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Understanding and Applying Basic Statistical Methods Using R.

By: Material type: TextTextSeries: New York Academy of Sciences SeriesPublisher: Newark : John Wiley & Sons, Incorporated, 2016Copyright date: ©2017Edition: 1st edDescription: 1 online resource (501 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781119061403
Subject(s): Genre/Form: Additional physical formats: Print version:: Understanding and Applying Basic Statistical Methods Using RDDC classification:
  • 519.50285513300003
LOC classification:
  • QA276.45.R3 .W553 2017
Online resources:
Contents:
Cover -- Title Page -- Copyright -- Contents -- List of Symbols -- Preface -- About the Companion Website -- Chapter 1 Introduction -- 1.1 Samples Versus Populations -- 1.2 Comments on Software -- 1.3 R Basics -- 1.3.1 Entering Data -- 1.3.2 Arithmetic Operations -- 1.3.3 Storage Types and Modes -- 1.3.4 Identifying and Analyzing Special Cases -- 1.4 R Packages -- 1.5 Access to Data Used in this Book -- 1.6 Accessing More Detailed Answers to the Exercises -- 1.7 Exercises -- Chapter 2 Numerical Summaries of Data -- 2.1 Summation Notation -- 2.2 Measures of Location -- 2.2.1 The Sample Mean -- 2.2.2 The Median -- 2.2.3 Sample Mean versus Sample Median -- 2.2.4 Trimmed Mean -- 2.2.5 R function mean, tmean, and median -- 2.3 Quartiles -- 2.3.1 R function idealf and summary -- 2.4 Measures of Variation -- 2.4.1 The Range -- 2.4.2 R function Range -- 2.4.3 Deviation Scores, Variance, and Standard Deviation -- 2.4.4 R Functions var and sd -- 2.4.5 The Interquartile Range -- 2.4.6 MAD and the Winsorized Variance -- 2.4.7 R Functions winvar, winsd, idealfIQR, and mad -- 2.5 Detecting Outliers -- 2.5.1 A Classic Outlier Detection Method -- 2.5.2 The Boxplot Rule -- 2.5.3 The MAD-Median Rule -- 2.5.4 R Functions outms, outbox, and out -- 2.6 Skipped Measures of Location -- 2.6.1 R Function MOM -- 2.7 Summary -- 2.8 Exercises -- Chapter 3 Plots Plus More Basics on Summarizing Data -- 3.1 Plotting Relative Frequencies -- 3.1.1 R Functions table, plot, splot, barplot, and cumsum -- 3.1.2 Computing the Mean and Variance Based on the Relative Frequencies -- 3.1.3 Some Features of the Mean and Variance -- 3.2 Histograms and Kernel Density Estimators -- 3.2.1 R Function hist -- 3.2.2 What Do Histograms Tell Us? -- 3.2.3 Populations, Samples, and Potential Concerns about Histograms -- 3.2.4 Kernel Density Estimators -- 3.2.5 R Functions Density and Akerd.
3.3 Boxplots and Stem-and-Leaf Displays -- 3.3.1 R Function stem -- 3.3.2 Boxplot -- 3.3.3 R Function boxplot -- 3.4 Summary -- 3.5 Exercises -- Chapter 4 Probability and Related Concepts -- 4.1 The Meaning of Probability -- 4.2 Probability Functions -- 4.3 Expected Values, Population Mean and Variance -- 4.3.1 Population Variance -- 4.4 Conditional Probability and Independence -- 4.4.1 Independence and Dependence -- 4.5 The Binomial Probability Function -- 4.5.1 R Functions dbinom and pbinom -- 4.6 The Normal Distribution -- 4.6.1 Some Remarks about the Normal Distribution -- 4.6.2 The Standard Normal Distribution -- 4.6.3 Computing Probabilities for Any Normal Distribution -- 4.6.4 R Functions pnorm and qnorm -- 4.7 Nonnormality and The Population Variance -- 4.7.1 Skewed Distributions -- 4.7.2 Comments on Transforming Data -- 4.8 Summary -- 4.9 Exercises -- Chapter 5 Sampling Distributions -- 5.1 Sampling Distribution of P, the Proportion of Successes -- 5.2 Sampling Distribution of the Mean Under Normality -- 5.2.1 Determining Probabilities Associated with the Sample Mean -- 5.2.2 But Typically Is Not Known. Now What? -- 5.3 Nonnormality and the Sampling Distribution of the Sample Mean -- 5.3.1 Approximating the Binomial Distribution -- 5.3.2 Approximating the Sampling Distribution of the Sample Mean: The General Case -- 5.4 Sampling Distribution of the Median and 20% Trimmed Mean -- 5.4.1 Estimating the Standard Error of the Median -- 5.4.2 R Function msmedse -- 5.4.3 Approximating the Sampling Distribution of the Sample Median -- 5.4.4 Estimating the Standard Error of a Trimmed Mean -- 5.4.5 R Function trimse -- 5.4.6 Estimating the Standard Error When Outliers Are Discarded: A Technically Unsound Approach -- 5.5 The Mean Versus the Median and 20% Trimmed Mean -- 5.6 Summary -- 5.7 Exercises -- Chapter 6 Confidence Intervals.
6.1 Confidence Interval for the Mean -- 6.1.1 Computing a Confidence Interval Given 2 -- 6.2 Confidence Intervals for the Mean Using s ( Not Known) -- 6.2.1 R Function t.test -- 6.3 A Confidence Interval for The Population Trimmed Mean -- 6.3.1 R Function trimci -- 6.4 Confidence Intervals for The Population Median -- 6.4.1 R Function msmedci -- 6.4.2 Underscoring a Basic Strategy -- 6.4.3 A Distribution-Free Confidence Interval for the Median Even When There Are Tied Values -- 6.4.4 R Function sint -- 6.5 The Impact of Nonnormality on Confidence Intervals -- 6.5.1 Student's T and Nonnormality -- 6.5.2 Nonnormality and the 20% Trimmed Mean -- 6.5.3 Nonnormality and the Median -- 6.6 Some Basic Bootstrap Methods -- 6.6.1 The Percentile Bootstrap Method -- 6.6.2 R Functions trimpb -- 6.6.3 Bootstrap-t -- 6.6.4 R Function trimcibt -- 6.7 Confidence Interval for The Probability of Success -- 6.7.1 Agresti-Coull Method -- 6.7.2 Blyth's Method -- 6.7.3 Schilling-Doi Method -- 6.7.4 R Functions acbinomci and binomLCO -- 6.8 Summary -- 6.9 Exercises -- Chapter 7 Hypothesis Testing -- 7.1 Testing Hypotheses about the Mean, Known -- 7.1.1 Details for Three Types of Hypotheses -- 7.1.2 Testing for Exact Equality and Tukey's Three-Decision Rule -- 7.1.3 p-Values -- 7.1.4 Interpreting p-Values -- 7.1.5 Confidence Intervals versus Hypothesis Testing -- 7.2 Power and Type II Errors -- 7.2.1 Power and p-Values -- 7.3 Testing Hypotheses about the mean, Not Known -- 7.3.1 R Function t.test -- 7.4 Student's T and Nonnormality -- 7.4.1 Bootstrap-t -- 7.4.2 Transforming Data -- 7.5 Testing Hypotheses about Medians -- 7.5.1 R Function msmedci and sintv2 -- 7.6 Testing Hypotheses Based on a Trimmed Mean -- 7.6.1 R Functions trimci, trimcipb, and trimcibt -- 7.7 Skipped Estimators -- 7.7.1 R Function momci -- 7.8 Summary -- 7.9 Exercises.
Chapter 8 Correlation and Regression -- 8.1 Regression Basics -- 8.1.1 Residuals and a Method for Estimating the Median of Y Given X -- 8.1.2 R function qreg and Qreg -- 8.2 Least Squares Regression -- 8.2.1 R Functions lsfit, lm, ols, plot, and abline -- 8.3 Dealing with Outliers -- 8.3.1 Outliers among the Independent Variable -- 8.3.2 Dealing with Outliers among the Dependent Variable -- 8.3.3 R Functions tsreg and tshdreg -- 8.3.4 Extrapolation Can Be Dangerous -- 8.4 Hypothesis Testing -- 8.4.1 Inferences about the Least Squares Slope and Intercept -- 8.4.2 R Functions lm, summary, and ols -- 8.4.3 Heteroscedcasticity: Some Practical Concerns and How to Address Them -- 8.4.4 R Function olshc4 -- 8.4.5 Outliers among the Dependent Variable: A Cautionary Note -- 8.4.6 Inferences Based on the Theil-Sen Estimator -- 8.4.7 R Functions regci and regplot -- 8.5 Correlation -- 8.5.1 Pearson's Correlation -- 8.5.2 Inferences about the Population Correlation, p -- 8.5.3 R Functions pcor and pcorhc4 -- 8.6 Detecting Outliers When Dealing with Two or More Variables -- 8.6.1 R Functions out and outpro -- 8.7 Measures of Association: Dealing with Outliers -- 8.7.1 Kendall's Tau -- 8.7.2 R Functions tau and tauci -- 8.7.3 Spearman's Rho -- 8.7.4 R Functions spear and spearci -- 8.7.5 Winsorized and Skipped Correlations -- 8.7.6 R Functions scor, scorci, scorciMC, wincor, and wincorci -- 8.8 Multiple Regression -- 8.8.1 Least Squares Regression -- 8.8.2 Hypothesis Testing -- 8.8.3 R Function olstest -- 8.8.4 Inferences Based on a Robust Estimator -- 8.8.5 R Function regtest -- 8.9 Dealing with Curvature -- 8.9.1 R Function lplot and rplot -- 8.10 Summary -- 8.11 Exercises -- Chapter 9 Comparing Two Independent Groups -- 9.1 Comparing Means -- 9.1.1 The Two-Sample Student's T Test -- 9.1.2 Violating Assumptions When Using Student's T.
9.1.3 Why Testing Assumptions Can Be Unsatisfactory -- 9.1.4 Interpreting Student's T When It Rejects -- 9.1.5 Dealing with Unequal Variances: Welch's Test -- 9.1.6 R Function t.test -- 9.1.7 Student's T versus Welch's Test -- 9.1.8 The Impact of Outliers When Comparing Means -- 9.2 Comparing Medians -- 9.2.1 A Method Based on the McKean-Schrader Estimator -- 9.2.2 A Percentile Bootstrap Method -- 9.2.3 R Functions msmed, medpb2, split, and fac2list -- 9.2.4 An Important Issue: The Choice of Method can Matter -- 9.3 Comparing Trimmed Means -- 9.3.1 R Functions yuen, yuenbt, and trimpb2 -- 9.3.2 Skipped Measures of Location and Deleting Outliers -- 9.3.3 R Function pb2gen -- 9.4 Tukey's Three-Decision Rule -- 9.5 Comparing Variances -- 9.5.1 R Function comvar2 -- 9.6 Rank-Based (Nonparametric) Methods -- 9.6.1 Wilcoxon-Mann-Whitney Test -- 9.6.2 R Function wmw -- 9.6.3 Handling Heteroscedasticity -- 9.6.4 R Functions cid and cidv2 -- 9.7 Measuring Effect Size -- 9.7.1 Cohen's d -- 9.7.2 Concerns about Cohen's d and How They Might Be Addressed -- 9.7.3 R Functions akp.effect, yuenv2, and med.effect -- 9.8 Plotting Data -- 9.8.1 R Functions ebarplot, ebarplot.med, g2plot, and boxplot -- 9.9 Comparing Quantiles -- 9.9.1 R Function qcomhd -- 9.10 Comparing Two Binomial Distributions -- 9.10.1 Improved Methods -- 9.10.2 R Functions twobinom and twobicipv -- 9.11 A Method for Discrete or Categorical Data -- 9.11.1 R Functions disc2com, binband, and splotg2 -- 9.12 Comparing Regression Lines -- 9.12.1 Classic ANCOVA -- 9.12.2 R Function CLASSanc -- 9.12.3 Heteroscedastic Methods for Comparing the Slopes and Intercepts -- 9.12.4 R Functions olsJ2 and ols2ci -- 9.12.5 Dealing with Outliers among the Dependent Variable -- 9.12.6 R Functions reg2ci, ancGpar, and reg2plot -- 9.12.7 A Closer Look at Comparing Nonparallel Regression Lines -- 9.12.8 R Function ancJN.
9.13 Summary.
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Cover -- Title Page -- Copyright -- Contents -- List of Symbols -- Preface -- About the Companion Website -- Chapter 1 Introduction -- 1.1 Samples Versus Populations -- 1.2 Comments on Software -- 1.3 R Basics -- 1.3.1 Entering Data -- 1.3.2 Arithmetic Operations -- 1.3.3 Storage Types and Modes -- 1.3.4 Identifying and Analyzing Special Cases -- 1.4 R Packages -- 1.5 Access to Data Used in this Book -- 1.6 Accessing More Detailed Answers to the Exercises -- 1.7 Exercises -- Chapter 2 Numerical Summaries of Data -- 2.1 Summation Notation -- 2.2 Measures of Location -- 2.2.1 The Sample Mean -- 2.2.2 The Median -- 2.2.3 Sample Mean versus Sample Median -- 2.2.4 Trimmed Mean -- 2.2.5 R function mean, tmean, and median -- 2.3 Quartiles -- 2.3.1 R function idealf and summary -- 2.4 Measures of Variation -- 2.4.1 The Range -- 2.4.2 R function Range -- 2.4.3 Deviation Scores, Variance, and Standard Deviation -- 2.4.4 R Functions var and sd -- 2.4.5 The Interquartile Range -- 2.4.6 MAD and the Winsorized Variance -- 2.4.7 R Functions winvar, winsd, idealfIQR, and mad -- 2.5 Detecting Outliers -- 2.5.1 A Classic Outlier Detection Method -- 2.5.2 The Boxplot Rule -- 2.5.3 The MAD-Median Rule -- 2.5.4 R Functions outms, outbox, and out -- 2.6 Skipped Measures of Location -- 2.6.1 R Function MOM -- 2.7 Summary -- 2.8 Exercises -- Chapter 3 Plots Plus More Basics on Summarizing Data -- 3.1 Plotting Relative Frequencies -- 3.1.1 R Functions table, plot, splot, barplot, and cumsum -- 3.1.2 Computing the Mean and Variance Based on the Relative Frequencies -- 3.1.3 Some Features of the Mean and Variance -- 3.2 Histograms and Kernel Density Estimators -- 3.2.1 R Function hist -- 3.2.2 What Do Histograms Tell Us? -- 3.2.3 Populations, Samples, and Potential Concerns about Histograms -- 3.2.4 Kernel Density Estimators -- 3.2.5 R Functions Density and Akerd.

3.3 Boxplots and Stem-and-Leaf Displays -- 3.3.1 R Function stem -- 3.3.2 Boxplot -- 3.3.3 R Function boxplot -- 3.4 Summary -- 3.5 Exercises -- Chapter 4 Probability and Related Concepts -- 4.1 The Meaning of Probability -- 4.2 Probability Functions -- 4.3 Expected Values, Population Mean and Variance -- 4.3.1 Population Variance -- 4.4 Conditional Probability and Independence -- 4.4.1 Independence and Dependence -- 4.5 The Binomial Probability Function -- 4.5.1 R Functions dbinom and pbinom -- 4.6 The Normal Distribution -- 4.6.1 Some Remarks about the Normal Distribution -- 4.6.2 The Standard Normal Distribution -- 4.6.3 Computing Probabilities for Any Normal Distribution -- 4.6.4 R Functions pnorm and qnorm -- 4.7 Nonnormality and The Population Variance -- 4.7.1 Skewed Distributions -- 4.7.2 Comments on Transforming Data -- 4.8 Summary -- 4.9 Exercises -- Chapter 5 Sampling Distributions -- 5.1 Sampling Distribution of P, the Proportion of Successes -- 5.2 Sampling Distribution of the Mean Under Normality -- 5.2.1 Determining Probabilities Associated with the Sample Mean -- 5.2.2 But Typically Is Not Known. Now What? -- 5.3 Nonnormality and the Sampling Distribution of the Sample Mean -- 5.3.1 Approximating the Binomial Distribution -- 5.3.2 Approximating the Sampling Distribution of the Sample Mean: The General Case -- 5.4 Sampling Distribution of the Median and 20% Trimmed Mean -- 5.4.1 Estimating the Standard Error of the Median -- 5.4.2 R Function msmedse -- 5.4.3 Approximating the Sampling Distribution of the Sample Median -- 5.4.4 Estimating the Standard Error of a Trimmed Mean -- 5.4.5 R Function trimse -- 5.4.6 Estimating the Standard Error When Outliers Are Discarded: A Technically Unsound Approach -- 5.5 The Mean Versus the Median and 20% Trimmed Mean -- 5.6 Summary -- 5.7 Exercises -- Chapter 6 Confidence Intervals.

6.1 Confidence Interval for the Mean -- 6.1.1 Computing a Confidence Interval Given 2 -- 6.2 Confidence Intervals for the Mean Using s ( Not Known) -- 6.2.1 R Function t.test -- 6.3 A Confidence Interval for The Population Trimmed Mean -- 6.3.1 R Function trimci -- 6.4 Confidence Intervals for The Population Median -- 6.4.1 R Function msmedci -- 6.4.2 Underscoring a Basic Strategy -- 6.4.3 A Distribution-Free Confidence Interval for the Median Even When There Are Tied Values -- 6.4.4 R Function sint -- 6.5 The Impact of Nonnormality on Confidence Intervals -- 6.5.1 Student's T and Nonnormality -- 6.5.2 Nonnormality and the 20% Trimmed Mean -- 6.5.3 Nonnormality and the Median -- 6.6 Some Basic Bootstrap Methods -- 6.6.1 The Percentile Bootstrap Method -- 6.6.2 R Functions trimpb -- 6.6.3 Bootstrap-t -- 6.6.4 R Function trimcibt -- 6.7 Confidence Interval for The Probability of Success -- 6.7.1 Agresti-Coull Method -- 6.7.2 Blyth's Method -- 6.7.3 Schilling-Doi Method -- 6.7.4 R Functions acbinomci and binomLCO -- 6.8 Summary -- 6.9 Exercises -- Chapter 7 Hypothesis Testing -- 7.1 Testing Hypotheses about the Mean, Known -- 7.1.1 Details for Three Types of Hypotheses -- 7.1.2 Testing for Exact Equality and Tukey's Three-Decision Rule -- 7.1.3 p-Values -- 7.1.4 Interpreting p-Values -- 7.1.5 Confidence Intervals versus Hypothesis Testing -- 7.2 Power and Type II Errors -- 7.2.1 Power and p-Values -- 7.3 Testing Hypotheses about the mean, Not Known -- 7.3.1 R Function t.test -- 7.4 Student's T and Nonnormality -- 7.4.1 Bootstrap-t -- 7.4.2 Transforming Data -- 7.5 Testing Hypotheses about Medians -- 7.5.1 R Function msmedci and sintv2 -- 7.6 Testing Hypotheses Based on a Trimmed Mean -- 7.6.1 R Functions trimci, trimcipb, and trimcibt -- 7.7 Skipped Estimators -- 7.7.1 R Function momci -- 7.8 Summary -- 7.9 Exercises.

Chapter 8 Correlation and Regression -- 8.1 Regression Basics -- 8.1.1 Residuals and a Method for Estimating the Median of Y Given X -- 8.1.2 R function qreg and Qreg -- 8.2 Least Squares Regression -- 8.2.1 R Functions lsfit, lm, ols, plot, and abline -- 8.3 Dealing with Outliers -- 8.3.1 Outliers among the Independent Variable -- 8.3.2 Dealing with Outliers among the Dependent Variable -- 8.3.3 R Functions tsreg and tshdreg -- 8.3.4 Extrapolation Can Be Dangerous -- 8.4 Hypothesis Testing -- 8.4.1 Inferences about the Least Squares Slope and Intercept -- 8.4.2 R Functions lm, summary, and ols -- 8.4.3 Heteroscedcasticity: Some Practical Concerns and How to Address Them -- 8.4.4 R Function olshc4 -- 8.4.5 Outliers among the Dependent Variable: A Cautionary Note -- 8.4.6 Inferences Based on the Theil-Sen Estimator -- 8.4.7 R Functions regci and regplot -- 8.5 Correlation -- 8.5.1 Pearson's Correlation -- 8.5.2 Inferences about the Population Correlation, p -- 8.5.3 R Functions pcor and pcorhc4 -- 8.6 Detecting Outliers When Dealing with Two or More Variables -- 8.6.1 R Functions out and outpro -- 8.7 Measures of Association: Dealing with Outliers -- 8.7.1 Kendall's Tau -- 8.7.2 R Functions tau and tauci -- 8.7.3 Spearman's Rho -- 8.7.4 R Functions spear and spearci -- 8.7.5 Winsorized and Skipped Correlations -- 8.7.6 R Functions scor, scorci, scorciMC, wincor, and wincorci -- 8.8 Multiple Regression -- 8.8.1 Least Squares Regression -- 8.8.2 Hypothesis Testing -- 8.8.3 R Function olstest -- 8.8.4 Inferences Based on a Robust Estimator -- 8.8.5 R Function regtest -- 8.9 Dealing with Curvature -- 8.9.1 R Function lplot and rplot -- 8.10 Summary -- 8.11 Exercises -- Chapter 9 Comparing Two Independent Groups -- 9.1 Comparing Means -- 9.1.1 The Two-Sample Student's T Test -- 9.1.2 Violating Assumptions When Using Student's T.

9.1.3 Why Testing Assumptions Can Be Unsatisfactory -- 9.1.4 Interpreting Student's T When It Rejects -- 9.1.5 Dealing with Unequal Variances: Welch's Test -- 9.1.6 R Function t.test -- 9.1.7 Student's T versus Welch's Test -- 9.1.8 The Impact of Outliers When Comparing Means -- 9.2 Comparing Medians -- 9.2.1 A Method Based on the McKean-Schrader Estimator -- 9.2.2 A Percentile Bootstrap Method -- 9.2.3 R Functions msmed, medpb2, split, and fac2list -- 9.2.4 An Important Issue: The Choice of Method can Matter -- 9.3 Comparing Trimmed Means -- 9.3.1 R Functions yuen, yuenbt, and trimpb2 -- 9.3.2 Skipped Measures of Location and Deleting Outliers -- 9.3.3 R Function pb2gen -- 9.4 Tukey's Three-Decision Rule -- 9.5 Comparing Variances -- 9.5.1 R Function comvar2 -- 9.6 Rank-Based (Nonparametric) Methods -- 9.6.1 Wilcoxon-Mann-Whitney Test -- 9.6.2 R Function wmw -- 9.6.3 Handling Heteroscedasticity -- 9.6.4 R Functions cid and cidv2 -- 9.7 Measuring Effect Size -- 9.7.1 Cohen's d -- 9.7.2 Concerns about Cohen's d and How They Might Be Addressed -- 9.7.3 R Functions akp.effect, yuenv2, and med.effect -- 9.8 Plotting Data -- 9.8.1 R Functions ebarplot, ebarplot.med, g2plot, and boxplot -- 9.9 Comparing Quantiles -- 9.9.1 R Function qcomhd -- 9.10 Comparing Two Binomial Distributions -- 9.10.1 Improved Methods -- 9.10.2 R Functions twobinom and twobicipv -- 9.11 A Method for Discrete or Categorical Data -- 9.11.1 R Functions disc2com, binband, and splotg2 -- 9.12 Comparing Regression Lines -- 9.12.1 Classic ANCOVA -- 9.12.2 R Function CLASSanc -- 9.12.3 Heteroscedastic Methods for Comparing the Slopes and Intercepts -- 9.12.4 R Functions olsJ2 and ols2ci -- 9.12.5 Dealing with Outliers among the Dependent Variable -- 9.12.6 R Functions reg2ci, ancGpar, and reg2plot -- 9.12.7 A Closer Look at Comparing Nonparallel Regression Lines -- 9.12.8 R Function ancJN.

9.13 Summary.

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