4. Using R for Introductory Statistics

The cost of statistical computing software has precluded many universities from installing these valuable computational and analytical tools. R, a powerful open-source software package, was created in response to this issue. It has enjoyed explosive growth since its introduction, owing to its coherence, flexibility, and free availability. While it is a valuable tool for students who are first learning statistics, proper introductory materials are needed for its adoption.

Using R for Introductory Statistics fills this gap in the literature, making the software accessible to the introductory student. The author presents a self-contained treatment of statistical topics and the intricacies of the R software. The pacing is such that students are able to master data manipulation and exploration before diving into more advanced statistical concepts. The book treats exploratory data analysis with more attention than is typical, includes a chapter on simulation, and provides a unified approach to linear models.

This text lays the foundation for further study and development in statistics using R. Appendices cover installation, graphical user interfaces, and teaching with R, as well as information on writing functions and producing graphics.

Chapters include:

• Univariate Data
• Bivariate Data
• Multivariate Data
• Random Data
• Simulations
• Exploratory Data Analysis
• Confidence Interval Estimation
• Hypothesis Testing
• Two-sample tests
• Chi Square Tests
• Regression Analysis
• Multiple Linear Regression
• Analysis of Variance
  

This is an ideal text for integrating the study of statistics with a powerful computational tool.

5. An Introduction to R

This tutorial manual provides a comprehensive introduction to R, a software package for statistical computing and graphics.

R supports a wide range of statistical techniques and is easily extensible via user-defined functions. One of R's strengths is the ease with which publication-quality plots can be produced in a wide variety of formats.

Chapters explore:

• Simple manipulations; numbers and vectors
• Objects, their modes and attributes
• Ordered and unordered functions
• Arrays and matrices
• Lists and data frames
• Reading data from files
• Probability distributions
• Grouping, loops and conditional execution
• Writing your own functions
• Statistical models in R
• Graphical procedures
• Packages
  

6. Practical Regression and Anova in R

Practical Regression and Anova in R is an intermediate text on the practice of regression and analysis of variance. The objective is to learn what methods are available and more importantly, when they should be applied. The book is not an introduction to R.

Chapters cover:

• Estimation
• Inference
• Errors in Predictors
• Generalized Least Squares
• Testing for Lack of Fit
• Diagnostics
• Transformation
• Scale Changes, Principal Components and Collinearity
• Variable Selection
• Statistical Strategy and Model Uncertainty
• Chicago Insurance Redlining - a complete example
• Robust and Registant Regression
• Missing Data
• Analysis of Covariance
• ANOVA
  

7. Introduction to Statistical Thinking (With R, Without Calculus)

Introduction to Statistical Thinking is targeted at college students who are required to learn statistics, students with little background in mathematics and often no motivation to learn more. This book uses the basic structure of generic introduction to statistics course.

Chapters cover:

• Short introduction to statistics and probability
• Data structures and variation
• Provides numerical and graphical tools for presenting and summarizing the distribution of data
• Fundamentals of probability: Concept of a random variable, Examples of special types of random variables, Normal random variable, Sampling distribution and presents the Central Limit Theorem and the Law of Large Numbers
• Discussion of statistical inference. It provides an overview of the topics that are presented in the subsequent chapter.
• Basic tools of statistical inference, namely point estimation, estimation with a confidence interval, and the testing of statistical hypothesis
• Discusses inference that involve the comparison of two measurements
• Analysis of two case studies
  

Large portions of this book are based on material from the online book "Collaborative Statistics" by Barbara Illowsky and Susan Dean.

The content of this book is licensed under the conditions of the Creative Commons Attribution License (CC-BY 3.0).

8. Multivariate Statistics with R

The objective of Multivariate Statistics with R is to cover a basic core of multivariate material in such a way that the core mathematical principles are covered, and to provide access to current applications and developments.

The author notes that numerous multivariate statistics books, but this book emphasises the applications (and introduces contemporary applications) with a little more mathematical detail than happens in many such "application/software" based books.

Chapters cover:

• Multivariate data including graphical and dynamic graphical methods (Chernoff's Faces, scatterplots, 3d scatterplots, and other methods), animated exploration
• Matrix manipulation: Vectors, Matrices, Crossproduct matrix, Matrix inversion, Eigen values and eigen vectors, Singular Value Decomposition, Extended Cauchy-Schwarz Inequality, and Partitioning
• Measures of distance: Mahalanobis Distance, Definitions, Distance between points, Quantitative variables - Interval scaled, Distance between variables, Quantitative variables: Ratio Scaled, Dichotomous data, Qualitative variables, Different variables, Properties of proximity matrices
• Cluster analysis: Introduction to agglomerative hierarchical cluster analysis, Cophenetic Correlation, Divisive hierarchical clustering, K-means clustering, K-centroids
• Multidimensional scaling: Metric Scaling, Visualising multivariate distance, Assessing the quality of fit
• Multivariate normality: Exceptations and moments of continuous random functions, Multivariate normality (including R estimation), Transformations
• Inference for the mean: Two sample Hotellin's T2 test, Constant Density Ellipses, Multivariate Analysis of Variance
• Discriminant analysis: Fisher discrimination, Accuracy of discrimination, Importance of variables in discrimination, Canonical discriminant functions, Linear discrimation
• Principal component analysis: Derivation of Principal Components, Some properties of principal components, Ilustration of Principal Components, Principal Components Regression, "Model" criticism for principal components analysis, Sphericity, How many components to retain, Intrepreting the principal components
• Canonical Correlation: Canonical variates, Interpretation, Computer example
• Factor analysis: Role of factor analysis, The factor analysis model, Principal component extraction, Maximum likelihood solutions, Rotation, Factor scoring
  

The content in this book is licensed under a Gnu Free Documentation Licence.

9. A Little Book of R for Biomedical Statistics

Little Book of R for Biomedical Statistics is a simple introduction to biomedical statistics using the R statistics software.

This booklet tells you how to use the R software to carry out some simple analyses that are common in biomedical statistics. In particular, the focus is on cohort and case-control studies that aim to test whether particular factors are associated with disease, randomised trials, and meta-analysis.

This booklet assumes that the reader has some basic knowledge of biomedical statistics, and the principal focus of the booklet is not to explain biomedical statistics analyses, but rather to explain how to carry out these analyses using R.

The booklet examines:

• Calculating Relative Risks for a Cohort Study
• Calculating Odds Ratios for a Cohort or Case-Control Study
• Testing for an Association Between Disease and Exposure, in a Cohort or Case-Control Study
• Calculating the (Mantel-Haenszel) Odds Ratio when there is a Stratifying Variable
• Testing for an Association Between Exposure and Disease in a Matched Case-Control Study
• Dose-response analysis
• Calculating the Sample Size Required for a Randomised Control Trial
• Calculating the Power of a Randomised Control Trial
• Making a Forest Plot for a Meta-analysis of Several Different Randomised Control Trials
  

The content in this book is licensed under a Creative Commons Attribution 3.0 License.

The author has written two other open source booklets about using R for time series analysis and for multivariate analysis. They can be viewed at alittle-book-of-r-for-time-series.readthedocs.org/ and littlebook-of-r-for-multivariate-analysis.readthedocs.org/ respectively.