134
5.5 Interpretation Under Heterogeneity, 136
5.6 Summary of 2 × 2 Examples and Recommendations, 137
5.7 Asymptotic Methods for J (2 × I ) Tables, 138

6. Risk Ratio Methods for Closed Cohort Data 143

6.1 Asymptotic Unconditional Methods for a Single 2 × 2 Table, 143
6.2 Asymptotic Unconditional Methods for J (2 × 2) Tables, 145
6.3 Mantel–Haenszel Estimate of the Risk Ratio, 148
6.4 Weighted Least Squares Methods for J (2 × 2) Tables, 149
6.5 Summary of Examples and Recommendations, 150

7. Risk Difference Methods for Closed Cohort Data 151

7.1 Asymptotic Unconditional Methods for a Single 2 × 2 Table, 151
7.2 Asymptotic Unconditional Methods for J (2 × 2) Tables, 152
7.3 Mantel–Haenszel Estimate of the Risk Difference, 155
7.4 Weighted Least Squares Methods for J (2 × 2) Tables, 157
7.5 Summary of Examples and Recommendations, 157

8. Survival Analysis 159

8.1 Open Cohort Studies and Censoring, 159
8.2 Survival Functions and Hazard Functions, 163
8.3 Hazard Ratio, 166
8.4 Competing Risks, 167

9. Kaplan–Meier and Actuarial Methods for Censored Survival Data 171

9.1 Kaplan–Meier Survival Curve, 171
9.2 Odds Ratio Methods for Censored Survival Data, 178
9.3 Actuarial Method, 189

10. Poisson Methods for Censored Survival Data 193

10.1 Poisson Methods for Single Sample Survival Data, 193
10.2 Poisson Methods for Unstratified Survival Data, 206
10.3 Poisson Methods for Stratified Survival Data, 218
CONTENTS ix

11. Odds Ratio Methods for Case-Control Data 229

11.1 Justification of the Odds Ratio Approach, 229
11.2 Odds Ratio Methods for Matched-Pairs Case-Control Data, 236
11.3 Odds Ratio Methods for (1 : M) Matched Case-Control Data, 244

12. Standardized Rates and Age–Period–Cohort Analysis 249

12.1 Population Rates, 249
12.2 Directly Standardized Death Rate, 251
12.3 Standardized Mortality Ratio, 255
12.4 Age–Period–Cohort Analysis, 258

13. Life Tables 263

13.1 Ordinary Life Table, 264
13.2 Multiple Decrement Life Table, 270
13.3 Cause-Deleted Life Table, 274
13.4 Analysis of Morbidity Using Life Tables, 276

14. Sample Size and Power 281

14.1 Sample Size for a Prevalence Study, 281
14.2 Sample Size for a Closed Cohort Study, 283
14.3 Sample Size for an Open Cohort Study, 285
14.4 Sample Size for an Incidence Case-Control Study, 287
14.5 Controlling for Confounding, 291
14.6 Power, 292

15. Logistic Regression and Cox Regression 295

15.1 Logistic Regression, 296
15.2 Cox Regression, 305

Appendix A Odds Ratio Inequality 307

Appendix B Maximum Likelihood Theory 311

B.1 Unconditional Maximum Likelihood, 311
B.2 Binomial Distribution, 313
B.3 Poisson Distribution, 320
B.4 Matrix Inversion, 323

Appendix C Hypergeometric and Conditional Poisson Distributions 325

C.1 Hypergeometric, 325
C.2 Conditional Poisson, 326
x CONTENTS

C.3 Hypergeometric Variance Estimate, 327

C.4 Conditional Poisson Variance Estimate, 328

Appendix D Quadratic Equation for the Odds Ratio 329

Appendix E Matrix Identities and Inequalities 331

E.1 Identities and Inequalities for J (1 × I ) and J (2 × I ) Tables, 331
E.2 Identities and Inequalities for a Single Table, 336
E.3 Hypergeometric Distribution, 336
E.4 Conditional Poisson Distribution, 337

Appendix F Survival Analysis and Life Tables 339

F.1 Single Cohort, 339
F.2 Comparison of Cohorts, 340
F.3 Life Tables, 341

Appendix G Confounding in Open Cohort and Case-Control Studies 343

G.1 Open Cohort Studies, 343
G.2 Case-Control Studies, 350

Appendix H Odds Ratio Estimate in a Matched Case-Control Study 353

H.1 Asymptotic Unconditional Estimate of Matched-Pairs Odds
Ratio, 353
H.2 Asymptotic Conditional Analysis of (1 : M) Matched
Case-Control Data, 354

References 359

Index 377
 Biostatistical Methods in Epidemiology. Stephen C. Newman
Copyright ¶ 2001 John Wiley & Sons, Inc.
ISBN: 0-471-36914-4

Preface

The aim of this book is to provide an overview of statistical methods that are im-
portant in the analysis of epidemiologic data, the emphasis being on nonregression
techniques. The book is intended as a classroom text for students enrolled in an epi-
demiology or biostatistics program, and as a reference for established researchers.
The choice and organization of material is based on my experience teaching bio-
statistics to epidemiology graduate students at the University of Alberta. In that set-
ting I emphasize the importance of exploring data using nonregression methods prior
to undertaking a more elaborate regression analysis. It is my conviction that most of
what there is to learn from epidemiologic data can usually be uncovered using non-
regression techniques.
I assume that readers have a background in introductory statistics, at least to the
stage of simple linear regression. Except for the Appendices, the level of mathemat-
ics used in the book is restricted to basic algebra, although admittedly some of the
formulas are rather complicated expressions. The concept of confounding, which is
central to epidemiology, is discussed at length early in the book. To the extent permit-
ted by the scope of the book, derivations of formulas are provided and relationships
among statistical methods are identified. In particular, the correspondence between
odds ratio methods based on the binomial model, and hazard ratio methods based
on the Poisson model are emphasized (Breslow and Day, 1980, 1987). Historically,
odds ratio methods were developed primarily for the analysis of case-control data.
Students often find the case-control design unintuitive, and this can adversely affect
their understanding of the odds ratio methods. Here, I adopt the somewhat uncon-
ventional approach of introducing odds ratio methods in the setting of closed cohort
studies. Later in the book, it is shown how these same techniques can be adapted
to the case-control design, as well as to the analysis of censored survival data. One
of the attractive features of statistics is that different theoretical approaches often
lead to nearly identical numerical results. I have attempted to demonstrate this phe-
nomenon empirically by analyzing the same data sets using a variety of statistical
techniques.
I wish to express my indebtedness to Allan Donner, Sander Greenland, John Hsieh,
David Streiner, and Stephen Walter, who generously provided comments on a draft
manuscript. I am especially grateful to Sander Greenland for his advice on the topic
of confounding, and to John Hsieh who introduced me to life table theory when I was

xi
xii PREFACE

a student. The reviewers did not have the opportunity to read the final manuscript
and so I alone am responsible for whatever shortcomings there may be in the book.
I also wish to acknowledge the professionalism and commitment demonstrated by
Steve Quigley and Lisa Van Horn of John Wiley & Sons. I am most interested in
receiving your comments, which can be sent by e-mail using a link at the website
www.stephennewman.com.
Prior to entering medicine and then epidemiology, I was deeply interested in a
particularly elegant branch of theoretical mathematics called Galois theory. While
studying the historical roots of the topic, I encountered a monograph having a preface
that begins with the sentence “I wrote this book for myself.” (Hadlock, 1978). After
this remarkable admission, the author goes on to explain that he wanted to construct
his own path through Galois theory, approaching the subject as an enquirer rather
than an expert. Not being formally trained as a mathematical statistician, I embarked
upon the writing of this book with a similar sense of discovery. The learning process
was sometimes arduous, but it was always deeply rewarding. Even though I wrote
this book partly “for myself,” it is my hope that others will find it useful.

S TEPHEN C. N EWMAN
Edmonton, Alberta, Canada
May 2001
 Biostatistical Methods in Epidemiology. Stephen C. Newman
Copyright ¶ 2001 John Wiley & Sons, Inc.
ISBN: 0-471-36914-4

CHAPTER 1

Introduction

In this chapter some background material from the theory of probability and statis-
tics is presented that will be useful throughout the book. Such fundamental concepts
as probability function, random variable, mean, and variance are defined, and sev-
eral of the distributions that are important in the analysis of epidemiologic data are
described. The Central Limit Theorem and normal approximations are discussed,
and the maximum likelihood and weighted least squares methods of parameter es-
timation are outlined. The chapter concludes with a discussion of different types of
random sampling. The presentation of material in this chapter is informal, the aim
being to give an overview of some key ideas rather than provide a rigorous mathe-
matical treatment. Readers interested in more complete expositions of the theoretical
aspects of probability and statistics are referred to Cox and Hinkley (1974), Silvey
(1975), Casella and Berger (1990), and Hogg and Craig (1994). References for the
theory of probability and statistics in a health-related context are Armitage and Berry
(1994), Rosner (1995), and Lachin (2000). For the theory of sampling, the reader is
referred to Kish (1965) and Cochran (1977).

1.1 PROBABILITY

1.1.1 Probability Functions and Random Variables

Probability theory is concerned with mathematical models that describe phenomena
having an element of uncertainty. Problems amenable to the methods of probabil-
ity theory range from the elementary, such as the chance of randomly selecting an
ace from a well-shuffled deck of cards, to the exceedingly complex, such as pre-
dicting the weather. Epidemiologic studies typically involve the collection, analysis,
and interpretation of health-related data where uncertainty plays a role. For example,
consider a survey in which blood sugar is measured in a random sample of the pop-
ulation. The aims of the survey might be to estimate the average blood sugar in the
population and to estimate the proportion of the population with diabetes (elevated
blood sugar). Uncertainty arises because there is no guarantee that the resulting esti-

1
2 INTRODUCTION

mates will equal the true population values (unless the entire population is enrolled
in the survey).
Associated with each probability model is a random variable, which we denote by
a capital letter such as X . We can think of X as representing a potential data point for
a proposed study. Once the study has been conducted, we have actual data points that
will be referred to as realizations (outcomes) of X . An arbitrary realization of X will
be denoted by a small letter such as x. In what follows we assume that realizations
are in the form of numbers so that, in the above survey, diabetes status would have
to be coded numerically—for example, 1 for present and 0 for absent. The set of all
possible realizations of X will be referred to as the sample space of X . For blood
sugar the sample space is the set of all nonnegative numbers, and for diabetes status
(with the above coding scheme) the sample space is {0, 1}. In this book we assume
that all sample spaces are either continuous, as in the case of blood sugar, or discrete,
as in the case of diabetes status. We say that X is continuous or discrete in accordance
with the sample space of the probability model.
There are several mathematically equivalent ways of characterizing a probabil-
ity model. In the discrete case, interest is mainly in the probability mass function,
denoted by P(X = x), whereas in the continuous case the focus is usually on the
probability density function, denoted by f (x). There are important differences be-
tween the probability mass function and the probability density function, but for
present purposes it is sufficient to view them simply as formulas that can be used to
calculate probabilities. In order to simplify the exposition we use the term probability
function to refer to both these constructs, allowing the context to make the distinc-
tion clear. Examples of probability functions are given in Section 1.1.2. The notation
P(X = x) has the potential to be confusing because both X and x are “variables.”
We read P(X = x) as the probability that the discrete random variable X has the
realization x. For simplicity it is often convenient to ignore the distinction between
X and x. In particular, we will frequently use x in formulas where, strictly speaking,
X should be used instead.
The correspondence between a random variable and its associated probability
function is an important concept in probability theory, but it needs to be empha-
sized that it is the probability function which is the more fundamental notion. In a
sense, the random variable represents little more than a convenient notation for re-
ferring to the probability function. However, random variable notation is extremely
powerful, making it possible to express in a succinct manner probability statements
that would be cumbersome otherwise. A further advantage is that it may be possi-
ble to specify a random variable of interest even when the corresponding probability
function is too difficult to describe explicitly. In what follows we will use several
expressions synonymously when describing random variables. For example, when
referring to the random variable associated with a binomial probability function we
will variously say that the random variable “has a binomial distribution,” “is binomi-
ally distributed,” or simply “is binomial.”
We now outline a few of the key definitions and results from introductory proba-
bility theory. For simplicity we focus on discrete random variables, keeping in mind
that equivalent statements can be made for the continuous case. One of the defining
PROBABILITY 3

properties of a probability function is the identity

P(X = x) = 1 (1.1)
x

where here, and in what follows, the summation is over all elements in the sample
space of X . Next we define two fundamental quantities that will be referred to re-
peatedly throughout the book. The mean of X , sometimes called the expected value
of X , is defined to be


E(X ) = x P(X = x) (1.2)
x

and the variance of X is defined to be

var(X ) = [x − E(X )]2 P(X = x). (1.3)
x

It is important to note that when the mean and variance exist, they are constants,
not random variables. In most applications the mean and variance are unknown and
must be estimated from study data. In what follows, whenever we refer to the mean
or variance of a random variable it is being assumed that these quantities exist—that
is, are finite constants.

Example 1.1 Consider the probability function given in Table 1.1. Evidently
(1.1) is satisfied. The sample space of X is {0, 1, 2}, and the mean and variance of X
are

E(X ) = (0 × .20) + (1 × .50) + (2 × .30) = 1.1

and

var(X ) = [(0 − 1.1)2 .20] + [(1 − 1.1)2 .50] + [(2 − 1.1)2 .30] = .49.

Transformations can be used to derive new random variables from an existing

random variable. Again we emphasize that what is meant by such a statement is that
we can derive new probability functions from an existing probability function. When
the probability function at hand has a known formula it is possible, in theory, to write
down an explicit formula for the transformed probability function. In practice, this

TABLE 1.1 Probability Function of X

x P(X = x)
0 .20
1 .50
2 .30
4 INTRODUCTION

TABLE 1.2 Probability Function of Y

y P(Y = y)
5 .20
7 .50
9 .30

may lead to a very complicated expression, which is one of the reasons for relying
on random variable notation.

Example 1.2 With X as in Example 1.1, consider the random variable Y =

2X + 5. The sample space of Y is obtained by applying the transformation to the
sample space of X , which gives {5, 7, 9}. The values of P(Y = x) are derived as
follows: P(Y = 7) = P(2X + 5 = 7) = P(X = 1) = .50. The probability function
of Y is given in Table 1.2.

The mean and variance of Y are

E(Y ) = (5 × .20) + (7 × .50) + (9 × .30) = 7.2

and

var(Y ) = [(5 − 7.2)2 .20] + [(7 − 7.2)2 .50] + [(9 − 7.2)2 .30] = 1.96.

Comparing Examples 1.1 and 1.2 we note that X and Y have the same probability
values but different sample spaces.
Consider a random variable which has as its only outcome the constant β, that
is, the sample space is {β}. It is immediate from (1.2) and (1.3) that the mean and
variance of the random variable are β and 0, respectively. Identifying the random
variable with the constant β, and allowing a slight abuse of notation, we can write
E(β) = β and var(β) = 0. Let X be a random variable, let α and β be arbitrary
constants, and consider the random variable α X + β. Using (1.2) and (1.3) it can be
shown that

E(α X + β) = α E(X ) + β (1.4)

and

var(α X + β) = α 2 var(X ). (1.5)

Applying these results to Examples 1.1 and 1.2 we find, as before, that E(Y ) =
2(1.1) + 5 = 7.2 and var(Y ) = 4(.49) = 1.96.

Example 1.3 Let X be an arbitrary random variable with mean µ and variance
σ 2 , where σ > 0, and consider the random variable (X − µ)/σ . With α = 1/σ and
PROBABILITY 5

β = −µ/σ in (1.4) and (1.5), it follows that

 X − µ
E =0
σ
and
 X − µ
var = 1.
σ
In many applications it is necessary to consider several related random variables.
For example, in a health survey we might be interested in age, weight, and blood
pressure. A probability function characterizing two or more random variables simul-
taneously is referred to as their joint probability function. For simplicity we discuss
the case of two discrete random variables, X and Y . The joint probability function of
the pair of random variables (X, Y ) is denoted by P(X = x, Y = y). For the present
discussion we assume that the sample space of the joint probability function is the
set of pairs {(x, y)}, where x is in the sample space of X and y is in the sample space
of Y . Analogous to (1.1), the identity



P(X = x, Y = y) = 1 (1.6)
x y

must be satisfied. In the joint distribution of X and Y , the two random variables are
considered as a unit. In order to isolate the distribution of X , we “sum over” Y to
obtain what is referred to as the marginal probability function of X ,


P(X = x) = P(X = x, Y = y).
y

Similarly, the marginal probability function of Y is

P(Y = y) = P(X = x, Y = y).
x

From a joint probability function we are to able obtain marginal probability func-
tions, but the process does not necessarily work in reverse. We say that X and Y are
independent random variables if P(X = x, Y = y) = P(X = x) P(Y = y), that is,
if the joint probability function is the product of the marginal probability functions.
Other than the case of independence, it is not generally possible to reconstruct a joint
probability function in this way.

Example 1.4 Table 1.3 is an example of a joint probability function and its as-
sociated marginal probability functions. For example, P(X = 1, Y = 3) = .30. The
marginal probability function of X is obtained by summing over Y , for example,

P(X = 1) = P(X = 1, Y = 1) + P(X = 1, Y = 2) + P(X = 1, Y = 3) = .50.

6 INTRODUCTION

TABLE 1.3 Joint Probability Function of X and Y

P(X = x, Y = y)
y
x 1 2 3 P(X = x)
0 .02 .06 .12 .20
1 .05 .15 .30 .50
2 .03 .09 .18 .30
P(Y = y) .10 .30 .60 1

It is readily verified that X and Y are independent, for example, P(X = 1, Y = 2) =

.15 = P(X = 1) P(Y = 2).
Now consider Table 1.4, where the marginal probability functions of X and Y are
the same as in Table 1.3 but where, as is easily verified, X and Y are not independent.
We now present generalizations of (1.4) and (1.5). Let X 1 , X 2 , . . . , X n be arbi-
n let α1 , α2 , . . . , αn , β be arbitrary constants, and consider the
trary random variables,
random variable i=1 αi X i + β. It can be shown that


n 

n
E αi X i + β = αi E(X i ) + β (1.7)
i=1 i=1

and, if the X i are independent, that


n 
n
var αi X i + β = αi2 var(X i ). (1.8)
i=1 i=1

In the case of two independent random variables X 1 and X 2 ,

E(X 1 + X 2 ) = E(X 1 ) + E(X 2 )

E(X 1 − X 2 ) = E(X 1 ) − E(X 2 )

TABLE 1.4 Joint Probability Function of X and Y

P(X = x, Y = y)
y
x 1 2 3 P(X = x)
0 .01 .05 .14 .20
1 .06 .18 .26 .50
2 .03 .07 .20 .30
P(Y = y) .10 .30 .60 1
PROBABILITY 7

and

var(X 1 + X 2 ) = var(X 1 − X 2 ) = var(X 1 ) + var(X 2 ). (1.9)

If X 1 , X 2 , . . . , X n are independent and all have the same distribution, we say the
X i are a sample from that distribution and that the sample size is n. Unless stated oth-
erwise, it will be assumed that all samples are simple random samples (Section 1.3).
With the distribution left unspecified, denote the mean and variance of X i by µ and
σ 2 , respectively. The sample mean is defined to be

1
n
X= Xi .
n i=1

Setting αi = 1/n and β = 0 in (1.7) and (1.8), we have

E(X) = µ (1.10)

and

σ2
var(X ) = . (1.11)
n

1.1.2 Some Probability Functions

We now consider some of the key probability functions that will be of importance in
this book.

Normal (Gaussian)
For reasons that will become clear after we have discussed the Central Limit The-
orem, the most important distribution is undoubtedly the normal distribution. The
normal probability function is
 
1 −(z − µ)2
f (z|µ, σ ) = √ exp
σ 2π 2σ 2

where the sample space is all numbers and exp stands for exponentiation to the
base e. We denote the corresponding normal random variable by Z . A normal distri-
bution is completely characterized by the parameters µ and σ > 0. It can be shown
that the mean and variance of Z are µ and σ 2 , respectively.
When µ = 0 and σ = 1 we say that Z has the standard normal distribution. For
0 < γ < 1, let z γ denote that point which cuts off the upper γ -tail probability of the
standard normal distribution; that is, P(Z ≥ z γ ) = γ . For example, z .025 = 1.96. In
some statistics books the notation z γ is used to denote the lower γ -tail. An important
property of the normal distribution is that, for arbitrary constants α and β > 0,
(Z −α)/β is also normally distributed. In particular this is true for (Z −µ)/σ which,
in view of Example 1.3, is therefore standard normal. This explains why statistics
8 INTRODUCTION

books only need to provide values of z γ for the standard normal distribution rather
than a series of tables for different values of µ and σ .
Another important property of the normal distribution is that it is additive. Let
Z 1 , Z 2 , . . . , Z n be independent normal random variables and suppose thatn Z i has
mean µi and variance σi2 (i = 1, 2, . . . , n). Then the randomvariable i=1 Z i is
n
also
n normally distributed and, from (1.7) and (1.8), it has mean µ
i=1 i and variance
i=1 σi .
2

Chi-Square
The formula for the chi-square probability function is complicated and will not be
presented here. The sample space of the distribution is all nonnegative numbers.
A chi-square distribution is characterized completely by a single positive integer r ,
which is referred to as the degrees of freedom. For brevity we write χ(r2 ) to indicate
that a random variable has a chi-square distribution with r degrees of freedom. The
mean and variance of the chi-square distribution with r degrees of freedom are r and
2r , respectively.
The importance of the chi-square distribution stems from its connection with the
normal distribution. Specifically, if Z is standard normal, then Z 2 , the transformation
of Z obtained by squaring, is χ(1) 2 . More generally, if Z is normal with mean µ

and variance σ then, as remarked above, (Z − µ)/σ is standard normal and so

2

[(Z − µ)/σ ]2 = (Z − µ)2 /σ 2 is χ(1) 2 . In practice, most chi-square distributions

with 1 degree of freedom originate as the square of a standard normal distribution.

This explains why the usual notation for a chi-square random variable is X 2 , or
sometimes χ 2 .
Like the normal distribution, the chi-square distribution has an additive property.
Let X 12 , X 22 , . . . , X n2 be independent chi-square random variables and suppose that
n
X i2 has ri degrees of freedom (i = 1, 2, . . . , n). Then i=1
 X i2 is chi-square with
n
i=1 ri degrees of freedom. As a special case of this result, let Z 1 , Z 2 , . . . , Z n be
independent normal random variables, where Z i has mean µi and variance σi2 (i =
1, 2, . . . , n). Then (Z i − µi )2 /σi2 is χ(1)
2 for all i, and so

n
(Z i − µi )2
X2 = (1.12)
i=1 σi2

is χ(n)
2 .

Binomial
The binomial probability function is
 
r
P(A = a|π) = π a (1 − π)r −a
a

where the sample space is the (finite) set of integers {0, 1, 2, . . . , r }. A binomial
distribution is completely characterized by the parameters π and r which, for conve-
PROBABILITY 9

nience, we usually write as (π, r ). Recall that, for 0 ≤ a ≤ r , the binomial coefficient
is defined to be
 
r r!
=
a a! (r − a)!

where r ! = r (r − 1) · · · 2 · 1. We adopt the usual convention that 0! = 1. The

binomial coefficient ar equals the number of ways of choosing a items out of r
without regard to order of selection. For example, the number of possible bridge
hands is 52
13 = 6.35 × 10 . It can be shown that
11

r  

r
π a (1 − π)r −a = [π + (1 − π)]r = 1
a=0
a

and so (1.1) is satisfied. The mean and variance of A are πr and π(1 − π)r , respec-
tively; that is,

r  
r
E(A) = a π a (1 − π)r −a = πr
a=0
a

and

r  
r
var(A) = (a − πr )2 π a (1 − π)r −a = π(1 − π)r.
a=0
a

Like the normal and chi-square distributions, the binomial distribution is additive.
Let A1 , A2 , . . . , An be independent binomial random variables
n and suppose that Ai
has parameters πi  = π and ri (i = 1, 2, . . . , n). Then i=1 Ai is binomial with
n
parameters π and i=1 ri . A similar result does not hold when the πi are not all
equal.
The binomial distribution is important in epidemiology because many epidemio-
logic studies are concerned with counted (discrete) outcomes. For instance, the bi-
nomial distribution can be used to analyze data from a study in which a group of r
individuals is followed over a defined period of time and the number of outcomes of
interest, denoted by a, is counted. In this context the outcome of interest could be,
for example, recovery from an illness, survival to the end of follow-up, or death from
some cause. For the binomial distribution to be applicable, two conditions need to
be satisfied: The probability of an outcome must be the same for each subject, and
subjects must behave independently; that is, the outcome for each subject must be
unrelated to the outcome for any other subject. In an epidemiologic study the first
condition is unlikely to be satisfied across the entire group of subjects. In this case,
one strategy is to form subgroups of subjects having similar characteristics so that,
to a greater or lesser extent, there is uniformity of risk within each subgroup. Then
the binomial distribution can be applied to each subgroup separately. As an example
where the second condition would not be satisfied, consider a study of influenza in a
10 INTRODUCTION

classroom of students. Since influenza is contagious, the risk of illness in one student
is not independent of the risk in others. In studies of noninfectious diseases, such as
cancer, stroke, and so on, the independence assumption is usually satisfied.

Poisson
The Poisson probability function is

e−ν ν d
P(D = d|ν) = (1.13)
d!
where the sample space is the (infinite) set of nonnegative integers {0, 1, 2, . . .}. A
Poisson distribution is completely characterized by the parameter ν, which is equal
to both the mean and variance of the distribution, that is,

∞  −ν d 
e ν
E(D) = d =ν
d=0
d!

and

∞  e−ν ν d 
var(D) = (d − ν)2 = ν.
d=0
d!

Similar to the other distributions considered above, the Poisson distribution has
an additive property. Let D1 , D2 , . . . , Dn be independent Poisson
n random variables,
where Di  has the parameter νi (i = 1, 2, . . . , n). Then i=1 Di is Poisson with
n
parameter i=1 νi .
Like the binomial distribution, the Poisson distribution can be used to analyze data
from a study in which a group of individuals is followed over a defined period of time
and the number of outcomes of interest, denoted by d, is counted. In epidemiologic
studies where the Poisson distribution is applicable, it is not the number of subjects
that is important but rather the collective observation time experienced by the group
as a whole. For the Poisson distribution to be valid, the probability that an outcome
will occur at any time point must be “small.” Expressed another way, the outcome
must be a “rare” event.
As might be guessed from the above remarks, there is a connection between the
binomial and Poisson distributions. In fact the Poisson distribution can be derived as
a limiting case of the binomial distribution. Let D be Poisson with mean ν, and let
A1 , A2 , . . . , Ai , . . . be an infinite sequence of binomial random variables, where Ai
has parameters (πi , ri ). Suppose that the sequence satisfies the following conditions:
πi ri = ν for all i, and the limiting value of πi equals 0. Under these circumstances
the sequence of binomial random variables “converges” to D; that is, as i gets larger
the distribution of Ai gets closer to that of D. This theoretical result explains why
the Poisson distribution is often used to model rare events. It also suggests that the
Poisson distribution with parameter ν can be used to approximate the binomial dis-
tribution with parameters (π, r ), provided ν = πr and π is “small.”
Other documents randomly have
different content
obliged to confess that in spite of all his efforts, the sick negress died on the
fourth day,—as the sorcerer had predicted. This fact must have strongly
confirmed his belief that the devil was at the bottom of the whole affair, and
caused him to doubt whether even a flogging of about three hundred lashes,
followed by a pimentade, was sufficient chastisement for the miserable black.
Perhaps the tradition of this frightful whipping may have had something to do
with the terror which still attaches to the name of the Dominican in Martinique.
The legal extreme punishment was twenty-nine lashes.
Père Labat also avers that in his time the negroes were in the habit of carrying
sticks which had the power of imparting to any portion of the human body
touched by them a most severe chronic pain. He at first believed, he says, that
these pains were merely rheumatic; but after all known remedies for rheumatism
had been fruitlessly applied, he became convinced there was something occult
and diabolical in the manner of using and preparing these sticks.... A fact worthy
of note is that this belief is still prevalent in Martinique!
One hardly ever meets in the country a negro who does not carry either a stick
or a cutlass, or both. The cutlass is indispensable to those who work in the
woods or upon plantations; the stick is carried both as a protection against
snakes and as a weapon of offence and defence in village quarrels, for unless a
negro be extraordinarily drunk he will not strike his fellow with a cutlass. The
sticks are usually made of a strong dense wood: those most sought after of a
material termed moudongue,[13] almost as tough as, but much lighter than, our
hickory. On inquiring whether any of the sticks thus carried were held to possess
magic powers, I was assured by many country people that there were men who
knew a peculiar method of "arranging" sticks so that to touch any person with
them even lightly, and through any thickness of clothing, would produce terrible
and continuous pain.
 LE CALVAIRE
Above the village of Fort-de-France a series
of fourteen little crosses lines the roadside to
the hilltop—each bearing a relievo
representing incidents of Christ's Passion.
Believing in these things, and withal unable to decide whether the sun revolved
about the earth, or the earth about the sun,[14] Père Labat was, nevertheless, no
more credulous and no more ignorant than the average missionary of his time: it
is only by contrast with his practical perspicacity in other matters, his worldly
rationalism and executive shrewdness, that this superstitious naïveté impresses
one as odd. And how singular sometimes is the irony of Time! All the wonderful
work the Dominican accomplished has been forgotten by the people; while all the
witchcrafts that he warred against survive and flourish openly; and his very name
is seldom uttered but in connection with superstitions,—has been, in fact,
preserved among the blacks by the power of superstition alone, by the belief in
zombis and even goblins.... "Mi! ti manmaille-là, main ké fai Pè Labatt vini
pouend ou!"...
[11]Vol. III, p. 382-3. Edition of 1722.
[12]The parrots of Martinique he describes as having been green, with slate-colored plumage on
the top of the head, mixed with a little red, and as having a few red feathers in the wings, throat,
and tail.
[13]The creole word moudongue is said to be a corruption of Mondongue, the name of an African
coast tribe who had the reputation of being cannibals. A Mondongue slave on the plantations was
generally feared by his fellow-blacks of other tribes; and the name of the cannibal race became
transformed into an adjective to denote anything formidable or terrible. A blow with a stick made
of the wood described being greatly dreaded, the term was applied first to the stick, and
afterward to the wood itself.
[14]Accounting for the origin of the trade-winds, he writes: "I say that the Trade-Winds do not
exist in the Torrid Zone merely by chance; forasmuch as the cause which produces them is very
necessary, very sure, and very continuous, since they result either from the movement of the
Earth around the Sun, or from the movement of the Sun around the Earth, Whether it he the one
or the other of these two great bodies which moves..." etc.

Few habitants of St. Pierre now remember that the beautiful park behind the
cathedral used to be called the Savanna of the White Fathers,—and the long
shadowed meadow beside the Roxelane, the Savanna of the Black Fathers: the
Jesuits. All the great religious orders have long since disappeared from the
colony: their edifices have been either converted to other uses or demolished;
their estates have passed into other hands.... Were their labors, then, productive
of merely ephemeral results?—was the colossal work of a Père Labat all in vain,
so far as the future is concerned? The question is not easily answered; but it is
worth considering.
Of course the material prosperity which such men toiled to obtain for their order
represented nothing more, even to their eyes, than the means of self-
maintenance, and the accumulation of force necessary for the future missionary
labors of the monastic community. The real ultimate purpose was, not the
acquisition of power for the order, but for the Church, of which the orders
represented only a portion of the force militant; and this purpose did not fail of
accomplishment. The orders passed away only when their labors had been
completed,—when Martinique had become (exteriorly, at least) more Catholic
than Rome itself,—after the missionaries had done all that religious zeal could do
in moulding and remoulding the human material under their control. These men
could scarcely have anticipated those social and political changes which the
future reserved for the colonies, and which no ecclesiastical sagacity could, in any
event, have provided against. It is in the existing religious condition of these
communities that one may observe and estimate the character and the probable
duration of the real work accomplished by the missions.
... Even after a prolonged residence in Martinique, its visible religious condition
continues to impress one as something phenomenal. A stranger, who has no
opportunity to penetrate into the home life of the people, will not, perhaps,
discern the full extent of the religious sentiment; but, nevertheless, however brief
his stay, he will observe enough of the extravagant symbolism of the cult to fill
him with surprise. Wherever he may choose to ride or to walk, he is certain to
encounter shrines, statues of saints, or immense crucifixes. Should he climb up to
the clouds of the peaks, he will find them all along the way;—he will perceive
them waiting for him, looming through the mists of the heights; and passing
through the loveliest ravines, he will see niches hollowed out in the volcanic
rocks, above and below him, or contrived in the trunks of trees bending over
precipices, often in places so difficult of access that he wonders how the work
could have been accomplished. All this has been done by the various property-
owners throughout the country: it is the traditional custom to do it—brings good-
luck! After a longer stay in the island, one discovers also that in almost every
room of every dwelling—stone residence, wooden cottage, or palm-thatched
ajoupa—there is a chapelle: that is, a sort of large bracket fastened to the wall,
on which crosses or images are placed, with vases of flowers, and lamps or wax-
tapers to be burned at night. Sometimes, moreover, statues are placed in
windows, or above door-ways;—and all passers-by take off their hats to these.
Over the porch of the cottage in a mountain village, where I lived for some
weeks, there was an absurd little window contrived,—a sort of purely ornamental
dormer,—and in this a Virgin about five inches high had been placed. At a little
distance it looked like a toy,—a child's doll forgotten there; and a doll I always
supposed it to be, until one day that I saw a long procession of black laborers
passing before the house, every one of whom took off his hat to it.... My
bedchamber in the same cottage resembled a religious museum. On the chapelle
there were no less than eight Virgins, varying in height from one to sixteen
inches,—a St. Joseph,—a St. John,—a crucifix,—and a host of little objects in the
shape of hearts or crosses, each having some special religious significance;—
while the walls were covered with framed certificates of baptism, "first-
communion," confirmation, and other documents commemorating the whole
church life of the family for two generations.
... Certainly the first impression created by this perpetual display of crosses,
statues, and miniature chapels is not pleasing,—particularly as the work is often
inartistic to a degree bordering upon the grotesque, and nothing resembling art is
anywhere visible. Millions of francs must have been consumed in these creations,
which have the rudeness of mediævalism without its emotional sincerity, and
which—amid the loveliness of tropic nature, the grace of palms, the many-colored
fire of liana blossoms—jar on the æsthetic sense with an almost brutal violence.
Yet there is a veiled poetry in these silent populations of plaster and wood and
stone. They represent something older than the Middle Ages, older than
Christianity,—something strangely distorted and transformed, it is true, but
recognizably conserved by the Latin race from those antique years when every
home had its beloved ghosts, when every wood or hill or spring had its gracious
divinity, and the boundaries of all fields were marked and guarded by statues of
gods.
Instances of iconoclasm are of course highly rare in a country of which no native
—rich or poor, white or half-breed—fails to doff his hat before every shrine, cross,
or image he may happen to pass. Those merchants of St. Pierre or of Fort-de-
France living only a few miles out of the city must certainly perform a vast
number of reverences on their way to or from business;—I saw one old
gentleman uncover his white head about twenty times in the course of a fifteen
minutes' walk. I never heard of but one image-breaker in Martinique; and his act
was the result of superstition, not of any hostility to popular faith or custom: it
was prompted by the same childish feeling which moves Italian fishermen
sometimes to curse St. Antony or to give his image a ducking in bad weather.
This Martinique iconoclast was a negro cattle-driver who one day, feeling badly in
need of a glass of tafia, perhaps, left the animals intrusted to him in care of a
plaster image of the Virgin, with this menace (the phrase is on record):—
"Moin ka quitté bef-la ba ou pou gàdé ba moin. Quand moin vini, si moin pa
trouvé compte-moin, moin ké fouté ou vingt-nèf coudfouètt!" (I leave these cattle
with you to take care of for me. When I come back, if I don't find them all here,
I'll give you twenty-nine lashes.)
 A WAYSIDE SHRINE
"There is a veiled poetry in these silent
populations of plaster and wood and stone.
Something older than the Middle Ages, older
than Christianity."
Returning about half an hour later, he was greatly enraged to find his animals
scattered in every direction;—and, rushing at the statue, he broke it from the
pedestal, fixing it upon the ground, and gave it twenty-nine lashes with his bull-
whip. For this he was arrested, tried, and sentenced to imprisonment, with hard
labor, for life! In those days there were no colored magistrates;—the judges were
all bêkés.
"Rather a severe sentence," I remarked to my informant, a planter who
conducted me to the scene of the alleged sacrilege.
"Severe, yes," he answered;—"and I suppose the act would seem to you more
idiotic than criminal. But here, in Martinique, there were large questions involved
by such an offence. Relying, as we have always done to some extent, upon
religious influence as a factor in the maintenance of social order, the negro's act
seemed a dangerous example."...

That the Church remains still rich and prosperous in Martinique there can be no
question; but whether it continues to wield any powerful influence in the
maintenance of social order is more than doubtful. A Polynesian laxity of morals
among the black and colored population, and the history of race-hatreds and
revolutions inspired by race-hate, would indicate that neither in ethics nor in
politics does it possess any preponderant authority. By expelling various religious
orders;—by establishing lay schools, lycées, and other educational institutions
where the teaching is largely characterized by aggressive antagonism to Catholic
ideas;—by the removal of crucifixes and images from public buildings, French
Radicalism did not inflict any great blow upon Church interests. So far as the
white, and, one may say, the wealthy, population is concerned, the Church
triumphs in her hostility to the Government schools; and to the same extent she
holds an educational monopoly. No white creole would dream of sending his
children to a lay school or a lycée—notwithstanding the unquestionable
superiority of the educational system in the latter institutions;—and, although
obliged, as the chief tax-paying class, to bear the burden of maintaining these
establishments, the whites hold them in such horror that the Government
professors are socially ostracized. No doubt the prejudice or pride which abhors
mixed schools aids the Church in this respect; she herself recognizes race-feeling,
keeps her schools unmixed, and even in her convents, it is said, obliges the
colored nuns to serve the white! For more than two centuries every white
generation has been religiously moulded in the seminaries and convents; and
among the native whites one never hears an overt declaration of free-thought
opinion. Except among the colored men educated in the Government schools, or
their foreign professors, there are no avowed free-thinkers;—and this, not
because the creole whites, many of whom have been educated in Paris, are
naturally narrow-minded, or incapable of sympathy with the mental expansion of
the age, but because the religious question at Martinique has become so
intimately complicated with the social and political one, concerning which there
can be no compromise whatever, that to divorce the former from the latter is
impossible. Roman Catholicism is an element of the cement which holds creole
society together; and it is noteworthy that other creeds are not represented. I
knew of only one Episcopalian and one Methodist in the island,—and heard a sort
of legend about a solitary Jew whose whereabouts I never could discover;—but
these were strangers.
It was only through the establishment of universal suffrage, which placed the
white population at the mercy of its former slaves, that the Roman Church
sustained any serious injury. All local positions are filled by blacks or men of
color; no white creole can obtain a public office or take part in legislation; and
the whole power of the black vote is ungenerously used against the interests of
the class thus politically disinherited. The Church suffers in consequence: her
power depended upon her intimate union with the wealthy and dominant class;
and she will never be forgiven by those now in power for her sympathetic
support of that class in other years. Politics yearly intensify this hostility; and as
the only hope for the restoration of the whites to power, and of the Church to its
old position, lies in the possibility of another empire or a revival of the monarchy,
the white creoles and their Church are forced into hostility against republicanism
and the republic. And political newspapers continually attack Roman Catholicism,
—mock its tenets and teachings,—ridicule its dogmas and ceremonies,—satirize
its priests.
In the cities and towns the Church indeed appears to retain a large place in the
affection of the poorer classes;—her ceremonies are always well attended;
money pours into her coffers; and one can still witness the curious annual
procession of the "converted,"—aged women of color and negresses going to
communion for the first time, all wearing snow-white turbans in honor of the
event. But among the country people, where the dangerous forces of revolution
exist, Christian feeling is almost stifled by ghastly beliefs of African origin;—the
images and crucifixes still command respect, but this respect is inspired by a
feeling purely fetichistic. With the political dispossession of the whites, certain
dark powers, previously concealed or repressed, have obtained formidable
development. The old enemy of Père Labat, the wizard (the quimboiseur),
already wields more authority than the priest, exercises more terror than the
magistrate, commands more confidence than the physician. The educated
mulatto class may affect to despise him;—but he is preparing their overthrow in
the dark. Astonishing is the persistence with which the African has clung to these
beliefs and practices, so zealously warred upon by the Church and so mercilessly
punished by the courts for centuries. He still goes to mass, and sends his children
to the priest; but he goes more often to the quimboiseur and the "magnetise."
He finds use for both beliefs, but gives large preference to the savage one,—just
as he prefers the pattering of his tamtam to the music of the military band at the
Savane du Fort.... And should it come to pass that Martinique be ever totally
abandoned by its white population,—an event by no means improbable in the
present order of things,—the fate of the ecclesiastical fabric so toilsomely reared
by the monastic orders is not difficult to surmise.

VI
From my window in the old Rue du Bois-Morin,—which climbs the foot of Morne
Labelle by successions of high stone steps,—all the southern end of the city is
visible as in a bird's-eye view. Under me is a long peaking of red-scaled roofs,—
gables and dormer-windows,—with clouds of bright green here and there,—
foliage of tamarind and corossolier;—westward purples and flames the great
circle of the Caribbean Sea;—east and south, towering to the violet sky, curve the
volcanic hills, green-clad from base to summit;—and right before me the
beautiful Morne d'Orange, all palm-plumed and wood-wrapped, trends seaward
and southward. And every night, after the stars come out, I see moving lights
there,—lantern fires guiding the mountain-dwellers home; but I look in vain for
the light of Père Labat.
And nevertheless,—although no believer in ghosts,—I see thee very plainly
sometimes, thou quaint White Father, moving through winter-mists in the
narrower Paris of another century; musing upon the churches that arose at thy
bidding under tropic skies; dreaming of the primeval valleys changed by thy will
to green-gold seas of cane,—and the strong mill that will bear thy name for two
hundred years (it stands solid unto this day),—and the habitations made for thy
brethren in pleasant palmy places,—and the luminous peace of thy Martinique
convent,—and odor of roasting parrots fattened upon grains de bois d'Inde and
guavas,—"l'odeur de muscade et de girofle qui fait plaisir"...
Eh, Père Labat!—what changes there have been since thy day! The White Fathers
have no place here now; and the Black Fathers, too, have been driven from the
land, leaving only as a memory of them the perfect and ponderous architecture
of the Perinnelle plantation-buildings, and the appellation of the river still known
as the Rivière des Pères. Also the Ursulines are gone, leaving only their name on
the corner of a crumbling street. And there are no more slaves; and there are
new races of colors thou wouldst deem scandalous though beautiful; and there
are no more parrots; and there are no more diablotins. And the grand woods
thou sawest in their primitive and inviolate beauty, as if fresh from the Creator's
touch in the morning of the world, are passing away; the secular trees are being
converted into charcoal, or sawn into timber for the boat-builders: thou shouldst
see two hundred men pulling some forest giant down to the sea upon the two-
wheeled screaming thing they call a "devil" (yon diabe),—cric-crac!—cric-crac!—
all chanting together:—
"Soh-soh!—yaïe-yah!
Rhâlé bois-canot!"
And all that ephemeral man has had power to change has been changed,—ideas,
morals, beliefs, the whole social fabric. But the eternal summer remains,—and
the Hesperian magnificence of azure sky and violet sea,—and the jewel-colors of
the perpetual hills;—the same tepid winds that rippled thy cane-fields two
hundred years ago still blow over Sainte-Marie;—the same purple shadows
lengthen and dwindle and turn with the wheeling of the sun. God's witchery still
fills this land; and the heart of the stranger is even yet snared by the beauty of
it; and the dreams of him that forsakes it will surely be haunted—even as were
thine own. Père Labat—by memories of its Eden-summer: the sudden leap of the
light over a thousand peaks in the glory of tropic dawn,—the perfumed peace of
enormous azure noons,—and shapes of palm wind-rocked in the burning of
colossal sunsets,—and the silent flickering of the great fire-flies through the
lukewarm darkness, when mothers call their children home.... "Mi fanal Pè
Labatt!—mi Pè Labatt ka vini pouend oi!"

LA GUIABLESSE

Night in all countries brings with it vaguenesses and illusions which terrify certain
imaginations;—but in the tropics it produces effects peculiarly impressive and
peculiarly sinister. Shapes of vegetation that startle even while the sun shines
upon them assume, after his setting, a grimness,—a grotesquery,—a
suggestiveness for which there is no name.... In the North a tree is simply a tree;
—here it is a personality that makes itself felt; it has a vague physiognomy, an
 indefinable Me: it is an Individual (with a capital I); it is a Being (with a
capital B).
From the high woods, as the moon mounts, fantastic darknesses
descend into the roads,—black distortions, mockeries, bad dreams,—an
endless procession of goblins. Least startling are the shadows flung
down by the various forms of palm, because instantly recognizable;—yet
these take the semblance of giant fingers opening and closing over the
way, or a black crawling of unutterable spiders....
Nevertheless, these phasma seldom alarm the solitary and belated
Bitaco: the darknesses that creep stealthily along the path have no
frightful signification for him,—do not appeal to his imagination;—if he
suddenly starts and stops and stares, it is not because of such shapes,
but because he has perceived two specks of orange light, and is not yet sure
whether they are only fire-flies, or the eyes of a trigonocephalus. The spectres of
his fancy have nothing in common with those indistinct and monstrous
umbrages: what he most fears, next to the deadly serpent, are human
witchcrafts. A white rag, an old bone lying in the path, might be a maléfice
which, if trodden upon, would cause his leg to blacken and swell up to the size of
the limb of an elephant;—an unopened bundle of plantain leaves or of bamboo
strippings, dropped by the way-side, might contain the skin of a Soucouyan. But
the ghastly being who doffs or dons his skin at will—and the Zombi—and the
Moun-Mò—may be quelled or exorcised by prayer; and the lights of shrines, the
white gleaming of crosses, continually remind the traveller of his duty to the
Powers that save. All along the way there are shrines at intervals, not very far
apart: while standing in the radiance of one niche-lamp, you may perhaps discern
the glow of the next, if the road be level and straight. They are almost
everywhere,—shining along the skirts of the woods, at the entrance of ravines,
by the verges of precipices;—there is a cross even upon the summit of the
loftiest peak in the island. And the night-walker removes his hat each time his
bare feet touch the soft stream of yellow light outpoured from the illuminated
shrine of a white Virgin or a white Christ. These are good ghostly company for
him;—he salutes them, talks to them, tells them his pains or fears: their blanched
faces seem to him full of sympathy;—they appear to cheer him voicelessly as he
strides from gloom to gloom, under the goblinry of those woods which tower
black as ebony under the stars.... And he has other companionship. One of the
greatest terrors of darkness in other lands does not exist here after the setting of
the sun,—the terror of Silence.... Tropical night is full of voices;—extraordinary
populations of crickets are trilling; nations of tree-frogs are chanting; the Cabri-
des-bois,[15] or cra-cra, almost deafens you with the wheezy bleating sound by
which it earned its creole name; birds pipe: everything that bells, ululates,
drones, clacks, guggles, joins the enormous chorus; and you fancy you see all
the shadows vibrating to the force of this vocal storm. The true life of Nature in
the tropics begins with the darkness, ends with the light.
And it is partly, perhaps, because of these conditions that the coming of the
dawn does not dissipate all fears of the supernatural. I ni pè zombi mênm gran'-
jou (he is afraid of ghosts even in broad daylight) is a phrase which does not
sound exaggerated in these latitudes,—not, at least, to any one knowing
something of the conditions that nourish or inspire weird beliefs. In the awful
peace of tropical day, in the hush of the woods, the solemn silence of the hills
(broken only by torrent voices that cannot make themselves heard at night),
even in the amazing luminosity, there is a something apparitional and weird,—
something that seems to weigh upon the world like a measureless haunting. So
still all Nature's chambers are that a loud utterance jars upon the ear brutally, like
a burst of laughter in a sanctuary. With all its luxuriance of color, with all its
violence of light, this tropical day has its ghostliness and its ghosts. Among the
people of color there are many who believe that even at noon—when the
boulevards behind the city are most deserted—the zombis will show themselves
to solitary loiterers.

[15]In creole, cabritt-bois—("the Wood-Kid")—a colossal cricket. Precisely at half-past four in the
morning it becomes silent; and for thousands of early risers too poor to own a dock, the cessation
of its song is the signal to get up.

II

... Here a doubt occurs to me,—a doubt regarding the precise nature of a word,
which I call upon Adou to explain. Adou is the daughter of the kind old capresse
from whom I rent my room in this little mountain cottage. The mother is almost
precisely the color of cinnamon; the daughter's complexion is brighter,—the ripe
tint of an orange.... Adou tells me creole stories and tim-tim. Adou knows all
about ghosts, and believes in them. So does Adou's extraordinarily tall brother,
Yébé,—my guide among the mountains.
—"Adou," I ask, "what is a zombi?"
The smile that showed Adou's beautiful white teeth has instantly disappeared;
and she answers, very seriously, that she has never seen a zombi, and does not
want to see one.
—"Moin pa té janmain ouè zombi,—pa 'lè ouè ça, moin!"
—"But, Adou, child, I did not ask you whether you ever saw It;—I asked you only
to tell me what It is like?"...
Adou hesitates a little, and answers:
—"Zombi? Mais ça fai désòde lanuitt, zombi!"
Ah! it is Something which "makes disorder at night." Still, that is not a
satisfactory explanation. "Is it the spectre of a dead person, Adou? Is it one who
comes back?"
—"Non, Misié,—non; çê pa ça."
—"Not that?... Then what was it you said the other night when you were afraid
to pass the cemetery on an errand,—ça ou té ka di, Adou?"
—"Moin té ka di: 'Moin pa lé k'allé bò cimétiè-là pa ouappò moun-mò ké barré
moin: moin pa sé pè vini enco.'" (I said, "I do not want to goby that cemetery
because of the dead folk;—the dead folk will bar the way and I cannot get back
again.")
—"And you believe that, Adou?"
—"Yes, that is what they say.... And if you go into the cemetery at night you
cannot come out again: the dead folk will stop you—moun-mò ké barré ou."...
—"But are the dead folk zombis, Adou?"
—"No; the moun-mò are not zombis. The zombis go everywhere: the dead folk
remain in the graveyard.... Except on the Night of All Souls: then they go to the
houses of their people everywhere."
—"Adou, if after the doors and windows were locked and barred you were to see
entering your room in the middle of the night, a Woman fourteen feet high?"...
—"Ah! pa pàlé ça!!"...
—"No! tell me, Adou?"
—"Why, yes: that would be a zombi. It is the zombis who make all those noises
at night one cannot understand.... Or, again, if I were to see a dog that high [she
holds her hand about five feet above the floor] coming into our house at night, I
would scream: Mi Zombi!"
... Then it suddenly occurs to Adou that her mother knows something about
zombis.
—"Ou! Mannam!"
—"Eti!" answers old Théréza's voice from the little out-building where the evening
meal is being prepared, over a charcoal furnace, in an earthen canari.
—"Missié-là ka mandé save ça ça yé yonne zombi;—vini ti bouin!"... The mother
laughs, abandons her canari, and comes in to tell me all she knows about the
weird word.
"I ni pè zombi"—I find from old Théréza's explanations—is a phrase indefinite as
our own vague expressions, "afraid of ghosts, afraid of the dark." But the word
"Zombi" also has special strange meanings.... "Ou passé nans grand chimin
lanuitt, épi ou ka ouè gouôs difé, épi plis ou ka vini assou difé-à pli ou ka ouè
difé-à ka màché: çé zombi ka fai ça.... Encò, chouval ka passé,—chouval ka ni
anni toua patt: ça zombi." (You pass along the high-road at night, and you see a
great fire, and the more you walk to get to it the more it moves away: it is the
zombi makes that.... Or a horse with only three legs passes you: that is a zombi.)
—"How big is the fire that the zombi makes?" I ask.
—"It fills the whole road," answers Théréza: "li ka rempli toutt chimin-là. Folk call
those fires the Evil Fires,—mauvai difé,—and if you follow them they will lead you
into chasms,—ou ké tombé adans labîme."...
And then she tells me this:
—"Baidaux was a mad man of color who used to live at St. Pierre, in the Street of
the Precipice. He was not dangerous,—never did any harm;—his sister used to
take care of him. And what I am going to relate is true,—çe zhistouè veritabe!
"One day Baidaux said to his sister: 'Moin ni yonne yche, va!—ou pa connaitt li! [I
have a child, ah!—you never saw it!] His sister paid no attention to what he said
that day; but the next day he said it again, and the next, and the next, and every
day after,—so that his sister at last became much annoyed by it, and used to cry
out: 'Ah! mais pé guiole ou, Baidaux! ou fou pou embêté moin conm ça!—ou bien
fou!'... But he tormented her that way for months and for years.
"One evening he went out, and only came home at midnight leading a child by
the hand,—a black child he had found in the street; and he said to his sister:—
"'Mi yche-là moin mené ba ou! Tou léjou moin té ka di ou moin tini yonne yche:
ou pa té 'lè couè,—eh, ben! MI Y!' [Look at the child I have brought you! Every
day I have been telling you I had a child: you would not believe me,—very well,
look at him!]
"The sister gave one look, and cried out: 'Baidaux, oti ou pouend yche-là?'... For
the child was growing taller and taller every moment.... And Baidaux,—because
he was mad,—kept saying: 'Çé yche-moin! çé yche moin!' [It is my child!]
"And the sister threw open the shutters and screamed to all the neighbors,
—'Sécou, sécou, sécou! Vint oué ça Baidaux mené ba moin!' [Help! help! Come
see what Baidaux has brought in here!] And the child said to Baidaux: 'Ou ni
bonhè ou fou!' [You are lucky that you are mad!]... Then all the neighbors came
running in; but they could not see anything: the Zombi was gone."...

III

... As I was saying, the hours of vastest light have their weirdness here;—and it
is of a Something which walketh abroad under the eye of the sun, even at high
noontide, that I desire to speak, while the impressions of a morning journey to
the scene of Its last alleged apparition yet remains vivid in my recollection.
You follow the mountain road leading from Calebasse over long meadowed levels
two thousand feet above the ocean, into the woods of La Couresse, where it
begins to descend slowly, through deep green shadowing, by great zigzags.
Then, at a turn, you find yourself unexpectedly looking down upon a planted
valley, through plumy fronds of arborescent fern. The surface below seems
almost like a lake of gold-green water,—especially when long breaths of
mountain-wind set the miles of ripening cane a-ripple from verge to verge: the
illusion is marred only by the road, fringed with young cocoa-palms, which
serpentines across the luminous plain. East, west, and north the horizon is almost
wholly hidden by surging of hills: those nearest are softly shaped and exquisitely
green; above them loftier undulations take hazier verdancy and darker shadows;
farther yet rise silhouettes of blue or violet tone, with one beautiful breast-
shaped peak thrusting up in the midst;—while, westward, over all, topping even
the Piton, is a vapory huddling of prodigious shapes—wrinkled, fissured, horned,
fantastically tall.... Such at least are the tints of the morning.... Here and there,
between gaps in the volcanic chain, the land hollows into gorges, slopes down
into ravines;—and the sea's vast disk of turquoise flames up through the interval.
Southwardly those deep woods, through which the way winds down, shut in the
view.... You do not see the plantation buildings till you have advanced some
distance into the valley;—they are hidden by a fold of the land, and stand in a
little hollow where the road turns: a great quadrangle of low gray antiquated
edifices, heavily walled and buttressed, and roofed with red tiles. The court they
form opens upon the main route by an immense archway. Farther along ajoupas
begin to line the way,—the dwellings of the field hands,—tiny cottages built with
trunks of the arborescent fern or with stems of bamboo, and thatched with cane-
straw: each in a little garden planted with bananas, yams, couscous, camanioc,
choux-caraibes, or other things,—and hedged about with roseaux d'Inde and
various flowering shrubs.
Thereafter, only the high whispering wildernesses of cane on either hand,—the
white silent road winding between its swaying cocoa-trees,—and the tips of hills
that seem to glide on before you as you walk, and that take, with the deepening
of the afternoon light, such amethystine color as if they were going to become
transparent.

IV

... It is a breezeless and cloudless noon. Under the dazzling downpour of light the
hills seem to smoke blue: something like a thin yellow fog haloes the leagues of
ripening cane,—a vast reflection. There is no stir in all the green mysterious front
of the vine-veiled woods. The palms of the roads keep their heads quite still, as if
listening. The canes do not utter a single susurration. Rarely is there such
absolute stillness among them: upon the calmest days there are usually rustlings
audible, thin cracklings, faint creepings: sounds that betray the passing of some
little animal or reptile—a rat or a manicou, or a zanoli or couresse,—more often,
however, no harmless lizard or snake, but the deadly fer-de-lance. To-day, all
these seem to sleep; and there are no workers among the cane to clear away the
weeds,—to uproot the pié-treffe, pié-poule, pié-balai, zhèbe-en-mè: it is the hour
of rest.
 PITONS DU CARBET
"The horizon is almost wholly hidden by
surging of hills: silhouettes of blue and
violet... a vapory huddling of prodigious
shapes."
A woman is coming along the road,—young, very swarthy, very tall, and
barefooted, and black-robed: she wears a high white turban with dark stripes,
and a white foulard is thrown about her fine shoulders; she bears no burden, and
walks very swiftly and noiselessly.... Soundless as shadow the motion of all these
naked-footed people is. On any quiet mountain-way, full of curves, where you
fancy yourself alone, you may often be startled by something you feel, rather
than hear, behind you,—surd steps, the springy movement of a long lithe body,
dumb oscillations of raiment;—and ere you can turn to look, the haunter swiftly
passes with creole greeting of "bonjou'" or "bonsouè, Missié." This sudden
"becoming aware" in broad daylight of a living presence unseen is even more
disquieting than that sensation which, in absolute darkness, makes one halt all
breathlessly before great solid objects, whose proximity has been revealed by
some mute blind emanation of force alone. But it is very seldom, indeed, that the
negro or half-breed is thus surprised: he seems to divine an advent by some
specialized sense,—like an animal,—and to become conscious of a look directed
upon him from any distance or from behind any covert;—to pass within the range
of his keen vision unnoticed is almost impossible.... And the approach of this
woman has been already observed by the habitants of the ajoupas;—dark faces
peer out from windows and door-ways;—one half-nude laborer even strolls out to
the road-side under the sun to watch her coming. He looks a moment, turns to
the hut again, and calls:—
—"Ou-ou! Fafa!"
—"Êti! Gabou!"
—"Vini ti bouin!—mi bel négresse!"
Out rushes Fafa, with his huge straw hat in his hand: "Oti, Gabou?"
—"Mi!"
—"Ah! quimbé moin!" cries black Fafa, enthusiastically; "fouinq! li bel!—Jésis-
Maïa! li doux!"... Neither ever saw that woman before; and both feel as if they
could watch her forever.
There is something superb in the port of a tall young mountain-griffone, or
negress, who is comely and knows that she is comely: it is a black poem of
artless dignity, primitive grace, savage exultation of movement.... "Ou marché
tête enlai cornu couresse qui ka passé lariviè" (You walk with, your head in the
air, like the couresse-serpent swimming a river) is a creole comparison which
pictures perfectly the poise of her neck and chin. And in her walk there is also a
serpentine elegance, a sinuous charm: the shoulders do not swing; the cambered
torso seems immobile;—but alternately from waist to heel, and from heel to
waist, with each long full stride, an indescribable undulation seems to pass; while
the folds of her loose robe oscillate to right and left behind her, in perfect
libration, with the free swaying of the hips. With us, only a finely trained dancer
could attempt such a walk;—with the Martinique woman of color it is natural as
the tint of her skin; and this allurement of motion unrestrained is most marked in
those who have never worn shoes and are clad lightly as the women of antiquity,
—in two very thin and simple garments;—chemise and robe-d'indienne.... But
whence is she?—of what canton? Not from Vauclin, nor from Lamentin, nor from
Marigot,—from Case-Pilote or from Case-Navire: Fafa knows all the people there.
Never of Sainte-Anne, nor of Sainte-Luce, nor of Sainte-Marie, nor of Diamant,
nor of Gros-Morne, nor of Carbet,—the birthplace of Gabou. Neither is she of the
village of the Abysms, which is in the Parish of the Preacher,—nor yet of Ducos
nor of François, which are in the Commune of the Holy Ghost....
 V

... She approaches the ajoupa: both men remove their big straw hats; and both
salute her with a simultaneous "Bonjou', Manzell."
—"Bonjou', Missié," she responds, in a sonorous alto, without appearing to notice
Gabou,—but smiling upon Fafa as she passes, with her great eyes turned full
upon his face.... All the libertine blood of the man flames under that look;—he
feels as if momentarily wrapped in a blaze of black lightning.
—"Ça ka fai moin pè," exclaims Gabou, turning his face towards the ajoupa.
Something indefinable in the gaze of the stranger has terrified him.
—"Pa ka fai moin pè—fouinq!" (She does not make me afraid) laughs Fafa, boldly
following her with a smiling swagger.
—"Fafa!" cries Gabou, in alarm. "Fafa, pa ça!"
But Fafa does not heed. The strange woman has slackened her pace, as if
inviting pursuit;—another moment and he is at her side.
—"Oti ou ka rété, chè?" he demands, with the boldness of one who knows
himself a fine specimen of his race.
—"Zaffai cabritt pa zaffai lapin," she answers, mockingly.
—"Mais pouki ou rhabillé toutt noué conm ça."
—"Moin pòté deil pou name moin mò."
—"Ale ya yaïe!... Non, voué!—ça ou kallé atouèlement?"
—"Lanmou pàti: moin pàti delé lanmou."
—"Ho!—ou ni guêpe, anh?"
—"Zanoli bail yon bal; épi maboya rentré ladans."
—"Di moin oti ou kallé, doudoux?"
—"Jouq lariviè Lezà."
—"Fouinq!—ni plis passé trente kilomett!"
—"Eh ben?—ess ou 'lè vini épi moin?"[16]
And as she puts the question she stands still and gazes at him;—her voice is no
longer mocking: it has taken another tone,—a tone soft as the long golden note
of the little brown bird they call the siffleur-de-montagne, the mountain-
whistler.... Yet Fafa hesitates. He hears the clear clang of the plantation bell
recalling him to duty;—he sees far down the road—(Ouill! how fast they have
been walking!)—a white and black speck in the sun: Gabou, uttering through his
joined hollowed hands, as through a horn, the ouklé, the rally call. For an instant
he thinks of the overseer's anger,—of the distance,—of the white road glaring in
the dead heat: then he looks again into the black eyes of the strange woman,
and answers:
—"Oui;—moin ké vini épi ou."
With a burst of mischievous laughter, in which Fafa joins, she walks on,—Fafa
striding at her side.... And Gabou, far off, watches them go,—and wonders that,
for the first time since ever they worked together, his comrade failed to answer
his ouklé.
—"Coument yo ka crié ou, chè?" asks Fafa, curious to know her name.
—"Châché nom moin ou-menm, duviné."
But Fafa never was a good guesser,—never could guess the simplest of tim-tim.
—"Ess Cendrine?"
—"Non, çé pa ça."
—"Ess Vitaline?"
—"Non, çé pa ça."
—"Ess Aza?"
—"Non, çé pa ça."
—"Ess Nini?"
—"Chaché encò."
—"Ess Tité?"
—"Ou pa save,—tant pis pou ou!"
—"Ess Youma?"
—"Pouki ou 'lè save nom moin?—ça ou ké fai épi y?"
—"Ess Yaiya?"
—"Non, çé pa y."
—"Ess Maiyotte?"
—"Non! ou pa ké janmain trouvé y!"
—"Ess Sounoune?—ess Loulouze?"
She does not answer, but quickens her pace and begins to sing,—not as the half-
breed, but as the African sings,—commencing with a low long weird intonation
that suddenly breaks into fractions of notes inexpressible, then rising all at once
to a liquid purling bird-tone, and descending as abruptly again to the first deep
quavering strain:—
"À tè—
moin ka dòmi toute longue;
Yon paillasse sé fai moin bien,
Doudoux!
À tè—
moin ka dòmi toute longue;
Yon robe biésé sé fai moin bien,
Doudoux!
À tè—
moin ka dòmi toute longue;
Dè jolis foulà sé fai moin bien,
Doudoux!
À tè—
moin ka dòmi toute longue;
Yon joli madras sé fai moin bien,
Doudoux!
À tè—
moin ka dòmi toute longue:
Çé à tè..."
... Obliged from the first to lengthen his stride in order to keep up with her, Fafa
has found his utmost powers of walking overtaxed, and has been left behind.
Already his thin attire is saturated with sweat; his breathing is almost a panting;
—yet the black bronze of his companion's skin shows no moisture; her rhythmic
step, her silent respiration, reveal no effort: she laughs at his desperate straining
to remain by her side.
—"Marché toujou' deïé moin,—anh, chè?—marché toujou' deïé!"...
And the involuntary laggard—utterly bewitched by the supple allurement of her
motion, by the black flame of her gaze, by the savage melody of her chant—
wonders more and more who she may be, while she waits for him with her
mocking smile.
But Gabou—who has been following and watching from afar off, and sounding his
fruitless ouklé betimes—suddenly starts, halts, turns, and hurries back, fearfully
crossing himself at every step.
He has seen the sign by which She is known....

[16]—"Where dost stay, dear?"

—"Affaire of the goat are not affaire of the rabbit."
—"But why art thou dressed all in black thus?"
—"I wear mourning for my dead soul."
—"Aïe ya yaïe!... No, true!... where art thou going now?"
—"Love is gone: I go after love."
—"Ho! thou hast a Wasp [lover]—eh?"
—"The zanoli gives a ball; the maboya enters unasked."
—"Tell me where thou art going, sweetheart?"
—"As far as the River of the Lizard."
—"Fouinq!—there are more than thirty kilometres!"
—"What of that?—do t thou want to come with me?"

VI

... None ever saw her by night. Her hour is the fulness of the sun's flood-tide:
she comes in the dead hush and white flame of windless noons,—when colors
appear to take a very unearthliness of intensity,—when even the flash of some
colibri, bosomed with living fire, shooting hither and thither among the grenadilla
blossoms, seemeth a spectral happening because of the great green trance of the
land....
Mostly she haunts the mountain roads, winding from plantation to plantation,
from hamlet to hamlet,—sometimes dominating huge sweeps of azure sea,
sometimes shadowed by mornes deep-wooded to the sky. But close to the great
towns she sometimes walks: she has been seen at mid-day upon the highway
which overlooks the Cemetery of the Anchorage, behind the cathedral of St.
Pierre.... A black Woman, simply clad, of lofty stature and strange beauty, silently
standing in the light, keeping her eyes fixed upon the Sun!...

VII

Day wanes. The further western altitudes shift their pearline gray to deep blue
where the sky is yellowing up behind them; and in the darkening hollows of
nearer mornes strange shadows gather with the changing of the light—dead
indigoes, fuliginous purples, rubifications as of scoriæ,—ancient volcanic colors
momentarily resurrected by the illusive haze of evening. And the fallow of the
canes takes a faint warm ruddy tinge. On certain far high slopes, as the sun
lowers, they look like thin golden hairs against the glow,—blond down upon the
skin of the living hills.
Still the Woman and her follower walk together,—chatting loudly, laughing,
chanting snatches of song betimes. And now the valley is well behind them;—
they climb the steep road crossing the eastern peaks,—through woods that seem
to stifle under burdening of creepers. The shadow of the Woman and the shadow
of the man,—broadening from their feet,—lengthening prodigiously,—sometimes,
mixing, fill all the way; sometimes, at a turn, rise up to climb the trees. Huge
masses of frondage, catching the failing light, take strange fiery color;—the sun's
rim almost touches one violet hump in the western procession of volcanic
silhouettes....

Sunset, in the tropics, is vaster than sunrise.... The dawn, upflaming swiftly from
the sea, has no heralding erubescence, no awful blossoming—as in the North: its
fairest hues are fawn-colors, dove-tints, and yellows,—pale yellows as of old dead
gold, in horizon and flood. But after the mighty heat of day has charged all the
blue air with translucent vapor, colors become strangely changed, magnified,
transcendentalized when the sun falls once more below the verge of visibility.
Nearly an hour before his death, his light begins to turn tint; and all the horizon
yellows to the color of a lemon. Then this hue deepens, through tones of
magnificence unspeakable, into orange; and the sea becomes lilac. Orange is the
light of the world for a little space; and as the orb sinks, the indigo darkness
comes—not descending, but rising, as if from the ground—all within a few
minutes. And during those brief minutes peaks and mornes, purpling into richest
velvety blackness, appear outlined against passions of fire that rise half-way to
the zenith,—enormous furies of vermilion.

... The Woman all at once leaves the main road,—begins to mount a steep
narrow path leading up from it through the woods upon the left. But Fafa
hesitates,—halts a moment to look back. He sees the sun's huge orange face sink
down,—sees the weird procession of the peaks vesture themselves in blackness
funereal,—sees the burning behind them crimson into awfulness; and a vague
fear comes upon him as he looks again up the darkling path to the left. Whither
is she now going?
—"Oti ou kallé là?" he cries.
—"Mais conm ça!—chimin tala plis cou't,—coument?"
It may be the shortest route, indeed;—but then, the fer-de-lance!...
—"Ni sèpent ciya,—en pile."
No: there is not a single one, she avers; she has taken that path too often not to
know:
—"Pa ni sèpent piess! Moin ni coutime passé là;—pa ni piess!"
... She leads the way.... Behind them the tremendous glow deepens;—before
them the gloom. Enormous gnarled forms of ceiba, balata, acoma, stand dimly
revealed as they pass; masses of viny drooping things take, by the failing light, a
sanguine tone. For a little while Fafa can plainly discern the figure of the Woman
before him;—then, as the path zigzags into shadow, he can descry only the white
turban and the white foulard;—and then the boughs meet overhead: he can see
her no more, and calls to her in alarm:—
—"Oti ou?—moin pa pè ouè arien!"
Forked pending ends of creepers trail cold across his face. Huge fire-flies sparkle
by,—like atoms of kindled charcoal thudding, blown by a wind.
—"Içitt!—quimbé lanmain-moin!"...
How cold the hand that guides him!... She walks swiftly, surely, as one knowing
the path by heart. It zigzags once more; and the incandescent color flames again
between the trees;—the high vaulting of foliage fissures overhead, revealing the
first stars. A cabritt-bois begins its chant. They reach the summit of the morne
under the clear sky.
The wood is below their feet now; the path curves on eastward between a long
swaying of ferns sable in the gloom,—as between a waving of prodigious black
feathers. Through the further purpling, loftier altitudes dimly loom; and from
some viewless depth, a dull vast rushing sound rises into the night.... Is it the
speech of hurrying waters, or only some tempest of insect voices from those
ravines in which the night begins?...
Her face is in the darkness as she stands;—Fafa's eyes are turned to the iron-
crimson of the western sky. He still holds her hand, fondles it,—murmurs
something to her in undertones.
—"Ess ou ainmein moin conm ça?" she asks, almost in a whisper.
Oh! yes, yes, yes!... more than any living being he loves her!... How much? Ever
so much,—gouôs conm caze!... Yet she seems to doubt him,—repeating her
question over and over:
—"Ess ou ainmein moin?"
And all the while,—gently, caressingly, imperceptibly,—she draws him a little
nearer to the side of the path, nearer to the black waving of the ferns, nearer to
the great dull rushing sound that rises from beyond them:
—"Ess ou ainmein moin?"
—"Oui, oui!" he responds,—"ou save ça!—oui, chè doudoux, ou save ça!"...
And she, suddenly,—turning at once to him and to the last red light, the goblin
horror of her face transformed,—shrieks with a burst of hideous laughter:
—"Atò, bô!"[17]
For the fraction of a moment he knows her name:—then, smitten to the brain
with the sight of her, reels, recoils, and, backward falling, crashes two thousand
feet down to his death upon the rocks of a mountain torrent.

[17]"Kiss me now!"

LA VÉRETTE

—St. Pierre, 1887.

One returning from the country to the city in the Carnival season is lucky to find
any comfortable rooms for rent. I have been happy to secure one even in a
 rather retired street,—so steep that it is really dangerous to sneeze
while descending it, lest one lose one's balance and tumble right across
the town. It is not a fashionable street, the Rue du Morne Mirait; but,
after all, there is no particularly fashionable street in this extraordinary
city, and the poorer the neighborhood, the better one's chance to see
something of its human nature.
One consolation is that I have Manm-Robert for a next-door neighbor,
who keeps the best bouts in town (those long thin Martinique cigars of
which a stranger soon becomes fond), and who can relate more queer
stories and legends of old times in the island than anybody else I know
of. Manm-Robert is yon màchonne lapacotte, a dealer in such cheap
articles of food as the poor live upon: fruits and tropical vegetables,
manioc-flour, "macadam" (a singular dish of rice stewed with salt fish—
diri épi coubouyon lamori), akras, etc.; but her bouts probably bring her
the largest profit—they are all bought up by the békés. Manm-Robert is
also a sort of doctor: whenever any one in the neighborhood falls sick
she is sent for, and always comes, and very often cures,—as she is skilled in the
knowledge and use of medical herbs, which she gathers herself upon the
mornes. But for these services she never accepts any remuneration: she is a sort
of Mother of the poor in her immediate vicinity. She helps everybody, listens to
everybody's troubles, gives everybody some sort of consolation, trusts everybody,
and sees a great deal of the thankless side of human nature without seeming to
feel any the worse for it. Poor as she must really be, she appears to have
everything that everybody wants; and will lend anything to her neighbors except
a scissors or a broom, which it is thought bad-luck to lend. And, finally, if
anybody is afraid of being bewitched (guimboisé) Manm-Robert can furnish him
or her with something that will keep the bewitchment away....

II

February 15th.
... Ash-Wednesday. The last masquerade will appear this afternoon,
notwithstanding; for the Carnival lasts in Martinique a day longer than elsewhere.
All through the country districts since the first week of January there have been
wild festivities every Sunday—dancing on the public highways to the pattering of
tamtams,—African dancing, too, such as is never seen in St. Pierre. In the city,
however, there has been less merriment than in previous years;—the natural
gaiety of the population has been visibly affected by the advent of a terrible and
unfamiliar visitor to the island,—La Vérette: she came by steamer from Colon.
... It was in September. Only two cases had been reported when every
neighboring British colony quarantined against Martinique. Then other West
Indian colonies did likewise. Only two cases of small-pox. "But there may be two
thousand in another month," answered the governors and the consuls to many
indignant protests. Among West Indian populations the malady has a signification
unknown in Europe or the United States: it means an exterminating plague.
Two months later the little capital of Fort-de-France was swept by the pestilence
as by a wind of death. Then the evil began to spread. It entered St. Pierre in
December, about Christmas time. Last week 173 cases were reported; and a
serious epidemic is almost certain. There were only 8500 inhabitants in Fort-de-
France; there are 28,000 in the three quarters of St. Pierre proper, not including
her suburbs; and there is no saying what ravages the disease may make here.

III

... Three o'clock, hot and clear.... In the distance there is a heavy sound of
drums, always drawing nearer: tam!—tam!—tamtamtam! The Grande Rue is
lined with expectant multitudes; and its tiny square,—the Batterie d'Esnotz,—
thronged with békés.—Tam!—tam!—tamtamtam!... In our own street the people
are beginning to gather at door-ways, and peer out of windows,—prepared to
descend to the main thoroughfare at the first glimpse of the procession.
—"Oti masque-à?" Where are the maskers?
It is little Mimi's voice: she is speaking for two besides herself, both quite as
anxious as she to know where the maskers are,—Maurice, her little fair-haired
and blue-eyed brother, three years old; and Gabrielle, her child-sister, aged four,
—two years her junior.
Every day I have been observing the three, playing in the door-way of the house
across the street. Mimi, with her brilliant white skin, black hair, and laughing
black eyes, is the prettiest,—though all are unusually pretty children. Were it not
for the fact that their mother's beautiful brown hair is usually covered with a
violet foulard, you would certainly believe them white as any children in the
world. Now there are children whom every one knows to be white, living not very
far from here, but in a much more silent street, and in a rich house full of
servants,—children who resemble these as one fleur-d'amour blossom resembles
another;—there is actually another Mimi (though she is not so called at home) so
like this Mimi that you could not possibly tell one from the other,—except by their
dress. And yet the most unhappy experience of the Mimi who wears white satin
slippers was certainly that punishment given her for having been once caught
playing in the street with this Mimi, who wears no shoes at all. What mischance
could have brought them thus together?—and the worst of it was they had fallen
in love with each other at first sight!... It was not because the other Mimi must
not talk to nice little colored girls, or that this one may not play with white
children of her own age: it was because there are cases.... It was not because
the other children I speak of are prettier or sweeter or more intelligent than
these now playing before me;—or because the finest microscopist in the world
could or could not detect any imaginable race difference between those delicate
satin skins. It was only because human nature has little changed since the day
that Hagar knew the hate of Sarah, and the thing was grievous in Abraham's
sight because of his son....
... The father of these children loved them very much: he had provided a home
for them,—a house in the Quarter of the Fort, with an allowance of two hundred
francs monthly; and he died in the belief their future was secured. But relatives
fought the will with large means and shrewd lawyers, and won!... Yzore, the
mother, found herself homeless and penniless, with three children to care for. But
she was brave;—she abandoned the costume of the upper class forever, put on
the douilette and the foulard,—the attire that is a confession of race,—and went
to work. She is still comely, and so white that she seems only to be
masquerading in that violet head-dress and long loose robe....
—"Vini ouè!—vini ouè!" cry the children to one another,—"come and see!" The
drums are drawing near;—everybody is running to the Grande Rue....

IV

Tam!—tam!—tamtamtam! ... The spectacle is interesting from the Batterie

d'Esnotz. High up the Rue Peysette,—up all the precipitous streets that ascend
the mornes,—a far gathering of showy color appears: the massing of maskers in
rose and blue and sulphur-yellow attire.... Then what a degringolade begins!—
what a tumbling, leaping, cascading of color as the troupes descend.
Simultaneously from north and south, from the Mouillage and the Fort, two
immense bands enter the Grande Rue;—the great dancing societies these,—the
Sans-souci and the Intrépides. They are rivals; they are the composers and
singers of those Carnival songs,—cruel satires most often, of which the local
meaning is unintelligible to those unacquainted with the incident inspiring the
improvisation,—of which the words are too often coarse or obscene,—whose
burdens will be caught up and re-echoed through all the burghs of the island.
Vile as may be the motive, the satire, the malice, these chants are preserved for
generations by the singular beauty of the airs; and the victim of a Carnival song
need never hope that his failing or his wrong will be forgotten: it will be sung of
long after he is in his grave.
... Ten minutes more, and the entire length of the street is thronged with a
shouting, shrieking, laughing, gesticulating host of maskers. Thicker and thicker
the press becomes;—the drums are silent: all are waiting for the signal of the
general dance. Jests and practical jokes are being everywhere perpetrated; there
is a vast hubbub, made up of screams, cries, chattering, laughter. Here and there
snatches of Carnival song are being sung:—"Cambronne, Cambronne;" or "Ti
fenm-là doux, li doux, li doux!"... "Sweeter than sirup the little woman is";—this
burden will be remembered when the rest of the song passes out of fashion.
Brown hands reach out from the crowd of masks, pulling the beards and patting
the faces of white spectators.... "Main connaitt! ou, chè!—moin connaitt ou,
doudoux! ba moin ti d'mi franc!" It is well to refuse the half-franc,—though you
do not know what these maskers might take a notion to do to-day.... Then all the
great drums suddenly boom together; all the bands strike up; the mad medley
kaleidoscopes into some sort of order; and the immense processional dance
begins. Prom the Mouillage to the Fort there is but one continuous torrent of
sound and color: you are dazed by the tossing of peaked caps, the waving of
hands, and twinkling of feet;—and all this passes with a huge swing,—a regular
swaying to right and left.... It will take at least an hour for all to pass; and it is an
hour well worth passing. Band after band whirls by; the musicians all garbed as
women or as monks in canary-colored habits;—before them the dancers are
dancing backward, with a motion as of skaters; behind them all leap and wave
hands as in pursuit. Most of the bands are playing creole airs,—but that of the
Sans-souci strikes up the melody of the latest French song in vogue,—Petits
amoureux aux plumes ("Little feathered lovers"[18]). Everybody now seems to
know this song by heart; you hear children only five or six years old singing it:
there are pretty lines in it, although two out of its four stanzas are commonplace
enough, and it is certainly the air rather than the words which accounts for its
sudden popularity.

[18] "Petits amoureux aux plumes,

Enfants d'un brillant séjour
Vous ignorez l'amertume,
Vous parlez souvent d'amour:...
Vous méprisez la dorure,
Les salons, et les bijoux;
 Vous chérissez la Nature,
Petits oiseaux, becquetez-vous!

"Voyez là bas, dans cette église,

Auprès d'un confessional,
Le prêtre, qui veut faire croire à Lise,
Qu'un baiser est un grand mal;—
Pour prouver à la mignonne
Qu'un baiser bien fait, bien doux,
N'a jamais damné personne
Petits oiseaux, becquetez-vous!"
[Translation.]
Little feathered lovers, cooing,
Children of the radiant air,
Sweet your speech,—the speech of wooing;
Ye have ne'er a grief to bear!
Gilded ease and jewelled fashion
Never own a charm for you;
Ye love Nature's truth with passion.
Pretty birdlings, bill and coo!

See that priest who, Lise confessing,

Wants to make the girl believe
That a kiss without a blessing
Is a fault for which to grieve!
Now to prove, to his vexation,
That no tender kiss and true
Ever caused a soul's damnation,
Pretty birdlings, bill and coo!

... Extraordinary things are happening in the streets through which the
procession passes. Pest-smitten women rise from their beds to costume
themselves,—to mask face already made unrecognizable by the hideous malady,
—and stagger out to join the dancers.... They do this in the Rue Longchamps, in
the Rue St. Jean-de-Dieu, in the Rue Peysette, in the Rue de Petit Versailles. And
in the Rue Ste.-Marthe there are three young girls sick with the disease, who
hear the blowing of the horns and the pattering of feet and clapping of hands in
chorus;—they get up to look through the slats of their windows on the
masquerade,—and the creole passion of the dance comes upon them. "Ah!" cries
one,—"nou ké amieusé nou!—c'est zaffai si nou mò!" [We will have our fill of fun:
what matter if we die after!] And all mask, and join the rout, and dance down to
the Savane, and over the river bridge into the high streets of the Fort, carrying
contagion with them!... No extraordinary example, this: the ranks of the dancers
hold many and many a verrettier.

VI

... The costumes are rather disappointing,—though the mummery has some
general characteristics that are not unpicturesque;—for example, the
predominance of crimson and canary-yellow in choice of color, and a marked
predilection for pointed hoods and high-peaked head-dresses. Mock religious
costumes also form a striking element in the general tone of the display,—
Franciscan, Dominion, or Penitent habits,—usually crimson or yellow, rarely sky-
blue. There are no historical costumes, few eccentricities or monsters: only a few
"vampire-bat" head-dresses abruptly break the effect of the peaked caps and the
hoods.... Still there are some decidedly local ideas in dress which deserve notice,
—the congo, the bébé (or ti-manmaille), the ti nègue gouos-sirop ("little
molasses-negro"); and the diablesse.
The congo is merely the exact reproduction of the dress worn by workers on the
plantations. For the women, a gray calico shirt and coarse petticoat of percaline;
with two coarse handkerchiefs (mouchoirs fatas), one for her neck, and one for
the head, over which is worn a monstrous straw hat;—she walks either barefoot
or shod with rude native sandals, and she carries a hoe. For the man the
costume consists of a gray shirt of rough material, blue canvas pantaloons, a
large mouchoir fatas to tie around his waist, and a chapeau Bacoué,—an
enormous hat of Martinique palm-straw. He walks barefooted and carries a
cutlass.
The sight of a troupe of young girls en bébé, in baby-dress, is really pretty. This
costume comprises only a loose embroidered chemise, laoe-edged pantalettes,
and a child's cap; the whole being decorated with bright ribbons of various
colors. As the dress is short and leaves much of the lower limbs exposed, there is
ample opportunity for display of tinted stockings and elegant slippers.
The "molasses-negro" wears nothing but a cloth around his loins;—his whole
body and face being smeared with an atrocious mixture of soot and molasses. He
is supposed to represent the original African ancestor.
The devilesses (diablesses)are few in number; for it requires a very tall woman to
play deviless. These are robed all in black, with a white turban and white foulard;
they wear black masks. They also carry boms (large tin cans), which they allow
to fall upon the pavement from time to time; and they walk barefoot.... The
deviless (in true Bitaco idiom, "guiablesse") represents a singular Martinique
superstition. It is said that sometimes at noonday a beautiful negress passes
silently through some isolated plantation,—smiling at the workers in the cane-
fields,—tempting men to follow her. But he who follows her never comes back
again; and when a field hand mysteriously disappears, his fellows say, "Y té ka
ouè la Guiablesse!"... The tallest among the devilesses always walks first,
chanting the question, "Jou ouvè?" (Is it yet daybreak?) And all the others reply
in chorus, "Jou pa'ncò ouvè." (It is not yet day.)
—The masks worn by the multitude include very few grotesques: as a rule, they
are simply white wire masks, having the form of an oval and regular human face;
—and they disguise the wearer absolutely, although they can be seen through
perfectly well from within. It struck me at once that this peculiar type of wire
mask gave an indescribable tone of ghostliness to the whole exhibition. It is not
in the least comical; it is neither comely nor ugly; it is colorless as mist,—
expressionless, void, dead;—it lies on the face like a vapor, like a cloud,—creating
the idea of a spectral vacuity behind it....

VII

... Now comes the band of the Intrépides, playing the bouèné. It is a dance
melody,—also the name of a mode of dancing, peculiar and unrestrained;—the
dancers advance and retreat face to face; they hug each other, press together,
and separate to embrace again. A very old dance, this,—of African origin;
perhaps the same of which Père Labat wrote in 1722:—
—"It is not modest. Nevertheless, it has not failed to become so popular with the
Spanish Creoles of America, and so much in vogue among them, that it now
forms the chief of their amusements, and that it enters even into their devotions.
They dance it even in their Churches, and in their Processions; and the Nuns
seldom fail to dance it Christmas Night, upon a stage erected in their Choir and
immediately in front of their iron grating, which is left open, so that the People
may share in the joy manifested by these good souls for the birth of the Saviour."
[19]...

[19]... "Cette danse est opposée à la pudeur. Avec tout cela, elle ne laisse pas d'être tellement du
goût des Espagnols Créolles de l'Amérique, & si fort en usage parmi eux, qu'elle fait la meilleure
partie de leurs divertissements, & qu'elle entre même dans leurs devotions. Ils la dansent même
dans leurs Églises & à leurs processions; et les Religieuses ne manquent guère de la danser la
Nuit de Noël, sur un théâtre élevé dans leur Chœur, vis-à-vis de leur grille, qui est ouverte, afin
que le Peuple ait sa part dans la joye que ces bonnes âmes témoignent pour la naissance du
Sauveur."

VIII

... Every year, on the last day of the Carnival, a droll ceremony used to take place
called the "Burial of the Bois-bois,"—the bois-bois being a dummy, a guy,
caricaturing the most unpopular thing in city life or in politics. This bois-bois,
after having been paraded with mock solemnity through all the ways of St.
Pierre, was either interred or "drowned,"—flung into the sea.... And yesterday the
dancing societies had announced their intention to bury a bois-bois laverette,—a
manikin that was to represent the plague. But this bois-bois does not make its
appearance. La Vérette is too terrible a visitor to be made fun of, my friends;—
you will not laugh at her, because you dare not....
No: there is one who has the courage,—a yellow goblin crying from behind his
wire mask, in imitation of the màchannes: "Ça qui 'lè quatòze graines laverette
pou yon sou?" (Who wants to buy fourteen verette-spots for a sou?)
Not a single laugh follows that jest.... And just one week from to-day, poor
mocking goblin, you will have a great many more than quatorze graines, which
will not cost you even a sou, and which will disguise you infinitely better than the
mask you now wear;—and they will pour quick-lime over you, ere ever they let
you pass through this street again—in a seven franc coffin!...

IX

And the multicolored clamoring stream rushes by,—swerves off at last through
the Rue des Ursulines to the Savane,—rolls over the new bridge of the Roxelane
to the ancient quarter of the Fort.
All of a sudden there is a hush, a halt;—the drums stop beating, the songs cease.
Then I see a sudden scattering of goblins and demons and devilesses in all
directions: they run into houses, up alleys,—hide behind door-ways. And the
crowd parts; and straight through it, walking very quickly, conies a priest in his
vestments, preceded by an acolyte who rings a little bell. C'est Bon-Dié ka passé!
("It is the Good-God who goes by!") The father is bearing the "viaticum" to some
victim of the pestilence: one must not appear masked as a devil or a deviless in
the presence of the Bon-Dié.
He goes by. The flood of maskers recloses behind the ominous passage;—the
drums boom again; the dance recommences; and all the fantastic mummery
ebbs swiftly out of sight.

Night falls;—the maskers crowd to the ball-rooms to dance strange tropical

measures that will become wilder and wilder as the hours pass. And through the
black streets, the Devil makes his last Carnival-round.
By the gleam of the old-fashioned oil lamps hung across the thoroughfares I can
make out a few details of his costume. He is clad in red, wears a hideous blood-
colored mask, and a cap of which the four sides are formed by four looking-
glasses;—the whole head-dress being surmounted by a red lantern. He has a
white wig made of horse-hair, to make him look weird and old,—since the Devil is
older than the world! Down the street he comes, leaping nearly his own height,—
chanting words without human signification,—and followed by some three
hundred boys, who form the chorus to his chant—all clapping hands together and
giving tongue with a simultaneity that testifies how strongly the sense of rhythm
enters into the natural musical feeling of the African,—a feeling powerful enough
to impose itself upon, all Spanish-America, and there create the unmistakable
characteristics of all that is called "creole music."
—"Bimbolo!"
—"Zimabolo!"
—"Bimbolo!"
—"Zimabolo!"
—"Et zimbolo!"
—"Et bolo-po!"
—sing the Devil and his chorus. His chant is cavernous, abysmal,—booms from
his chest like the sound of a drum beaten in the bottom of a well.... Ti maillelà,
baill moin lavoix! ("Give me voice, little folk,—give me voice!") And all chant after
him, in a chanting like the rushing of many waters, and with triple clapping of
hands:—"Ti marmaille-là, baill moin lavoix!"... Then he halts before a dwelling in
the Rue Peysette, and thunders:—
—"Eh! Marie-sans-dent!—mi! diabe-là derhò!"
That is evidently a piece of spite-work: there is somebody living there against
whom he has a grudge.... "Hey! Marie-without-teeth! look! the Devil is outside!"
And the chorus catch the clue.
DEVIL.—"Eh! Marie-sans-dent!"...
CHORUS.—"Marie-sans-dent! mi!—diabe-là derhò!"
D.—"Eh! Marie-sans-dent!"...
C.—"Marie-sans-dent! mi!—diabe-là derhò!"
D.—"Eh! Marie-sans-dent!"... etc.
The Devil at last descends to the main street, always singing the same song;—I
follow the chorus to the Savanna, where the rout makes for the new bridge over
the Roxelane, to mount the high streets of the old quarter of the Fort; and the
chant changes as they cross over:—
DEVIL.—"Oti ouè diabe-là passé lariviè?" (Where did you see the Devil going over
the river?) And all the boys repeat the words, falling into another rhythm with
perfect regularity and ease:—"Oti ouè diabe-là passé lariviè?"
DEVIL.—"Oti ouè diabe?"...
CHORUS.—"Oti ouè diabe-là passé lariviè?"
D.—"Oti ouè diabe?"
C.—"Oti ouè diabe-là passé lariviè?"
D.—"Oti ouè diabe?"... etc.

About midnight the return of the Devil and his following arouses me from sleep:
—all are chanting a new refrain, "The Devil and the zombis sleep anywhere and
everywhere!" (Diabe épi zombi ka dòmi tout-pàtout.) The voices of the boys are
still clear, shrill, fresh,—clear as a chant of frogs;—they still clap hands with a
precision of rhythm that is simply wonderful,—making each time a sound almost
exactly like the bursting of a heavy wave:—
DEVIL.—"Diabe épi zombi."...
CHORUS.—"Diabe épi zombi ka dàmi tout-pàtout!"
D.—"Diabe épi zombi."...
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