R Companion to Elementary Applied Statistics: 1st Edition (Paperback) book cover

R Companion to Elementary Applied Statistics

1st Edition

By Christopher Hay-Jahans

Chapman and Hall/CRC

358 pages | 80 B/W Illus.

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Description

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.

 

Table of Contents

  1. Preliminaries
  2. 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

  3. Bringing Data Into and Out of R
  4. 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

  5. Accessing Contents of Data Structures
  6. 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

  7. Altering and Manipulating Data
  8. 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

  9. Summaries and Statistics
  10. 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

  11. More on Computing with R
  12. 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

  13. Basic Charts for Categorical Data
  14. 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

  15. Basic Plots for Numeric Data
  16. 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

  17. Scatterplots, Lines, and Curves
  18. 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

  19. More Graphics Tools
  20. 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

  21. Tests for One and Two Proportions
  22. 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

  23. Tests for More than Two Proportions
  24. 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

  25. Tests of Variances and Spread
  26. 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

  27. Tests for One or Two Means
  28. 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

  29. Tests for More than Two Means
  30. 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

  31. Selected Tests for Medians, and More
  32. 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

  33. Dependence and Independence

Assessing Bivariate Normality

Pearson’s Correlation Coefficient

An Interval Estimate of ρ

Testing the Significance of ρ

Testing a Null Hypothesis with ρ ≠

Kendall’s Correlation Coefficient

An Interval Estimate of τ

Exact Test of the Significance of τ

Approximate Test of the Significance of τ

Spearman’s Rank Correlation Coefficient

Exact Test of the Significance of ρS

Approximate Test of the Significance ρS

Correlations in General — Comments and Cautions

Chi-square Test of Independence

For the Curious — Distributions of rK and rS

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.

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
REF000000
REFERENCE / General