Foundations and applications of statistics : an introduction using R
 Author/Creator
 Pruim, Randall J.
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, c2011.
 Physical description
 xviii, 615 p. : ill. ; 27 cm.
 Series
 Pure and applied undergraduate texts ; 13.
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QA276.45 .R3 P78 2011
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QA276.45 .R3 P78 2011
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Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Machine generated contents note: ch. 1 Summarizing Data
 1.1.Data in R
 1.2.Graphical and Numerical Summaries of Univariate Data
 1.3.Graphical and Numerical Summaries of Multivariate Data
 1.4.Summary
 Exercises
 ch. 2 Probability and Random Variables
 2.1.Introduction to Probability
 2.2.Additional Probability Rules and Counting Methods
 2.3.Discrete Distributions
 2.4.Hypothesis Tests and pValues
 2.5.Mean and Variance of a Discrete Random Variable
 2.6.Joint Distributions
 2.7.Other Discrete Distributions
 2.8.Summary
 Exercises
 ch. 3 Continuous Distributions
 3.1.pdfs and cdfs
 3.2.Mean and Variance
 3.3.Higher Moments
 3.4.Other Continuous Distributions
 3.5.Kernel Density Estimation
 3.6.QuantileQuantile Plots
 3.7.Joint Distributions
 3.8.Summary
 Exercises
 ch. 4 Parameter Estimation and Testing
 4.1.Statistical Models
 4.2.Fitting Models by the Method of Moments
 4.3.Estimators and Sampling Distributions
 4.4.Limit Theorems
 4.5.Inference for the Mean (Variance Known)
 4.6.Estimating Variance
 4.7.Inference for the Mean (Variance Unknown)
 4.8.Confidence Intervals for a Proportion
 4.9.Paired Tests
 4.10.Developing New Tests
 4.11.Summary
 Exercises
 ch. 5 LikelihoodBased Statistics
 5.1.Maximum Likelihood Estimators
 5.2.Likelihood Ratio Tests
 5.3.Confidence Intervals
 5.4.Goodness of Fit Testing
 5.5.Inference for TwoWay Tables
 5.6.Rating and Ranking Based on Pairwise Comparisons
 5.7.Bayesian Inference
 5.8.Summary
 Exercises
 ch. 6 Introduction to Linear Models
 6.1.The Linear Model Framework
 6.2.Simple Linear Regression
 6.3.Inference for Simple Linear Regression
 6.4.Regression Diagnostics
 6.5.Transformations in Linear Regression
 6.6.Categorical Predictors
 6.7.Categorical Response (Logistic Regression)
 6.8.Simulating Linear Models to Check Robustness
 6.9.Summary
 Exercises
 ch. 7 More Linear Models
 7.1.Additive Models
 7.2.Assessing the Quality of a Model
 7.3.OneWay ANOVA
 7.4.TwoWay ANOVA
 7.5.Interaction and Higher Order Terms
 7.6.Model Selection
 7.7.More Examples
 7.8.Permutation Tests and Linear Models
 7.9.Summary
 Exercises
 Appendix A A Brief Introduction to R
 A.1.Getting Up and Running
 A.2.Working with Data
 A.3.Lattice Graphics in R
 A.4.Functions in R
 A.5.Some Extras in the fastR Package
 A.6.More R Topics
 Exercises
 Appendix B Some Mathematical Preliminaries
 B.1.Sets
 B.2.Functions
 B.3.Sums and Products
 Exercises
 Appendix C Geometry and Linear Algebra Review
 C.1.Vectors, Spans, and Bases
 C.2.Dot Products and Projections
 C.3.Orthonormal Bases
 C.4.Matrices
 Exercises
 Appendix D Review of Chapters 14
 D.1.R Infrastructure
 D.2.Data
 D.3.Probability Basics
 D.4.Probability Toolkit
 D.5.Inference
 D.6.Important Distributions
 Exercises.
 Publisher's Summary
 Foundations and Applications of Statistics simultaneously emphasises 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 pvalue 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 $\textsf{R}$ 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 twosemester course in undergraduate probability and statistics. A onesemester course based on the book will cover hypothesis testing and confidence intervals for the most common situations..
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2011
 Responsibility
 Randall Pruim.
 Series
 Pure and applied undergraduate texts ; v. 13
 ISBN
 9780821852330
 0821852337