Statistics For Dummies

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

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