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Probability and statistics with R

Material type: BookPublisher: Boca Raton CRC Press 2016Edition: 2nd ed.Description: xxxiii, 949 p.ISBN: 9781466504394.DDC classification: 519.502855133 Summary: Since the publication of the popular first edition of this comprehensive textbook, the contributed R packages on CRAN have increased from around 1,000 to over 6,000. Designed for an intermediate undergraduate course, Probability and Statistics with R, Second Edition explores how some of these new packages make analysis easier and more intuitive as well as create more visually pleasing graphs. New to the Second Edition • Improvements to existing examples, problems, concepts, data, and functions • New examples and exercises that use the most modern functions • Coverage probability of a confidence interval and model validation • Highlighted R code for calculations and graph creation Gets Students Up to Date on Practical Statistical Topics Keeping pace with today’s statistical landscape, this textbook expands your students’ knowledge of the practice of statistics. It effectively links statistical concepts with R procedures, empowering students to solve a vast array of real statistical problems with R. Web Resources A supplementary website offers solutions to odd exercises and templates for homework assignments while the data sets and R functions are available on CRAN. (https://www.crcpress.com/Probability-and-Statistics-with-R-Second-Edition/Ugarte-Militino-Arnholt/9781466504394)
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1. What Is R?

1.1. Introduction to R
1.3. Vectors
1.4. Mode and Class of an Object
1.5. Getting Help
1.6. External Editors
1.7. RStudio
1.8. Packages
1.9. R Data Structures
1.10. Reading and Saving Data in R
1.11. Working with Data
1.12. Using Logical Operators with Data Frames
1.13. Tables
1.14. Summarizing Functions
1.15. Probability Functions
1.16. Flow Control
1.17. Creating Functions
1.18. Simple Imputation
1.19. Using plot()
1.20. Coordinate Systems and Traditional Graphic’s States

2. Exploring Data

2.1. What Is Statistics?
2.2. Data
2.3. Displaying Qualitative Data
2.4. Displaying Quantitative Data
2.5. Summary Measures of Location
2.6. Summary Measures of Spread
2.7. Bivariate Data
2.8. Complex Plot Arrangements
2.9. Multivariate Data

3. General Probability and Random Variables

3.1. Introduction
3.2. Counting Techniques
3.3. Axiomatic Probability
3.4. Random Variables
3.5. Moment Generating Functions

4. Univariate Probability Distributions

4.1. Introduction
4.2. Discrete Univariate Distributions
4.3. Continuous Univariate Distributions

5. Multivariate Probability Distributions

5.1. Joint Distribution of Two Random Variables
5.2. Independent Random Variables
5.3. Several Random Variables
5.4. Conditional Distributions
5.5. Expected Values, Covariance, and Correlation
5.6. Multinomial Distribution
5.7. Bivariate Normal Distribution

6. Sampling and Sampling Distributions

6.1. Sampling
6.2. Parameters
6.3. Estimators
6.4. Sampling Distribution of the Sample Mean
6.5. Sampling Distribution for a Statistic from an Infinite Population
6.6. Sampling Distributions Associated with the Normal Distribution

7. Point Estimation

7.1. Introduction
7.2. Properties of Point Estimators
7.3. Point Estimation Techniques

8. Confidence Intervals

8.1. Introduction
8.2. Confidence Intervals for Population Means
8.3. Confidence Intervals for Population Variances
8.4. Confidence Intervals Based on Large Samples

9. Hypothesis Testing

9.1. Introduction
9.2. Type I and Type II Errors
9.3. Power Function
9.4. Uniformly Most Powerful Test
9.5. ρ-Value or Critical Level
9.6. Tests of Significance
9.7. Hypothesis Tests for Population Means
9.8. Hypothesis Tests for Population Variances
9.9. Hypothesis Tests for Population Proportions

10. Nonparametric Methods

10.1. Introduction
10.2. Sign Test
10.3. Wilcoxon Signed-Rank Test
10.4. The Wilcoxon Rank-Sum or the Mann-Whitney U-Test
10.5. The Kruskal-Wallis Test
10.6. Friedman Test for Randomized Block Designs
10.7. Goodness-of-Fit Tests
10.8. Categorical Data Analysis
10.9. Nonparametric Bootstrapping
10.10. Permutation Tests

11. Experimental Design

11.1. Introduction
11.2. Fixed Effects Model
11.3. Analysis of Variance (ANOVA) for the One-Way Fixed Effects Model
11.4. Power and the Non-Central F Distribution
11.5. Checking Assumptions
11.6. Fixing Problems
11.7. Multiple Comparisons of Means
11.8. Other Comparisons among the Means
11.9. Summary of Comparisons of Means
11.10. Random Effects Model (Variance Components Model)
11.11. Randomized Complete Block Design
11.12. Two-Factor Factorial Design

12. Regression

12.1. Introduction
12.2. Simple Linear Regression
12.3. Multiple Linear Regression
12.4. Ordinary Least Squares
12.5. Properties of the Fitted Regression Line
12.6. Using Matrix Notation with Ordinary Least Squares
12.7. The Method of Maximum Likelihood
12.8. The Sampling Distribution of β
12.9. ANOVA Approach to Regression
12.10. General Linear Hypothesis
12.11. Model Building
12.12. Model Validation
12.13. Interpreting a Logarithmically Transformed Model
12.14. Qualitative Predictors
12.15. Estimation of the Mean Response for New Values Xh
12.16. Prediction and Sampling Distribution of New Observations Yh(new)
12.17. Simultaneous Confidence Intervals

Since the publication of the popular first edition of this comprehensive textbook, the contributed R packages on CRAN have increased from around 1,000 to over 6,000. Designed for an intermediate undergraduate course, Probability and Statistics with R, Second Edition explores how some of these new packages make analysis easier and more intuitive as well as create more visually pleasing graphs.

New to the Second Edition

• Improvements to existing examples, problems, concepts, data, and functions
• New examples and exercises that use the most modern functions
• Coverage probability of a confidence interval and model validation
• Highlighted R code for calculations and graph creation

Gets Students Up to Date on Practical Statistical Topics

Keeping pace with today’s statistical landscape, this textbook expands your students’ knowledge of the practice of statistics. It effectively links statistical concepts with R procedures, empowering students to solve a vast array of real statistical problems with R.

Web Resources

A supplementary website offers solutions to odd exercises and templates for homework assignments while the data sets and R functions are available on CRAN.

(https://www.crcpress.com/Probability-and-Statistics-with-R-Second-Edition/Ugarte-Militino-Arnholt/9781466504394)

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