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
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
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
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
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
Reporting results 194
Calculating margin of error for a sample mean 195
Being confident you’re right 197
Determining the Impact of Sample Size 197
Sample size and margin of error 198
Bigger isn’t always (that much) better! 198
Keeping margin of error in perspective 199
Chapter 13: Confidence Intervals: Making Your Best Guesstimate 201
Not All Estimates Are Created Equal 202
Linking a Statistic to a Parameter 203
Getting with the Jargon 203
Interpreting Results with Confidence 204
Zooming In on Width 205
Choosing a Confidence Level 206
Factoring In the Sample Size 208
Counting On Population Variability 209
Calculating a Confidence Interval for a Population Mean 210
Case 1: Population standard deviation is known 210
Case 2: Population standard deviation is unknown and/or n is small 212
Figuring Out What Sample Size You Need 213
Determining the Confidence Interval for One Population Proportion 214
Creating a Confidence Interval for the Difference of Two Means 216
Case 1: Population standard deviations are known 216
Case 2: Population standard deviations are unknown and/or sample sizes are small 218
Estimating the Difference of Two Proportions 219
Spotting Misleading Confidence Intervals 221
Chapter 14: Claims, Tests, and Conclusions 223
Setting Up the Hypotheses 224
Defining the null 224
What’s the alternative? 225
Gathering Good Evidence (Data) 226
Compiling the Evidence: The Test Statistic 226
Gathering sample statistics 227
Measuring variability using standard errors 227
Understanding standard scores 228
Calculating and interpreting the test statistic 228
Weighing the Evidence and Making Decisions: p-Values 229
Connecting test statistics and p-values 229
Defining a p-value 230
Calculating a p-value 230
Making Conclusions 231
Setting boundaries for rejecting Ho 232
Testing varicose veins 233
Assessing the Chance of a Wrong Decision 233
Making a false alarm: Type-1 errors 234
Missing out on a detection: Type-2 errors 234
Chapter 15: Commonly Used Hypothesis Tests:
Formulas and Examples 237
Testing One Population Mean 238
Handling Small Samples and Unknown Standard Deviations: The t-Test 240
Putting the t-test to work 241
Relating t to Z 241
Handling negative t-values 242
Examining the not-equal-to alternative 242
Testing One Population Proportion 243
Comparing Two (Independent) Population Averages 245
Testing for an Average Difference (The Paired t-Test) 247
Comparing Two Population Proportions 251
Part 5: Statistical Studies And The Hunt For A Meaningful Relationship 255
Chapter 16: Polls, Polls, and More Polls 257
Recognizing the Impact of Polls 258
Getting to the source 258
Surveying what’s hot 260
Impacting lives 260
Behind the Scenes: The Ins and Outs of Surveys 262
Planning and designing a survey 263
Selecting the sample 266
Carrying out a survey 268
Interpreting results and finding problems 271
Chapter 17: Experiments: Medical Breakthroughs or Misleading Results? 275
Boiling Down the Basics of Studies 276
Looking at the lingo of studies 276
Observing observational studies 277
Examining experiments 278
Designing a Good Experiment 278
Designing the experiment to make comparisons 279
Selecting the sample size 281
Choosing the subjects 283
Making random assignments 283
Controlling for confounding variables 284
Respecting ethical issues 286
Collecting good data 287
Analyzing the data properly 289
Making appropriate conclusions 290
Making Informed Decisions 292
Chapter 18: Looking for Links: Correlation and Regression 293
Picturing a Relationship with a Scatterplot 294
Making a scatterplot 295
Interpreting a scatterplot 296
Quantifying Linear Relationships Using the Correlation 297
Calculating the correlation 297
Interpreting the correlation 298
Examining properties of the correlation 300
Working with Linear Regression 301
Figuring out which variable is X and which is Y 301
Checking the conditions 302
Calculating the regression line 302
Interpreting the regression line 304
Putting it all together with an example: The regression line for the crickets 306
Making Proper Predictions 306
Explaining the Relationship: Correlation versus Cause and Effect 308
Chapter 19: Two-Way Tables and Independence 311
Organizing a Two-Way Table 312
Setting up the cells 313
Figuring the totals 314
Interpreting Two-Way Tables 315
Singling out variables with marginal distributions 315
Examining all groups — a joint distribution 317
Comparing groups with conditional distributions 321
Checking Independence and Describing Dependence 324
Checking for independence 324
Describing a dependent relationship 327
Cautiously Interpreting Results 329
Checking for legitimate cause and effect 329
Projecting from sample to population 330
Making prudent predictions 331
Resisting the urge to jump to conclusions 332
Part 6: The Part Of Tens 333
Chapter 20: Ten Tips for the Statistically Savvy Sleuth 335
Pinpoint Misleading Graphs 335
Pie charts 336
Bar graphs 336
Time charts 337
Histograms 339
Uncover Biased Data 339
Search for a Margin of Error 340
Identify Non-Random Samples 341
Sniff Out Missing Sample Sizes 342
Detect Misinterpreted Correlations 343
Reveal Confounding Variables 344
Inspect the Numbers 344
Report Selective Reporting 345
Expose the Anecdote 346
Chapter 21: Ten Surefire Exam Score Boosters 349
Know What You Don’t Know, and then Do Something about It 350
Avoid “Yeah-Yeah” Traps 351
Yeah-yeah trap #1 352
Yeah-yeah trap #2 352
Make Friends with Formulas 354
Make an “If-Then-How” Chart 355
Figure Out What the Question Is Asking 357
Label What You’re Given 358
Draw a Picture 360
Make the Connection and Solve the Problem 361
Do the Math — Twice 362
Analyze Your Answers 363
Appendix: Tables For Reference 365
Index 375
