Foundations and Applications of Statistics
eBook - PDF

Foundations and Applications of Statistics

An Introduction Using $\mathsf {R}$, Second Edition

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Foundations and Applications of Statistics

An Introduction Using $\mathsf {R}$, Second Edition

About this book

Foundations and Applications of Statistics simultaneously emphasizes both the foundational and the computational aspects of modern statistics. Engaging and accessible, this book is useful to undergraduate students with a wide range of backgrounds and career goals.The exposition immediately begins with statistics, presenting concepts and results from probability along the way. Hypothesis testing is introduced very early, and the motivation for several probability distributions comes from p-value computations. Pruim develops the students' practical statistical reasoning through explicit examples and through numerical and graphical summaries of data that allow intuitive inferences before introducing the formal machinery. The topics have been selected to reflect the current practice in statistics, where computation is an indispensible tool. In this vein, the statistical computing environment $\mathsf{R}$ is used throughout the text and is integral to the exposition. Attention is paid to developing students' mathematical and computational skills as well as their statistical reasoning. Linear models, such as regression and ANOVA, are treated with explicit reference to the underlying linear algebra, which is motivated geometrically.Foundations and Applications of Statistics discusses both the mathematical theory underlying statistics and practical applications that make it a powerful tool across disciplines. The book contains ample material for a two-semester course in undergraduate probability and statistics. A one-semester course based on the book will cover hypothesis testing and confidence intervals for the most common situations.In the second edition, the $\mathsf{R}$ code has been updated throughout to take advantage of new $\mathsf{R}$ packages and to illustrate better coding style. New sections have been added covering bootstrap methods, multinomial and multivariate normal distributions, the delta method, numerical methods for Bayesian inference, and nonlinear least squares. Also, the use of matrix algebra has been expanded, but remains optional, providing instructors with more options regarding the amount of linear algebra required.

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1.2.
Graphical
and
Numerical
Summaries
Data
11
Figure
1.3.
A
default
histogram
produced
with
gf_histogram
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and
three
histograms
with
user-defined
bins.
Figure
1.2
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that
part
of
the
variation
in
sepal
length
is
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with
the
differences
in
species.
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generally
shorter,
virginica
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and
versicolor
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The
right-hand
plot
in
Figure
1.5
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created
using
histogram04
gf_histogram
(
~
Sepal.Length
|
Species
~
.,
data
=
iris,
bins
=
15
)
0
10
20
3
0
4
6
8
10
S
ep
a
l.Length
count
0.0
0.1
0.2
0.
3
0.4
4
6
8
10
S
ep
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l.Length
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ity
Figure
1.4.
Count
and
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unequal
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because
it
distorts
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view
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the
data.

Table of contents

  1. Cover
  2. Title page
  3. Contents
  4. Preface to the Second Edition
  5. Preface to the First Edition
  6. What Is Statistics?
  7. Chapter 1. Data
  8. Chapter 2. Probability and Random Variables
  9. Chapter 3. Continuous Distributions
  10. Chapter 4. Parameter Estimation and Testing
  11. Chapter 5. Likelihood
  12. Chapter 6. Introduction to Linear Models
  13. Chapter 7. More Linear Models
  14. Appendix A. A Brief Introduction to R
  15. Appendix B. Some Mathematical Preliminaries
  16. Appendix C. Geometry and Linear Algebra Review
  17. Hints, Answers, and Solutions to Selected Exercises
  18. Bibliography
  19. Index to R Functions, Packages, and Data Sets
  20. Index
  21. Back Cover