Introduction 1 About This Book 1 Foolish Assumptions 2 Icons Used in This Book 3 Beyond the Book 3 Where to Go from Here 4 Part 1: Getting Off to a Statistically Significant Start 5 Chapter 1: Summarizing Categorical Data: Counts and Percents 7 Counting On the Frequency 7 Relating with Percentages 9 Interpreting Counts and Percents with Caution 11 Answers to Problems in Summarizing Categorical Data 13 Chapter 2: Summarizing Quantitative Data: Means, Medians, and More 17 Finding and Interpreting Measures of Center 18 Finding and Interpreting Measures of Spread 20 Using Percentiles and the Interquartile Range 22 Answers to Problems in Summarizing Quantitative Data 24 Chapter 3: Organizing Categorical Data: Charts and Graphs 27 Making, Interpreting, and Evaluating Pie Charts 27 Making, Interpreting, and Evaluating Bar Graphs 32 Answers to Problems in Organizing Categorical Data 37 Chapter 4: Organizing Quantitative Data: Charts and Graphs 43 Creating a Histogram 44 Making Sense of Histograms 47 Straightening Out Skewed Data 51 Spotting a Misleading Histogram 53 Making Box Plots 55 Interpreting Box Plots 56 Looking at Line Graphs 58 Understanding the Empirical Rule 60 Answers to Problems in Organizing Quantitative Data 63 Part 2: Probability, Distributions, and the Central Limit Theorem (Are You Having Fun Yet?) 73 Chapter 5: Understanding Probability Basics 75 Grasping the Rules of Probability 75 Avoiding Probability Misconceptions 78 Making Predictions Using Probability 79 Answers to Problems in Probability 81 Chapter 6: Measures of Relative Standing and the Normal Distribution 83 Mastering the Normal Distribution 83 Finding and Interpreting Standard (Z) Scores 86 Knowing Where You Stand with Percentiles 88 Finding Probabilities for a Normal Distribution 90 Finding the Percentile (Backwards Normal) 92 Answers to Problems in Normal Distribution 95 Chapter 7: The Binomial Distribution 105 Characterizing the Binomial Distribution 105 Finding Probabilities Using the Binomial Formula for small n 107 Finding Probabilities Using the Binomial Table for Medium-Sized n 109 Calculating the Mean and Variance of the Binomial 110 Estimating Probabilities in Large Cases - the Normal Approximation 112 Answers to Problems in the Binomial Distribution 114 Chapter 8: The t-Distribution 117 Getting to Know the t-Distribution 117 Working with the t-Table and Degrees of Freedom 120 Answers to Problems in the t-Distribution 122 Chapter 9: Demystifying Sampling Distributions and the Central Limit Theorem 123 Exactly What is a Sampling Distribution? 124 Clearing Up the Central Limit Theorem (Once and for All) 126 Finding Probabilities with the Central Limit Theorem 129 When Your Sample's Too Small: Employing the t-Distribution 131 Answers to Problems in Sampling Distributions and the Central Limit Theorem 133 Part 3: Guesstimating and Hypothesizing with Confidence 137 Chapter 10: Making Sense of Margin of Error 139 Reviewing Margin of Error 139 Calculating the Margin of Error for Means and Proportions 142 Increasing and Decreasing Margin of Error 144 Interpreting Margin of Error Correctly 146 Answers to Problems in Making Sense of Margin of Error 148 Chapter 11: Calculating Confidence Intervals 151 Walking through a Confidence Interval 151 Deriving a Confidence Interval for a Population Mean 154 Figuring a Confidence Interval for a Population Proportion 156 Calculating a Confidence Interval for the Difference of Two Means 158 Computing a Confidence Interval for the Difference of Two Proportions 160 Answers to Problems in Calculating Confidence Intervals 163 Chapter 12: Deciphering Your Confidence Interval 169 Interpreting Confidence Intervals the Right Way 169 Evaluating Confidence Interval Results: What the Formulas Don't Tell You 173 Answers to Problems in Confidence Intervals 175 Chapter 13: Testing Hypotheses 177 Walking Through a Hypothesis Test 177 Testing a Hypothesis about a Population Mean 181 Testing a Hypothesis about a Population Proportion 183 Testing for a Difference between Two Population Means 185 Testing for a Mean Difference (Paired t-Test) 188 Testing a Hypothesis about Two Population Proportions 190 Answers to Problems in Testing Hypotheses 192 Chapter 14: Taking the Guesswork Out of p-Values and Type I and II Errors 197 Understanding What p-Values Measure 198 Test (Statistic) Time: Figuring Out p-Values 199 The Value Breakdown: Interpreting p-Values Properly 201 Deciphering Type I Errors 204 Deciphering and Distinguishing Type II Errors 205 Answers to Problems in p-Values and Type I and II Errors 208 Part 4: Statistical Studies and the Hunt for a Meaningful Relationship 211 Chapter 15: Examining Polls and Surveys 213 Planning and Designing a Survey 214 Selecting a Random Sample 215 Carrying Out a Survey Properly 217 Interpreting and Evaluating Survey Results 218 Answers to Problems in Polls and Surveys 220 Chapter 16: Evaluating Experiments 223 Distinguishing Experiments from Observational Studies 223 Designing a Good Experiment 225 Looking for Cause and Effect: Interpreting Experiment Results 228 Answers to Problems in Evaluating Experiments 230 Chapter 17: Looking for Links in Categorical Data: Two-Way Tables 233 Understanding Two-Way Tables Inside and Out 234 Working with Intersection, Unions, and the Addition Rule 237 Figuring Marginal Probabilities 240 Nailing Down Conditional Probabilities and the Multiplication Rule 242 Inspecting the Independence of Categorical Variables 246 Answers to Problems in Two-Way Tables 250 Chapter 18: Searching for Links in Quantitative Data: Correlation and Regression 259 Relating X and Y with a Scatterplot 259 Toeing the Line of Correlation 262 Picking Out the Best Fitting Regression Line 265 Interpreting the Regression Line and Making Predictions 267 Checking the Fit of the Regression Line 269 Answers to Problems in Correlation and Regression 272 Part 5: The Part of Tens 277 Chapter 19: Math Review: Ten Steps to a Better Grade 279 Know Your Math Symbols 279 Uproot Roots and Powers 280 Treat Fractions with Extra Care 280 Obey the Order of Operations 281 Avoid Rounding Errors 282 Get Comfortable with Formulas 283 Stay Calm When Formulas Get Tough 283 Feel Fine about Functions 285 Know When Your Answer is Wrong 286 Show Your Work 287 Chapter 20: Top Ten Statistical Formulas 289 Mean (or Average) 289 Median 290 Sample Standard Deviation 291 Correlation 292 Margin of Error for the Sample Mean 293 Sample Size Needed for Estimating 294 Test Statistic for the Mean 295 Margin of Error for the Sample Proportion 296 Sample Size Needed for Estimating p 297 Test Statistic for the Proportion 298 Chapter 21: Ten Ways to Spot Common Statistical Mistakes 301 Scrutinizing Graphs 301 Searching for and Specifying Bias 302 Marking the Margin of Error 303 Scanning for Sample Size 303 Studying Sample Selection (Gotta Be Random) 304 Checking for Confounding Variables 305 Considering Correlation 305 Doing the Math 306 Detecting Selective Reporting 306 Avoiding the Anecdote 307 Appendix: Tables for Reference 309 Index 319
Deborah J. Rumsey, PhD is a longtime statistics professor at The Ohio State University specializing in statistics education. She authored Statistics For Dummies, Statistics II For Dummies, and Probability For Dummies.