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 μ 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
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