Deborah J. Rumsey, PhD, is Professor of Statistics and Statistics Education Specialist at The Ohio State University. She is the author of Statistics Workbook For Dummies, Statistics II For Dummies, and Probability For Dummies.

Introduction 1

Part 1: Vital Statistics about Statistics 7

Chapter 1: Statistics in a Nutshell 9

Chapter 2: The Statistics of Everyday Life 23

Chapter 3: Taking Control: So Many Numbers, So Little Time 35

Chapter 4: Tools of the Trade 47

Part 2: Number-Crunching Basics 69

Chapter 5: Means, Medians, and More 71

Chapter 6: Getting the Picture: Graphing Categorical Data 95

Chapter 7: Going by the Numbers: Graphing Numerical Data 107

Part 3: Distributions and the Central Limit Theorem 133

Chapter 8: Random Variables and the Binomial Distribution 135

Chapter 9: The Normal Distribution 149

Chapter 10: The t-Distribution 165

Chapter 11: Sampling Distributions and the Central Limit Theorem 171

Part 4: Guesstimating and Hypothesizing with Confidence 187

Chapter 12: Leaving Room for a Margin of Error 189

Chapter 13: Confidence Intervals: Making Your Best Guesstimate 201

Chapter 14: Claims, Tests, and Conclusions 223

Chapter 15: Commonly Used Hypothesis Tests: Formulas and Examples 237

Part 5: Statistical Studies and the Hunt for a Meaningful Relationship 255

Chapter 16: Polls, Polls, and More Polls 257

Chapter 17: Experiments: Medical Breakthroughs or Misleading Results? 275

Chapter 18: Looking for Links: Correlation and Regression 293

Chapter 19: Two-Way Tables and Independence 311

Part 6: The Part of Tens 333

Chapter 20: Ten Tips for the Statistically Savvy Sleuth 335

Chapter 21: Ten Surefire Exam Score Boosters 349

Appendix: Tables for Reference 365

Index 375

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Table of Contents

Introduction 1

About This Book 1

Conventions Used in This Book 2

What You're Not to Read 3

Foolish Assumptions 3

How This Book Is Organized 3

Part 1: Vital Statistics about Statistics 3

Part 2: Number-Crunching Basics 4

Part 3: Distributions and the Central Limit Theorem 4

Part 4: Guesstimating and Hypothesizing with Confidence 4

Part 5: Statistical Studies and the Hunt for a Meaningful Relationship 5

Part 6: The Part of Tens 5

Icons Used in This Book 6

Where to Go from Here 6

Part 1: Vital Statistics About Statistics 7

Chapter 1: Statistics in a Nutshell 9

Thriving in a Statistical World 10

Designing Appropriate Studies 11

Surveys 11

Experiments 12

Collecting Quality Data 13

Selecting a good sample 13

Avoiding bias in your data 14

Creating Effective Summaries 14

Descriptive statistics 15

Charts and graphs 15

Determining Distributions 16

Performing Proper Analyses 17

Margin of error and confidence intervals 18

Hypothesis tests 19

Correlation, regression, and two-way tables 20

Drawing Credible Conclusions 21

Reeling in overstated results 21

Questioning claims of cause and effect 21

Becoming a Sleuth, Not a Skeptic 22

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Chapter 2: The Statistics of Everyday Life 23

Statistics and the Media: More Questions than Answers? 24

Probing popcorn problems 24

Venturing into viruses 24

Comprehending crashes 25

Mulling malpractice 26

Belaboring the loss of land 26

Scrutinizing schools 27

Studying sports 28

Banking on business news 28

Touring the travel news 29

Surveying sexual stats 29

Breaking down weather reports 30

Musing about movies 30

Highlighting horoscopes 31

Using Statistics at Work 31

Delivering babies - and information 31

Posing for pictures 32

Poking through pizza data 32

Statistics in the office 33

Chapter 3: Taking Control: So Many Numbers, So Little Time 35

Detecting Errors, Exaggerations, and Just Plain Lies 36

Checking the math 36

Uncovering misleading statistics 37

Looking for lies in all the right places 44

Feeling the Impact of Misleading Statistics 44

Chapter 4: Tools of the Trade 47

Statistics: More than Just Numbers 47

Grabbing Some Basic Statistical Jargon 49

Data 50

Data set 51

Variable 51

Population 51

Sample, random, or otherwise 52

Statistic 54

Parameter 54

Bias 55

Mean (Average) 55

Median 56

Standard deviation 56

Percentile 57

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Standard score 57

Distribution and normal distribution 58

Central Limit Theorem 59

z-values 60

Experiments 60

Surveys (Polls) 62

Margin of error 62

Confidence interval 63

Hypothesis testing 64

p-values 65

Statistical significance 66

Correlation versus causation 67

Part 2: Number-crunching Basics 69

Chapter 5: Means, Medians, and More 71

Summing Up Data with Descriptive Statistics 71

Crunching Categorical Data: Tables and Percents 72

Measuring the Center with Mean and Median 75

Averaging out to the mean 75

Splitting your data down the median 77

Comparing means and medians: Histograms 78

Accounting for Variation 80

Reporting the standard deviation 81

Being out of range 84

Examining the Empirical Rule (68-95-99.7) 85

Measuring Relative Standing with Percentiles 87

Calculating percentiles 88

Interpreting percentiles 89

Gathering a five-number summary 93

Exploring interquartile range 94

Chapter 6: Getting the Picture: Graphing Categorical Data 95

Take Another Little Piece of My Pie Chart 96

Tallying personal expenses 96

Bringing in a lotto revenue 97

Ordering takeout 98

Projecting age trends 99

Raising the Bar on Bar Graphs 101

Tracking transportation expenses 101

Making a lotto profit 103

Tipping the scales on a bar graph 104

Pondering pet peeves 105

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Chapter 7: Going by the Numbers: Graphing Numerical Data 107

Handling Histograms 108

Making a histogram 108

Interpreting a histogram 111

Putting numbers with pictures 115

Detecting misleading histograms 117

Examining Boxplots 120

Making a boxplot 120

Interpreting a boxplot 121

Tackling Time Charts 127

Interpreting time charts 127

Understanding variability: Time charts versus histograms 128

Spotting misleading time charts 128

Part 3: Distributions and the Central Limit Theorem 133

Chapter 8: Random Variables and the Binomial Distribution 135

Defining a Random Variable 136

Discrete versus continuous 136

Probability distributions 137

The mean and variance of a discrete random variable 138

Identifying a Binomial 139

Checking binomial conditions step by step 140

No fixed number of trials 140

More than success or failure 141

Trials are not independent 141

Probability of success (p) changes 141

Finding Binomial Probabilities Using a Formula 142

Finding Probabilities Using the Binomial Table 144

Finding probabilities for specific values of X 145

Finding probabilities for X greater-than, less-than, or between two values 146

Checking Out the Mean and Standard Deviation of the Binomial 146

Chapter 9: The Normal Distribution 149

Exploring the Basics of the Normal Distribution 150

Meeting the Standard Normal (Z-) Distribution 152

Checking out Z 153

Standardizing from X to Z 153

Finding probabilities for Z with the Z-table 155

Finding Probabilities for a Normal Distribution 156

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Finding X When You Know the Percent 158

Figuring out a percentile for a normal distribution 159

Translating tricky wording in percentile problems 161

Normal Approximation to the Binomial 162

Chapter 10: The t-Distribution 165

Basics of the t-Distribution 165

Comparing the t- and Z-distributions 165

Discovering the effect of variability on t-distributions 167

Using the t-Table 167

Finding probabilities with the t-table 168

Figuring percentiles for the t-distribution 168

Picking out t*-values for confidence intervals 169

Studying Behavior Using the t-Table 170

Chapter 11: Sampling Distributions and the Central Limit

Theorem 171

Defining a Sampling Distribution 172

The Mean of a Sampling Distribution 174

Measuring Standard Error 174

Sample size and standard error 175

Population standard deviation and standard error 176

Looking at the Shape of a Sampling Distribution 178

Case 1: The distribution of X is normal 178

Case 2: The distribution of X is not normal-enter the Central Limit Theorem 178

Finding Probabilities for the Sample Mean 181

The Sampling Distribution of the Sample Proportion 183

Finding Probabilities for the Sample Proportion 185

Part 4: Guesstimating and Hypothesizing With Confidence 187

Chapter 12: Leaving Room for a Margin of Error 189

Seeing the Importance of That Plus or Minus 190

Finding the Margin of Error: A General Formula 191

Measuring sample variability 191

Calculating margin of error for a sample proportion 193