Statistics with R

Robert Stinerock has more than 30 years of experience teaching statistics and probability to students at both the undergraduate and graduate level. He has taught classes at Columbia, Trinity, Rutgers, Fairleigh Dickinson, the Stevens Institute of Technology, Catolica de Lisboa (Portugal), and the Faculdade de Economia, Universidade Nova de Lisboa (Portugal). Since 2014, he has taught statistics at the Executive MBA program at Baruch College of the City University of New York.He has received several awards for excellence in the classroom: the Stevens Howe School Outstanding Undergraduate Teacher Award; the Stevens Alumni Association Outstanding Teacher Award; and the Fairleigh Dickinson Distinguished Faculty Award for Teaching.He has published numerous research articles in academic journals, most recently in the Journal of Macromarketing, the Journal of Business Research, and Geoforum.He earned his bachelor’s, master’s, and PhD degrees, all from Columbia University.He and his wife, Jyoti, live in New York City.

This book is a treasure for both instructors and students. It is written by a master, award-winning teacher with an unparalleled expertise of getting difficult concepts across in a deceptively simple fashion. Written in clear functional English, it both teaches the usual applied statistical methods, as well as provides a gentle introduction to Bayesian methods throughout the book. This is, in essence, more of a new book than just a new edition of an existing one. However, the features that made the first edition so successful have been retained: a student needs only basic algebra to understand the conceptual formulations that are illustrated with hands-on real-life examples that will appeal to students and motivate them to understand the importance of statistics in their daily lives.

• Chapter 1: Introduction and R InstructionsBasic TerminologyData: Qualitative or QuantitativeData: Cross-Sectional or LongitudinalDescriptive StatisticsProbabilityStatistics: Estimation and InferenceChapter 2: Descriptive Statistics: Tabular and Graphical MethodsMethods of Summarizing and Displaying Qualitative DataMethods of Summarizing and Displaying Quantitative DataCross Tabulations and Scatter PlotsChapter 3: Descriptive Statistics: Numerical MethodsMeasures of Central TendencyMeasures of LocationExploratory Data Analysis: The Box Plot DisplayMeasures of VariabilityThe z-Score: A Measure of Relative LocationMeasures of Association: The Bivariate CaseThe Geometric MeanChapter 4: Introduction to ProbabilitySome Important DefinitionsCounting RulesAssigning ProbabilitiesEvents and ProbabilitiesProbabilities of Unions and Intersections of EventsConditional ProbabilityBayes′ Theorem and EventsChapter 5: Discrete Probability DistributionsThe Discrete Uniform Probability DistributionThe Expected Value and Standard Deviation of a Discrete Random VariableThe Binomial Probability DistributionThe Poisson Probability DistributionThe Hypergeometric Probability DistributionThe Hypergeometric Probability Distribution: The General CaseBayes′ Theorem and Discrete Random VariablesChapter 6: Continuous Probability DistributionsContinuous Uniform Probability DistributionNormal Probability DistributionExponential Probability DistributionOptional Material: Derivation of the Cumulative Exponential Probability Func- tionBayes′ Theorem and Continuous Random VariablesChapter 7: Point Estimation and Sampling DistributionsPopulations and SamplesThe Simple Random SampleThe Sample Statistic: x, s, and pThe Sampling Distribution of xThe Sampling Distribution of pSome Other Commonly Used Sampling MethodsBayes′ Theorem: Approximate Bayesian ComputationChapter 8: Confidence Interval EstimationInterval Estimate of µ When σ Is KnownInterval Estimate of µ When σ Is UnknownSample Size Determination in the Case of µInterval Estimate of pSample Size Determination in the Case of pBayes’ Theorem: Confidence Intervals or Credible IntervalsChapter 9: Hypothesis Tests: Introduction, Basic Concepts, and an ExampleChapter 10: Hypothesis Tests about Means and Proportions: ApplicationsThe Lower-Tail Hypothesis Test about μ: σ Is KnownThe Two-Tail Hypothesis Test about μ: σ Is KnownThe Upper-Tail Hypothesis Test about μ: σ Is UnknownThe Two-Tail Hypothesis Test about μ: σ is UnknownHypothesis Tests about pCalculating the Probability of a Type II Error: βAdjusting the Sample Size to Control the Size of βBayes’ Theorem and an Inferential Approach to pChapter 11: Comparisons of Means and ProportionsThe Difference between μ1 and μ2: Independent SamplesThe Difference between μ1 and μ2: Paired SamplesThe Difference between p1 and p2: Independent SamplesBayes’ Theorem and the Difference between p1 and p2Chapter 12: Simple Linear RegressionSimple Linear Regression: The ModelThe Estimated Regression EquationGoodness of Fit: The Coefficient of Determination, r2The Hypothesis Test about β1Alternative Approaches to Testing SignificanceSo Far, We Have Tested Only b1. Will We Also Test b0?Assumptions: What Are They?Assumptions: How Are They Validated?Optional Material: Derivation of the Expressions for the Least-Squares Estimates of β0 and β1Bayes’ Theorem: Using Stan to Estimate the Relationship between Two VariablesChapter 13: Multiple RegressionSimple Linear Regression: A RepriseMultiple Regression: The ModelMultiple Regression: The Multiple Regression EquationThe Estimated Multiple Regression EquationMultiple Regression: The 2 Independent Variable CaseAssumptions: What Are They? Can We Validate Them?Tests of Significance: The Overall Regression ModelTests of Signicance: The Independent VariablesThere Must Be An Easier Way Than This, Right?Using the Estimated Regression Equation for PredictionIndependent Variable Selection: The Best-Subsets MethodLogistic Regression: The Zero-One Dependent VariableBayes′ Theorem: Stan and Multiple Regression Analysis