R Companion to Elementary Applied Statistics

The R Companion to Elementary Applied Statistics includes traditional applications covered in elementary statistics courses as well as some additional methods that address questions that might arise during or after the application of commonly used methods. Beginning with basic tasks and computations with R, readers are then guided through ways to bring data into R, manipulate the data as needed, perform common statistical computations and elementary exploratory data analysis tasks, prepare customized graphics, and take advantage of R for a wide range of methods that find use in many elementary applications of statistics. Features: Requires no familiarity with R or programming to begin using this book. Can be used as a resource for a project-based elementary applied statistics course, or for researchers and professionals who wish to delve more deeply into R. Contains an extensive array of examples that illustrate ideas on various ways to use pre-packaged routines, as well as on developing individualized code. Presents quite a few methods that may be considered non-traditional, or advanced. Includes accompanying carefully documented script files that contain code for all examples presented, and more. R is a powerful and free product that is gaining popularity across the scientific community in both the professional and academic arenas. Statistical methods discussed in this book are used to introduce the fundamentals of using R functions and provide ideas for developing further skills in writing R code. These ideas are illustrated through an extensive collection of examples. About the Author: Christopher Hay-Jahans received his Doctor of Arts in mathematics from Idaho State University in 1999. After spending three years at University of South Dakota, he moved to Juneau, Alaska, in 2002 where he has taught a wide range of undergraduate courses at University of Alaska Southeast.

Preliminaries First Steps Running Code in R Some Terminology Hierarchy of Data Classes Data Structures Operators Functions R Packages Probability Distributions Coding Conventions Some Book-keeping and Other Tips Getting Quick Coding Help Bringing Data Into and Out of R Entering Data Through Coding Number and Sample Generating Tricks The R Data Editor Reading Text Files Reading Data from Other File Formats Reading Data from the Keyboard Saving and Exporting Data Accessing Contents of Data Structures Extracting Data from Vectors Conducting Data Searches in Vectors Working with Factors Navigating Data Frames Lists Choosing an Access/Extraction Method Additional Notes More About the attach Function About Functions and their Arguments Alternative Argument Assignments in Function Calls Altering and Manipulating Data Altering Entries in Vectors Transformations Manipulating Character Strings Sorting Vectors and Factors Altering Data Frames Sorting Data Frames Moving Between Lists and Data Frames Additional Notes on the merge Function Summaries and Statistics Univariate Frequency Distributions Bivariate Frequency Distributions Statistics for Univariate Samples Measures of Central Tendency Measures of Spread Measures of Position Measures of Shape Five-Number Summaries and Outliers Elementary Five-Number Summary Tukey’s Five-Number The boxplotstats Function More on Computing with R Computing with Numeric Vectors Working with Lists, Data Frames and Arrays The sapply Function The tapply Function The by Function The aggregate Function The apply Function The sweep Function For-loops Conditional Statements and the switch Function The if-then Statement The if-then-else Statement The switch Function Preparing Your Own Functions Basic Charts for Categorical Data Preliminary Comments Bar Charts Dot Charts Pie Charts Exporting Graphics Images Additional Notes Customizing Plotting Windows The plotnew and plotwindow Functions More on the paste Function The title Function More on the legend Function More on the mtext Function The text Function Basic Plots for Numeric Data Histograms Boxplots Stripcharts QQ-Plots Normal Probability QQ-Plots Interpreting Normal Probability QQ-Plots More on Reference Lines for QQ-Plots QQ-Plots for Other Distributions Additional Notes More on the ifelse Function Revisiting the axis Function Frequency Polygons and Ogives Scatterplots, Lines, and Curves Scatterplots Basic Plots Manipulating Plotting Characters Plotting Transformed Data Matrix Scatterplots The matplot Function Graphs of Lines Graphs of Curves Superimposing Multiple Lines and/or Curves Time-series Plots More Graphics Tools Partitioning Graphics Windows The layout Function The splitscreen Function Customizing Plotted Text and Symbols Inserting Mathematical Annotation in Plots More Low-level Graphics Functions The points and symbols Functions The grid, segments and arrows Functions Boxes, Rectangles and Polygons Error Bars Computing Bounds for Error Bars The errorBarplot Function Purpose and Interpretation of Error Bars More R Graphics Resources Tests for One and Two Proportions Relevant Probability Distributions Binomial Distributions Hypergeometric Distributions Normal Distributions Chi-square Distributions Single Population Proportions Estimating a Population Proportion Hypotheses for Single Proportion Tests A Normal Approximation Test A Chi-square Test An Exact Test Which Approach Should be Used? Two Population Proportions Estimating Differences Between Proportions Hypotheses for Two Proportions Tests A Normal Approximation Test A Chi-square Test Fisher’s Exact Test Which Approach Should be Used? Additional Notes Normal Approximations of Binomial Distributions One- versus Two-sided Hypothesis Tests Tests for More than Two Proportions Equality of Three or More Proportions Pearson’s Homogeneity of Proportions Test Marascuilo’s Large Sample Procedure Cohen’s Small Sample Procedure Simultaneous Pairwise Comparisons Marascuilo’s Large Sample Procedure Cohen’s Small Sample Procedure Linear Contrasts of Proportions Marascuilo’s Large Sample Approach Cohen’s Small Sample Approach The Chi-square Goodness-of-Fit Test Tests of Variances and Spread Relevant Probability Distributions F Distributions Using a Sample to Assess Normality Single Population Variances Estimating a Variance Testing a Variance Exactly Two Population Variances Estimating the Ratio of Two Variances Testing the Ratio of Two Variances What if the Normality Assumption is Violated? Two or More Population Variances Assessing Spread Graphically Levene’s Test Levene’s Test with Trimmed Means Brown-Forsythe Test Fligner-Killeen Test Tests for One or Two Means Student’s t-Distribution Single Population Means Verifying the Normality Assumption Estimating a Mean Testing a Mean Can a Normal Approximation be Used Here? Exactly Two Population Means Verifying Assumptions The Test for Dependent Samples Tests for Independent Samples Tests for More than Two Means Relevant Probability Distributions Studentized Range Distribution Dunnett’s Test Distribution Studentized Maximum Modulus Distribution Setting the Stage Equality of Means — Equal Variances Case Pairwise Comparisons — Equal Variances Bonferroni’s Procedure Tukey’s Procedure t Tests and Comparisons with a Control Dunnett’s Test and Comparisons with a Control Which Procedure to Choose Equality of Means — Unequal Variances Case Large-sample Chi-square Test Welch’s F Test Hotelling’s T Test Pairwise Comparisons — Unequal Variances Large-sample Chi-square Test Dunnett’s C Procedure Dunnett’s T Procedure Comparisons with a Control Which Procedure to Choose The Nature of Differences Found All Possible Pairwise Comparisons Comparisons with a Control Selected Tests for Medians, and More Relevant Probability Distributions Distribution of the Signed Rank Statistic Distribution of the Rank Sum Statistic The One-sample Sign Test The Exact Test The Normal Approximation Paired Samples Sign Test Independent Samples Median Test Equality of Medians Pairwise Comparisons of Medians Single Sample Signed Rank Test The Exact Test The Normal Approximation Paired Samples Signed Rank Test Rank Sum Test of Medians The Exact Mann-Whitney Test The Normal Approximation The Wilcoxon Rank Sum Test Using the Kruskal-Wallis Test to Test Medians Working with Ordinal Data Paired Samples Independent Samples More than Two Independent Samples Some Comments on the Use of Ordinal Data Dependence and Independence Assessing Bivariate Normality Pearson’s Correlation Coefficient An Interval Estimate of ? Testing the Significance of ? Testing a Null Hypothesis with ? ? Kendall’s Correlation Coefficient An Interval Estimate of t Exact Test of the Significance of t Approximate Test of the Significance of t Spearman’s Rank Correlation Coefficient Exact Test of the Significance of ?S Approximate Test of the Significance ?S Correlations in General — Comments and Cautions Chi-square Test of Independence For the Curious — Distributions of rK and rS

Christopher Hay-Jahans received his Doctor of Arts in mathematics from Idaho State University in 1999. After spending three years at University of South Dakota, he moved to Juneau, Alaska, in 2002 where he has taught a wide range of undergraduate courses at University of Alaska Southeast.