Table Of ContentSTATIST ICAL
A N A L Y S I S
A Computer
Oriented
Approach
A. A. AFIFI
UNIVERSITY OF CALIFORNIA, LOS ANGELES
S. P. AZEN
UNIVERSITY OF SOUTHERN CALIFORNIA, LOS ANGELES
A C A D E M I C PRESS New York and London
C O P Y R I G H T © 1972, B Y A C A D E M I C P R E S S , I N C .
ALL RIGHTS RESERVED
N O PART O F THIS BOOK M A Y B E REPRODUCED IN A N Y F O R M ,
BY PHOTOSTAT, M I C R O F I L M , RETRIEVAL S Y S T E M , OR A N Y
OTHER M E A N S , W I T H O U T W R I T T E N P E R M I S S I O N F R O M
T H E PUBLISHERS.
A C A D E M I C P R E S S , I N C .
I l l Fifth Avenue, New York, New York 10003
United Kingdom Edition published by
A C A D E M I C P R E S S , I N C . ( L O N D O N ) L T D .
24/28 Oval Road, London NW1
LIBRARY O F C O N G R E S S CATALOG C A R D N U M B E R : 70-182654
PR I N T E D IN T H E U N I T E D STATES O F AMERICA
To our
MOTHERS : Nazira Afifi — Shirley Azen
W I V E S : Beverly Afifi — Coleen Azen
C H I L D R E N : Lolita, Osama, and Mostafa Afifi
and prospective Azens
PREFACE
When a prospective reader picks up a statistics book he usually asks the questions :
(1) What is the level of this book? (2) What are its contents? (3) Why is it
different from the many available statistics books? and (4) What are its uses?
The answers to these questions are as follows:
1. Level of this book. This book is written for readers with one elementary
course in the fundamentals of statistical inference and no previous training in
computer applications or programming. Appendix I serves as a review of the
principles of statistical inference and Chapter 1 introduces the reader to the
computer terminology and techniques used throughout the book. The minimum
required level of mathematics is college algebra. Although we discuss concepts
requiring mathematical sophistication beyond college algebra, such concepts
are immediately "translated" into their operational meaning and usage. In
addition, the book includes starred sections in which greater detail is given for
the mathematically advanced reader.
2. Content of the book. This book contains both elementary and advanced
topics. The reader will find a review of the probabilistic foundations of statistics
and the standard statistical inference procedures. In addition, regression and
correlation analysis, as well as the analysis of variance and multivariate analysis
are explained. To cover such a wide range of material, we have eliminated
mathematical derivations and computational formulas and concentrated on the
essentials—the applications and interpretations of the statistical tools.
3. Uniqueness of the book, (a) It assumes that computations are performed
on a digital computer. This enables us to eliminate the boring computational
details usually found in standard texts. It also enables us to discuss techniques
such as stepwise regression and stepwise discriminant analysis, which heretofore
have been accessible only on an advanced mathematical level.
xi
xii P R E F A C E
(b) Many complicated topics are explained in words as well as in equations.
Examples from actual research assist in motivating the concepts.
(c) We show how simple programs can be used for complicated analysis.
For example, we show how simple linear regression may be performed using a
packaged descriptive program.
(d) We demonstrate how a packaged program can be used for data analysis,
for example, transforming variables to induce normality, examining residuals to
verify the assumptions of the model, and so forth.
(e) We illustrate original uses for packaged programs. For example, we
demonstrate how a factorial analysis of variance program may be used to analyze
a Latin square design. We also show how a descriptive program may be used to
test for the linearity of the regression model.
(f) Interspersed throughout the text are comments which highlight im
portant supplementary information.
4. Uses of book. This book will serve as a reference book on statistics for
researchers, particularly those with access to packaged computer programs.
Since manuals accompanying these packaged programs usually describe only the
mechanics of the programs, that is, how to set up the input in order to obtain the
prescribed output, this book serves as a supplement to such manuals.
As a textbook this book could be used for a variety of courses. The following
diagrams give four different courses at various levels:
Course 1 Elementary Applied Statistical Analysis
(1 semester, undergraduate)
Appendix I
Chapter 1
Chapter 2
Course 2 Applied Statistical Analysis
(1 year, first-year graduate)
Appendix I
Chapter 1
Chapter 2
or
PREFACE xiii
Course 3 Applied Multivariate Analysis
(1 semester, second year graduate)
Chapter 1
and
Sections 3.2-3.4 I Chapter 5
Course 4 Intensive Course in Data Analysis
(1 week, 8 hours per day)
Chapter 1
and
Sections Sections Section Sections
2.4-2.5 3.1,3.3 4.6 5.3-5.5
The numbering system of the book is as follows: Sections follow sequentially
within a chapter; subsections, equations, comments, figures and tables follow
sequentially within a section. Thus,
Section i.j means section j of Chapter i
Section i.j.k means subsection k of Section i.j
Equation i.j.k means equation k of Section i.j
Table i.j.k means table k of Section i.j
Figure i.j.k means figure k of Section i.j
Comments i.j.k means comments k of Section i.j
In the text
Comment i.j.k.h means comment h within Comments i.j.k.
Finally, as mentioned earlier, Comments identified by * are accessible only to the
more mathematically advanced reader and may be skipped without loss of
meaning.
A C K N O W L E D G M E N T S
We wish to give our special thanks to our students Takamura Ashikaga, Anthony
Auriemma, Stuart Beal, Charles Breverman, Ikbal Fahmy, Thomas Farver,
Ronald Huss, Vinnie Liu, George Meier, Susan Sacks, and Girma Wolde-Tsadik
for their comments, criticisms, and assistance in performing many of the com
putations in the book. We also thank Shirley Azen and Colleen Gillen Azen for
their editorial and technical assistance.
We are indebted to Professor Richard Bellman of the University of Southern
California for his interest, encouragement, and advice in the inception and
completion of this book. Thanks also to Virginia Zoitl and Leona Povandra
whose administrative talents were indispensible in "getting it together."
Our appreciation goes to the marvelous typists who miraculously translated
our scrawls into real words—Ann Eiseman, Betty Horvath, Kay Isleib, Georgia
Lum, Jean Roth, Kathy Scofield, and Shari Wilcox.
Most of the data used in examples in the book was obtained from Afifi's
association with the Shock Research Unit of the University of Southern Cali
fornia. Much of the insight into the data discussed in the book was chiefly due
to our discussion and work with Doctors Max H. Weil and Herbert Shubin of
the Shock Unit. To them we owe a special measure of gratitude.
In addition, we would like to thank Norm Palley and David Erbeck of the
same unit for valuable discussion of the data processing parts of the book, and
to Professor Virginia Clark of the University of California, Los Angeles, for
other valuable discussions.
The data for Example 1.4.2 and for many problems in the text was obtained
from the Los Angeles County Heart Study with the kind permission of Dr. John
XV
xvi A C K N O W L E D G M E N T S
Chapman and Mrs. Anne H. Coulson of the University of California, Los
Angeles.
We are indebted to the Literary Executor of the late Sir Ronald A. Fisher,
F.R.S., to Dr. Frank Yates, F.R.S., and to Oliver and Boyd, Edinburgh, for
permission to reprint Table III from their book "Statistical Tables for Biological,
Agricultural and Medical Research."
We also wish to thank the staff and reviewers of Academic Press for their
assistance, editorial remarks, etc.
Computing assistance was obtained from the Health Science's Computing
Facility, UCLA, sponsored by N I H Special Research Resources Grant RR-3.
The work was done with partial support from National Institutes of Health
Grant No. G M 16197-03, the United States Public Health Service research
grants HE05570 and G M 16462 from the National Heart Institute, and grant
HS00238 from the National Center for Health Services Research and Develop
ment.
A PARTIAL LIST
OF C O M M O N L Y USED N O T A T I O N S
The following is a list of the symbols introduced in Appendix I.
Symbol Description Section
bn(i,p) binomial distribution 1.2.1
cdf cumulative distribution function 1.1.4
E(X) expected value of a random variable X 1.1.5
f(x) density of a continuous random variable X 1.1.4
F(x) cumulative distribution function of a random variable X 1.1.4
v v
^ X i 9 i) F distribution with vl and v2 degres of fredom 1.2.8
Fq/l00(vi ,v2) qth percentile of the F distribution with v{ and v 2 de
gres of fredom 1.2.8
Gesund practicing physician 1.1.1
H0 nul hypothesis 1.5
Hx alternative hypothesis 1.5
N(0,1) standard normal distribution 1.2.5
2
Ν(μ,σ ) normal distribution 1.2.5
Ν ( μ , Σ ) multivariate normal distribution 1.6.3
F F value 1.5.2
ρ (χ) probability function of a discrete random variable X 1.1.4
Pr(E) probability of the event Ε 1.1.3
xvii
xviii A P A R T I A L L I S T O F C O M M O N L Y U S E D N O T A T I O N S
Symbol Description Section
s sample standard deviation 1.4.2
2
s sample variance 1.4.2
t(v) Student's t distribution with ν degres of fredom 1.2.7
v
*<z/ioo( ) tfth percentile of the Student's t distribution with ν de
gres of fredom 1.2.7
U(a,b) uniform distribution on la, b~] 1.2.3
V(X) variance of a random variable X 1.1.5
w individual or experimental unit in population 1.1.1
W population or universe 1.1.1
χ realization, observation or measurement 1.1.2
X random variable 1.1.2
p x 1
X random vector [.6.1
pXm
X random matrix 1.6.1
χ sample mean 1.4.2
χ sample mean vector 1.6.2
z q / l 0 0 qth percentile of N(0,1) distribution 1.2.6
α significance level 1.5
1 — a confidence level 1.5
β probability of type I eror 1.5
μ population mean 1.1.5
μ population mean vector 1.6.3
ν degres of fredom 1.2.6
π power 1.5
σ population standard deviation 1.1.5
2
σ population variance 1.1.5
Gij covariance betwen X{ and Xj 1.6.2
Σ covariance matrix 1.6.3
Θ parameter 1.4.2
Θ estimate of parameter Θ 1.4.2
Φ(ζ) cdforJV(0,1) 1.2.5
φ (ζ) frequency curve for N(0,1) 1.2.5
2
χ (ν) chi square distribution with ν degres of fredom 1.2.6
v tn
Xq/ioo ( ) <7 percentile of the chi square distribution with ν de
gres of fredom 1.2.6
