 ©2015 by Dr. John F. Loase, Concordia College, New York  Textbook, 505 pages 
PREFACE
PHILOSOPHY
Statistical Modeling with SPSS is the result of over twenty years of teaching Elementary
and Intermediate Statistics on the undergraduate level and Advanced Statistics and Mathematical
Modeling at the graduate level.
This text has been used to prepare students for the International Contest in Mathematical
Modeling and for minicourses for college and university faculty interested in innovating
mathematical modeling programs.
Statistical Modeling with SPSS was sponsored by the National Science Foundation. A
distinguished advisory council and team of editors assisted with concepts and editorial
suggestions throughout the book's development. They will be acknowledged at the conclusion of
the preface.
PREREQUISITES
Statistical Modeling with SPSS is written as a senior level/graduate level text for
mathematics, statistics, computer science or engineering majors. It reviews elementary statistics
in Chapter One. The rest of the text assumes that the student has completed three semesters of
Calculus, CalculusBased Probability and Statistics, and at least one course in computer
programing.
The text has been used to train students for the International Contest in Mathematical
Modeling. In its early development, this book was focused on graduate level mathematical modeling (with a statistical focus) and for advanced mathematics students preparing for the
contest in modeling.
TECHNOLOGY
Statistical Modeling with SPSS makes extensive use of SPSS to test student initiated
hypotheses from a set of real data included with the test. The data set is the result of coding the
104 responses (variables) of 542 undergraduates at Concordia College NY and Iona College to
the Marketing and Sigfluence Survey, included in Appendix A.
For students who need more extensive review of elementary statistics, an extensive TI83
based Primer is included in Appendix B.
ORGANIZATION
Chapter One Selected Topics from Elementary Statistics
A review of hypothesis testing, confidence intervals, correlation, and single variable and
multiple regression analysis. An extensive review of these topics is included in Appendix B, for
the interested student, geared to the TI83 calculator.
At the conclusion of Chapter One, the student can immediately test hypotheses and
perform multiple regression analyses with the enclosed set of data. Step by step instructions on
the proper use of SPSS for testing hypotheses and performing regression analysis are featured in
the book.
Chapter Two Selected Topics from CalculusBased Statistics and Probability
A review of the essential topics from Calculus Based Probability and Statistics that form
the foundation of Statistical Modeling.
Chapter Three  Input Probability Distributions
Goodness of fit tests using the Poisson, normal, uniform, and exponential density
functions.
The chapter concludes with SPSS exercises to test the included data set for exponential,
normal, m1d uniform density functions.
Chapter Four Rm1dom Number Generators
Linear congruential number theory and current research in irrational numbers as sources
of rm1dom numbers.
Chapter Five  Generating Random Variables
The inverse transform method with discrete and continuous modeling exm11ples.
A current research approach, validating multiple regression results with a statistical
model, is presented together with myriad research possibilities for the student in Appendix F.
Chapter Six Application from Linear Algebra
An applied problem from Linear Algebra solved using elementary matrix operations.
Chapter Seven  Two Modeling Exercises
Chapter Eight Two Problems and Outstanding Solutions from the International Contest in
Mathematical Modeling
Two outstanding papers are reprinted with permission of COMAP.
SPSS
One of the principal features of this book is the opportunity for students to use SPSS to
analyze a 50 variable by 542 row (respondent matrix). The student should take the Marketing
and Sigfluence Survey early in the course and then explore new insights into our college
students' beliefs about money and meaning. It took two years for my two graduate students,
Teresa Osadnik and Grace Dickson, to enter the 104 responses for each of the 542
undergraduates who completed the survey. For the next year we deleted variables as a result of
data mining and correlational methods and arrived at the 50 variable data set.
The 50 variables were all mapped to the interval (0, 1) to further explore graphical and
subtle relationships. A 50 variable set has virtually unlimited potential for statistical insights.
For example, there are 50 C 5 = 2, 118,760 combinations of five variables we could isolate
for multiple regression.
SIGFLUENCE
My doctorate was the first awarded in Mathematics (emphasis Statistics) and Psychology
(Measurement, Research and Evaluation in Psychology and Education) from Columbia
University Teachers College. In 1984 I invented the new word "sigfluence" to define significant,
longterm, positive influence. My 8111 book, The Sigjluence Generation: Our Young People's
Potential to Transform America, is free for you to download from my website sigfluence.com. It
took over 20 years of Statistical Modeling to discover that our 1825 year olds reported
dramatically high potential and need to effect sigfluence. As the book develops, you can use the
data set to discover "Golden Nuggets" of significant relationships. For example, it took 18
months for my wonderful graduate students Teresa Osadnik and Grace Dickson to enter the data.
Then in one afternoon, I was able to peruse 10,000 correlations that over time led to the exciting
discovery that our young people can positively transform the world if we Baby Boomers serve as
mentors and guides.
Statistical Modeling is foundational to recognizing and remedying real world problems.
Without Statistical Modeling we rely on appearance and convenience, forever spinning our
wheels in futile attempts at making the world a better place.
ACKNOWLEDGMENTS
Thanks are due Dr. Henry Ricardo (CUNY) and Professor Rowan Lindley (SUNY), who
edited the test and to Professor Joyce McQuade, who completed the Solution Set. Professor
Louis Rolando (SUNY) served as my mentor, department chair, and valued colleague for
eighteen years.
I am especially grateful to Dr. Catherine Ricardo (Chair Graduate Computer Science at
Iona College), who offered me my first course in graduate Mathematical Modeling in 1988. We
are very thankful for the leadership furthering mathematical modeling and the award of our
National Science Foundation grant (19921996). Our distinguished advisory council provided
encouragement, invaluable suggestions, and were partners in our minicourses and lectures,
which were outgrowths of the NSF grant.
Also, special recognition and deep gratitude is due Mrs. Barbara Boyce for her
painstaking attention to detail and consistent loyalty for three decades of typing and editing of
this, our eleventh book.
Front Matter
TABLE OF CONTENTS
Chapter 1  Selected Topics from Elementary Statistics
Hypothesis testing, confidence intervals, regression and
correlation. Using SPSS to analyze large data set.
Chapter 2 Selected Topics from CalculusBased Statistics and Probability
Random variables, density functions, distribution functions.
Chapter 3  Input Probability Distributions
Goodness of fit tests, Poisson, normal, uniform density
functions. Using SPSS to test data for goodness of fit to key
density functions.
Chapter 4  Random Number Generators
Linear congruential generators, empirical tests.
Chapter 5  Generating Random Variables
Inverse transform, uniform, exponential densities. Statistical
modeling examples with SPSS.
Chapter 6  Application from Linear Algebra
A current applied problem in modeling.
Chapter 7  Two Modeling Exercises
Two detailed problems which are practical applications of
mathematical modeling.
Chapter 8  Two Exemplary Student Solutions from the International Contest in
Mathematical Modeling
Two solutions are reprinted with permission granted by COMAP.
Appendix A Marketing and Sigfluence Survey
Appendix B  TI83 Based Primer on Basic Statistics
Appendix C  Future Research Direction  The Triad
Solutions to the Odd Exercises Chapters 15
Support Software:
SanDisk SecureAccess 2.0
IBM SPSS Statistics Desktop
