Business Statistics: Communicating with Numbers, 4th Edition

Cover
Business Statistics
Dedication
About the Authors
Acknowledgments
Brief Contents
Contents
Part One: Introduction
chapter 1: Data and Data Preparation
1.1 Types of Data
Sample and Population Data
Cross-Sectional and Time Series Data
Structured and Unstructured Data
Big Data
Data on the Web
1.2 Variables and Scales of Measurement
The Measurement Scales
1.3 Data Preparation
Counting and Sorting
A Note on Handling Missing Values
Subsetting
A Note on Subsetting Based on Data Ranges
1.4 Writing with Data
Conceptual Review
Additional Exercises
Part Two: Descriptive Statistics
chapter 2: Tabular and Graphical Methods
2.1 Methods to Visualize a Categorical Variable
A Frequency Distribution for a Categorical Variable
A Bar Chart
A Pie Chart
Cautionary Comments When Constructing or Interpreting Charts or Graphs
2.2 Methods to Visualize the Relationship Between Two Categorical Variables
A Contingency Table
A Stacked Column Chart
2.3 Methods to Visualize a Numerical Variable
A Frequency Distribution for a Numerical Variable
A Histogram
A Polygon
An Ogive
Using Excel and R Construct a Polygon and an Ogive
2.4 More Data Visualization Methods
A Scatterplot
A Scatterplot with a Categorical Variable
A Line Chart
2.5 A Stem-and-Leaf Diagram
2.6 Writing with Data
Conceptual Review
Additional Exercises
Appendix 2.1: Guidelines for Other Software Packages
chapter 3: Numerical Descriptive Measures
3.1 Measures of Central Location
The Mean
The Median
The Mode
Using Excel and R to Calculate Measures of Central Location
Note on Symmetry
Subsetted Means
The Weighted Mean
3.2 Percentiles and Boxplots
A Percentile
A Boxplot
3.3 The Geometric Mean
The Geometric Mean Return
Arithmetic Mean versus Geometric Mean
The Average Growth Rate
3.4 Measures of Dispersion
The Range
The Mean Absolute Deviation
The Variance and the Standard Deviation
The Coefficient of Variation
3.5 Mean-Variance Analysis and the Sharpe Ratio
3.6 Analysis of Relative Location
Chebyshev’s Theorem
The Empirical Rule
z-Scores
3.7 Measures of Association
3.8 Writing with Data
Conceptual Review
Additional Exercises
Appendix 3.1: Guidelines for Other Software Packages
Part three: Probability and Probability Distributions
chapter 4: Introduction to Probability
4.1 Fundamental Probability Concepts
Events
Assigning Probabilities
4.2 Rules of Probability
4.3 Contingency Tables and Probabilities
A Note on Independence with Empirical Probabilities
4.4 The Total Probability Rule and Bayes’ Theorem
The Total Probability Rule and Bayes’ Theorem
Extensions of the Total Probability Rule and Bayes’ Theorem
4.5 Counting Rules
4.5 Writing with Data
Conceptual Review
Additional Exercises
chapter 5: Discrete Probability Distributions
5.1 Random Variables and Discrete Probability Distributions
The Discrete Probability Distribution
5.2 Expected Value, Variance, and Standard Deviation
Summary Measures
Risk Neutrality and Risk Aversion
5.3 Portfolio Returns
Properties of Random Variables
Summary Measures for a Portfolio
5.4 The Binomial Distribution
Using Excel and R to Obtain Binomial Probabilities
5.5 The Poisson Distribution
Using Excel and R to Obtain Poisson Probabilities
5.6 The Hypergeometric Distribution
Using Excel and R to Obtain Hypergeometric Probabilities
5.7 Writing with Data
Case Study
Conceptual Review
Additional Exercises
Appendix 5.1: Guidelines for Other Software Packages
chapter 6: Continuous Probability Distributions
6.1 Continuous Random Variables and the Uniform Distribution
The Continuous Uniform Distribution
6.2 The Normal Distribution
Characteristics of the Normal Distribution
The Standard Normal Distribution
Finding a Probability for a Given z Value
Finding a z Value for a Given Probability
The Transformation of Normal Random Variables
Using R for the Normal Distribution
A Note on the Normal Approximation of the Binomial Distribution
6.3 Other Continuous Probability Distributions
The Exponential Distribution
Using R for the Exponential Distribution
The Lognormal Distribution
Using R for the Lognormal Distribution
6.4 Writing with Data
Conceptual Review
Additional Exercises
Appendix 6.1: Guidelines for Other Software Packages
Part four: Basic Inference
chapter 7: Sampling and Sampling Distributions
7.1 Sampling
Classic Case of a “Bad” Sample: The Literary Digest Debacle of 1936
Trump’s Stunning Victory in 2016
Sampling Methods
Using Excel and R to Generate a Simple Random Sample
7.2 The Sampling Distribution of the Sample Mean
The Expected Value and the Standard Error of the Sample Mean
Sampling from a Normal Population
The Central Limit Theorem
7.3 The Sampling Distribution of the Sample Proportion
The Expected Value and the Standard Error of the Sample Proportion
7.4 The Finite Population Correction Factor
7.5 Statistical Quality Control
Control Charts
Using Excel and R to Create a Control Chart
7.6 Writing With Data
Conceptual Review
Additional Exercises
Appendix 7.1: Derivation of the Mean and the Variance for X and P
Appendix 7.2: Properties of Point Estimators
Appendix 7.3: Guidelines for Other Software Packages
chapter 8: Interval Estimation
8.1 Confidence Interval For The Population Mean When Is Known
Constructing a Confidence Interval for When Is Known
The Width of a Confidence Interval
Using Excel and R to Construct a Confidence Interval for μ When σ Is Known
8.2 Confidence Interval For The Population Mean When σ Is Unknown
The t Distribution
Summary of the tdf Distribution
Locating tdf Values and Probabilities
Constructing a Confidence Interval for μ When σ Is Unknown
Using Excel and R to Construct a Confidence Interval for μ When σ Is Unknown
8.3 Confidence Interval for the Population Proportion
8.4 Selecting the Required Sample Size
Selecting n to Estimate μ
Selecting n to Estimate p
8.5 Writing with Data
Conceptual Review
Additional Exercises
Appendix 8.1: Guidelines for Other Software Packages
chapter 9: Hypothesis Testing
9.1 Introduction to Hypothesis Testing
The Decision to “Reject” or “Not Reject” the Null Hypothesis
Defining the Null and the Alternative Hypotheses
Type I and Type II Errors
9.2 Hypothesis Test For The Population Mean When Is Known
The p-Value Approach
Confidence Intervals and Two-Tailed Hypothesis Tests
One Last Remark
9.3 Hypothesis Test For The Population Mean When Is Unknown
Using Excel and R to Test μ When σ is Unknown
9.4 Hypothesis Test for the Population Proportion
9.5 Writing with Data
Conceptual Review
Additional Exercises
Appendix 9.1: The Critical Value Approach
Appendix 9.2: Guidelines for Other Software Packages
chapter 10: Statistical Inference Concerning Two Populations
10.1 Inference Concerning the Difference Between Two Means
Confidence Interval for μ1 − μ2
Hypothesis Test for μ1 − μ2
Using Excel and R for Testing Hypotheses about μ1 − μ2
A Note on the Assumption of Normality
10.2 Inference Concerning Mean Differences
Recognizing a Matched-Pairs Experiment
Confidence Interval for μD
Hypothesis Test for μD
Using Excel and R for Testing Hypotheses about μD
One Last Note on the Matched-Pairs Experiment
10.3 Inference Concerning the Difference Between Two Proportions
Confidence Interval for p1 − p2
Hypothesis Test for p1 − p2
10.4 Writing with Data
Conceptual Review
Additional Exercises
Appendix 10.1: Guidelines for Other Software Packages
chapter 11: Statistical Inference Concerning Variance
11.1 Inference Concerning the Population Variance
Sampling Distribution of S2
Finding χ df 2 Values and Probabilities
Confidence Interval for the Population Variance
Hypothesis Test for the Population Variance
Note on Calculating the p-Value for a Two-Tailed Test Concerning σ2
Using Excel and R to Test σ2
11.2 Inference Concerning the Ratio of Two Population Variances
Sampling Distribution of S12∕S2
Finding F ( df1 , df2) Values and Probabilities
Confidence Interval for the Ratio of Two Population Variances
Hypothesis Test for the Ratio of Two Population Variances
Using Excel and R to Test σ12 ∕ σ22
11.3 Writing with Data
Conceptual Review
Additional Exercises
Appendix 11.1: Guidelines for Other Software Packages
chapter 12: Chi-Square Tests
12.1 Goodness-of-Fit Test for a Multinomial Experiment
Using R to Conduct a Goodness-of-Fit Test
12.2 Chi-Square Test for Independence
Calculating Expected Frequencies
Using R to Conduct a Test for Independence
12.3 Chi-Square Tests for Normality
The Goodness-of-Fit Test for Normality
The Jarque-Bera Test
Writing with Data
Conceptual Review
Additional Exercises
Appendix 12.1: Guidelines for Other Software Packages
Part five: Advanced Inference
chapter 13: Analysis of Variance
13.1 One-Way Anova Test
Between-Treatments Estimate of σ2: MSTR
Within-Treatments Estimate of σ2: MSE
The One-Way ANOVA Table
Using Excel and R to Construct a One-Way ANOVA Table
13.2 Multiple Comparison Methods
Fisher’s Least Significant Difference (LSD) Method
Tukey’s Honestly Significant Difference (HSD) Method
Using R to Construct Tukey Confidence Intervals for μ1 − μ2
13.3 Two-Way Anova Test: No Interaction
The Sum of Squares for Factor A, SSA
The Sum of Squares for Factor B, SSB
The Error Sum of Squares, SSE
Using Excel and R for a Two-Way ANOVA Test—No Interaction
13.4 Two-Way Anova Test: With Interaction
The Total Sum of Squares, SST
The Sum of Squares for Factor A, SSA, and the Sum of Squares for Factor B, SSB
The Sum of Squares for the Interaction of Factor A and Factor B, SSAB
The Error Sum of Squares, SSE
Using Excel and R for a Two-Way ANOVA Test—With Interaction
13.5 Writing with Data
Conceptual Review
Additional Exercises
Appendix 13.1: Guidelines for Other Software Packages
chapter 14: Regression Analysis
14.1 Hypothesis Test for the Correlation Coefficient
Testing the Correlation Coefficient ρxy
Using Excel and R to Conduct a Hypothesis Test for ρxy
14.2 The Linear Regression Model
The Simple Linear Regression Model
The Multiple Linear Regression Model
Using Excel and R to Estimate a Linear Regression Model
14.3 Goodness-of-Fit Measures
The Standard Error of the Estimate
The Coefficient of Determination, R2
The Adjusted R2
A Cautionary Note Concerning Goodness-of-fit Measures
14.4 Writing with Data
Conceptual Review
Additional Exercises
Appendix 14.1: Guidelines for Other Software Packages
chapter 15: Inference with Regression Models
15.1 Tests of Significance
Test of Joint Significance
Test of Individual Significance
Using a Confidence Interval to Determine Individual Significance
A Test for a Nonzero Slope Coefficient
Reporting Regression Results
15.2 A General Test of Linear Restrictions
Using R to Conduct Partial F Tests
15.3 Interval Estimates for the Response Variable
Using R to Find Interval Estimates for the Response Variable
15.4 Model Assumptions and Common Violations
Residual Plots
Assumption 1.
Detecting Nonlinearities
Remedy
Assumption 2.
Detecting Multicollinearity
Remedy
Assumption 3.
Detecting Changing Variability
Remedy
Assumption 4.
Detecting Correlated Observations
Remedy
Assumption 5.
Remedy
Assumption 6.
Summary of Regression Modeling
Using Excel and R for Residual Plots, and R for Robust Standard Errors
15.5 Writing with Data
Conceptual Review
Additional Exercises
Appendix 15.1: Guidelines for Other Software Packages
chapter 16: Regression Models for Nonlinear Relationships
16.1 Polynomial Regression Models
The Quadratic Regression Model
Using R to Estimate a Quadratic Regression Model
The Cubic Regression Model
16.2 Regression Models with Logarithms
A Log-Log Model
The Logarithmic Model
The Exponential Model
Using R to Estimate Log-Transformed Models
Comparing Linear and Log-Transformed Models
Using Excel and R to Compare Linear and Log-Transformed Models
A Cautionary Note Concerning Goodness-of-fit Measures
16.3 Writing with Data
Conceptual Review
Additional Exercises
Appendix 16.1: Guidelines for Other Software Packages
chapter 17: Regression Models with Dummy Variables
17.1 Dummy Variables
A Categorical Explanatory Variable with Two Categories
Using Excel and R to Make Dummy Variables
Assessing Dummy Variable Models
A Categorical Explanatory Variable with Multiple Categories
17.2 Interactions with Dummy Variables
Using R to Estimate a Regression Model with a Dummy Variable and an Interaction Variable
17.3 The Linear Probability Model and the Logistic Regression Models
The Linear Probability Model
The Logistic Regression Model
Using R to Estimate a Logistic Regression Model
Accuracy of Binary Choice Models
Using R to Find the Accuracy Rate
17.4 Writing with Data
Conceptual Review
Additional Exercises
Appendix 17.1: Guidelines for Other Software Packages
Part six: Supplementary Topics
chapter 18: Forecasting with Time Series Data
18.1 The Forecasting Process for Time Series
Forecasting Methods
Model Selection Criteria
18.2 Simple Smoothing Techniques
The Moving Average Technique
The Simple Exponential Smoothing Technique
Using R for Exponential Smoothing
18.3 Linear Regression Models for Trend and Seasonality
The Linear Trend Model
The Linear Trend Model with Seasonality
Estimating a Linear Trend Model with Seasonality with R
A Note on Causal Models for Forecasting
18.4 Nonlinear Regression Models for Trend and Seasonality
The Exponential Trend Model
Using R to Forecast with an Exponential Trend Model
The Polynomial Trend Model
Nonlinear Trend Models with Seasonality
Using R to Forecast a Quadratic Trend Model with Seasons
18.5 Causal Forecasting Methods
Lagged Regression Models
Using R to Estimate Lagged Regression Models
18.6 Writing with Data
Conceptual Review
Additional Exercises
Appendix 18.1: Guidelines for Other Software Packages
chapter 19: Returns, Index Numbers, and Inflation
19.1 Investment Return
The Adjusted Closing Price
Nominal versus Real Rates of Return
19.2 Index Numbers
A Simple Price Index
An Unweighted Aggregate Price Index
A Weighted Aggregate Price Index
19.3 Using Price Indices to Deflate a Time Series
Inflation Rate
19.4 Writing with Data
Conceptual Review
Additional Exercises
chapter 20: Nonparametric Tests
20.1 Testing a Population Median
The Wilcoxon Signed-Rank Test for a Population Median
Using a Normal Distribution Approximation for T
Using R to Test a Population Median
20.2 Testing Two Population Medians
The Wilcoxon Signed-Rank Test for a Matched-Pairs Sample
Using R to Test for Median Differences from a Matched-Pairs Sample
The Wilcoxon Rank-Sum Test for Independent Samples
Using R to Test for Median Differences from Independent Samples
Using a Normal Distribution Approximation for W
20.3 Testing Three or More Population Medians
The Kruskal-Wallis Test for Population Medians
Using R to Conduct a Kruskal-Wallis Test
20.4 The Spearman Rank Correlation Test
Using R to Conduct the Spearman Rank Correlation Test
Summary of Parametric and Nonparametric Tests
20.5 The Sign Test
20.6 Tests Based on Runs
The Method of Runs Above and Below the Median
Using R to Conduct the Runs Test
20.7 Writing with Data
Conceptual Review
Additional Exercises
Appendix 20.1: Guidelines for Other Software Packages
Appendixes
appendix A: Getting Started with R
Appendix B: Tables
Appendix C: Answers to Selected Even- Numbered Exercises
Glossary
Index