Statistics: Principles and Methods

Chapter 1: INTRODUCTION TO STATISTICS

• • 1 The Subject and Scope of Statistics
• • 2 Statistics in Aid of Scientific Inquiry
• • 3 Two Basic Concepts—Population and Sample
• • 4 The Purposeful Collection of Data
• • Case Study: Statistics in Context
• • 5 Objectives of Statistics

Chapter 2: ORGANIZATION AND DESCRIPTION OF DATA

• • 1 Main Types of Data
• • 2 Describing Data by Tables and Graphs
• • 3 Measures of Center
• • 4 Measures of Variation
• • 5 Checking the Stability of the Observations over Time
• • 6 More on Graphics
• • Case Study: Statistics in Context

Chapter 3: DESCRIPTIVE STUDY OF BIVARIATE DATA

• • 1 Summarization of Bivariate Categorical Data
• • 2 A Designed Experiment for Making a Comparison
• • 3 Scatter Diagram of Bivariate Measurement Data
• • 4 The Correlation Coefficient—A Measure of Linear Relation
• • 5 Prediction of One Variable from another (Linear Regression)

Chapter 4: PROBABILITY

• • 1 Probability of an Event
• • 2 Methods of Assigning Probability
• • 3 Event Operations and Two Laws of Probability
• • 4 Conditional Probability and Independence
• • 5 Bayes’ Theorem
• • 6 Random Sampling from a Finite Population
• • Case Study: Statistics in Context

Chapter 5: PROBABILITY DISTRIBUTIONS

• • 1 Random Variables
• • 2 Probability Distribution of a Discrete Random Variable
• • 3 Mean (Expected Value) and Standard Deviation of a Probability Distribution
• • 4 Successes and Failures—Bernoulli Trials
• • 5 The Binomial Distribution
• • 6 The Poisson Distribution and Rare Events

Chapter 6: THE NORMAL DISTRIBUTION

• • 1 Probability Model for a Continuous Random Variable
• • 2 The Normal Distribution—Its General Features
• • 3 The Standard Normal Distribution
• • 4 Probability Calculations with Normal Distributions
• • 5 The Normal Approximation to the Binomial
• • 6 Checking the Plausibility of a Normal Model
• • 7 Transforming Observations to Attain Near Normality

Chapter 7: VARIATION IN REPEATED SAMPLES—SAMPLING DISTRIBUTIONS

• • 1 The Sampling Distribution of a Statistic
• • 2 Distribution of the Sample Mean and the Central Limit Theorem
• • Case Study: Statistics in Context

Chapter 8: DRAWING INFERENCES FROM LARGE SAMPLES

• • 1 Two Types of Statistical Inference: Estimation and Testing
• • 2 Point Estimation of a Population Mean
• • 3 Confidence Interval Estimation of a Population Mean
• • 4 Testing Hypotheses about a Population Mean
• • 5 Inferences about a Population Proportion

Chapter 9: SMALL SAMPLE INFERENCES FOR NORMAL POPULATIONS

• • 1 Student’s t Distribution
• • 2 Inferences about —Small Sample Size
• • 3 Relationship between Tests and Confidence Intervals
• • 4 Inferences about the Standard Deviation (The Chi-Square Distribution)
• • 5 Robustness of Inference Procedures

Chapter 10: COMPARING TWO TREATMENTS

• • 1 Two Designs: Independent Samples and Matched Pairs Sample
• • 2 Inferences about the Difference of Means—Independent Large Samples
• • 3 Inferences about the Difference of Means—Independent Small Samples from Normal Populations
• • 4 Randomization and Its Role in Inference
• • 5 Matched Pairs Comparisons
• • 6 Choosing Between Independent Samples and a Matched Pairs Sample
• • 7 Comparing Two Population Proportions

Chapter 11: REGRESSION ANALYSIS I Simple Linear Regression

• • 1 Regression with a Single Predictor
• • 2 A Straight Line Regression Model
• • 3 The Method of Least Squares
• • 4 The Sampling Variability of the Least Squares Estimators—Tools for Inference
• • 5 Important Inference Problems
• • 6 The Strength of a Linear Relation
• • 7 Remarks about the Straight Line Model Assumptions

Chapter 12: REGRESSION ANALYSIS II Multiple Linear Regression and Other Topics

• • 1 Nonlinear Relations and Linearizing Transformations
• • 2 Multiple Linear Regression
• • 3 Residual Plots to Check the Adequacy of a Statistical Model

Chapter 13: ANALYSIS OF CATEGORICAL DATA

• • 1 Formulating Testing Problems Concerning Categorical Data
• • 2 Pearson’s χ2 Test for Goodness of Fit
• • 3 Contingency Table with One Margin Fixed (Test of Homogeneity)
• • 4 Contingency Table with Neither Margin Fixed (Test of Independence)

Chapter 14: ANALYSIS OF VARIANCE (ANOVA)

• • 1 Comparison of Several Treatments—One-Way Analysis of Variance
• • 2 Population Model and Inferences for a One-Way Analysis of Variance
• • 3 Simultaneous Confidence Intervals
• • 4 Graphical Diagnostics and Displays to Supplement ANOVA
• • 5 Randomized Block Experiments for Comparing k Treatments

Chapter 15: NONPARAMETRIC INFERENCE

• • 1 The Wilcoxon Rank-Sum Test for Comparing Two Treatments
• • 2 Matched Pairs Comparisons
• • 3 Measure of Correlation Based on Ranks
• • 4 Concluding Remarks

Chapter APPENDIX A1: SUMMATION NOTATION

Chapter APPENDIX A2: RULES FOR COUNTING

Chapter APPENDIX A3: EXPECTATION AND STANDARD DEVIATION—PROPERTIES

Chapter APPENDIX A4: THE EXPECTED VALUE AND STANDARD DEVIATION OF X

Chapter APPENDIX B: TABLES

• • Table 1 Random Digits
• • Table 2 Cumulative Binomial Probabilities
• • Table 3 Cumulative Poisson Probabilities
• • Table 4 Standard Normal Probabilities
• • Table 5 Percentage Points _t_ of _t_ Distributions
• • Table 6 Percentage Points χ2 of χ2 Distributions
• • Table 7 Percentage Points of _F_( v1, v2 ) Distributions
• • Table 8 Selected Tail Probabilities for the Null Distribution of Wilcoxon’s Rank-Sum Statistic
• • Table 9 Selected Tail Probabilities for the Null Distribution of Wilcoxon’s Signed-Rank Statistic
• • Table F1 General Formulas for Inferences about a Mean (), Difference of Two Means ( 1 − 2 )
• • Table F2 Inference about Proportions
• • Summary of Formulas Useful for Exams

Chapter DATA BANK: DATA BANK

Chapter ANSWERS TO SELECTED ODD-NUMBERED EXERCISES: ANSWERS TO SELECTED ODD-NUMBERED EXERCISES