Statistics All-in-One For Dummies

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 Unit 1: Getting Started with Statistics 5 Chapter 1: The Statistics of Everyday Life 7 Statistics and the Media: More Questions than Answers? 8 Probing popcorn problems 8 Venturing into viruses 8 Comprehending crashes 9 Mulling malpractice 9 Belaboring the loss of land 10 Scrutinizing schools 10 Scanning sports 10 Banking on business news 11 Touring the travel news 12 Surveying sexual stats 12 Breaking down weather reports 13 Using Statistics at Work 13 Delivering babies — and information 13 Posing for pictures 14 Poking through pizza data 14 Statistics in the office 14 Chapter 2: Taking Control: So Many Numbers, So Little Time 15 Detecting Errors, Exaggerations, and Just Plain Lies 16 Checking the math 16 Uncovering misleading statistics 17 Looking for lies in all the right places 22 Feeling the Impact of Misleading Statistics 23 Chapter 3: Tools of the Trade 25 Thriving in a Statistical World 25 Statistics: More than Just Numbers 26 Designing Appropriate Studies 28 Surveys (Polls) 28 Experiments 29 Collecting Quality Data 30 Sample, random, or otherwise 30 Bias 32 Grabbing Some Basic Statistical Jargon 33 Data 33 Data set 34 Variable 34 Population 34 Statistic 35 Parameter 35 Mean (Average) 36 Median 36 Standard deviation 36 Percentile 37 Standard score 37 Distribution and normal distribution 38 Central Limit Theorem 38 z-values 39 Margin of error 39 Confidence interval 40 Hypothesis testing 41 p-values 42 Statistical significance 42 Correlation, regression, and two-way tables 43 Drawing Credible Conclusions 44 Reeling in overstated results 44 Questioning claims of cause and effect 44 Becoming a Sleuth, Not a Skeptic 45 Unit 2: Number-Crunching Basics 47 Chapter 4: Crunching Categorical Data 49 Summing Up Data with Descriptive Statistics 49 Crunching Categorical Data: Tables and Percents 50 Counting on the frequency 50 Relating with percentages 52 Two-way tables: Summarizing multiple measures 54 Interpreting counts and percents with caution 55 Practice Questions Answers and Explanations 57 Whaddya Know? Chapter 4 Quiz 60 Answers to Chapter 4 Quiz 62 Chapter 5: Means, Medians, and More 65 Measuring the Center with Mean and Median 65 Averaging out to the mean 66 Splitting your data down the median 68 Comparing means and medians: Histograms 70 Accounting for Variation 74 Reporting the standard deviation 75 Being out of range 78 Examining the Empirical Rule (68-95-99.7) 79 Measuring Relative Standing with Percentiles 83 Calculating percentiles 83 Interpreting percentiles 85 Gathering a five-number summary 88 Exploring interquartile range 89 Practice Questions Answers and Explanations 90 Whaddya Know? Chapter 5 Quiz 97 Answers to Chapter 5 Quiz 98 Chapter 6: Getting the Picture: Graphing Categorical Data 99 Take Another Little Piece of My Pie Chart 100 Tallying personal expenses 100 Bringing in a lotto revenue 101 Ordering takeout 102 Projecting age trends 103 Raising the Bar on Bar Graphs 108 Tracking transportation expenses 108 Making a lotto profit 110 Tipping the scales on a bar graph 110 Pondering pet peeves 111 Practice Questions Answers and Explanations 117 Whaddya Know? Chapter 6 Quiz 123 Answers to Chapter 6 Quiz 124 Chapter 7: Going by the Numbers: Graphing Numerical Data 125 Handling Histograms 126 Making a histogram 126 Interpreting a histogram 130 Putting numbers with pictures 137 Detecting misleading histograms 139 Examining Boxplots 143 Making a boxplot 143 Interpreting a boxplot 146 Tackling Time Charts 152 Interpreting time charts 152 Understanding variability: Time charts versus histograms 153 Spotting misleading time charts 153 Practice Questions Answers and Explanations 159 Whaddya Know? Chapter 7 Quiz 165 Answers to Chapter 7 Quiz 166 Unit 3: Distributions and the Central Limit Theorem 167 Chapter 8: Coming to Terms with Probability 169 A Set Notation Overview 169 Noting outcomes: Sample spaces 170 Noting subsets of sample spaces: Events 171 Noting a void in the set: Empty sets 172 Putting sets together: Unions, intersections, and complements 172 Probabilities of Events Involving A and/or B 173 Probability notation 174 Marginal probabilities 175 Union probabilities 175 Intersection ( joint) probabilities 175 Complement probabilities 176 Conditional probabilities 176 Understanding and Applying the Rules of Probability 178 The complement rule (for opposites, not for flattering a date) 178 The multiplication rule (for intersections, not for rabbits) 179 The addition rule (for unions of the nonmarital nature) 180 Recognizing Independence in Multiple Events 182 Checking independence for two events with the definition 182 Using the multiplication rule for independent events 183 Including Mutually Exclusive Events 184 Recognizing mutually exclusive events 184 Simplifying the addition rule with mutually exclusive events 185 Distinguishing Independent from Mutually Exclusive Events 186 Comparing and contrasting independence and exclusivity 186 Checking for independence or exclusivity in a 52-card deck 187 Avoiding Probability Misconceptions 189 Predictions Using Probability 190 Practice Questions Answers and Explanations 192 Whaddya Know? Chapter 8 Quiz 196 Answers to Chapter 8 Quiz 197 Chapter 9: Random Variables and the Binomial Distribution 199 Defining a Random Variable 200 Discrete versus continuous 200 Probability distributions 202 The mean and variance of a discrete random variable 202 Identifying a Binomial 203 Checking binomial conditions step by step 204 No fixed number of trials 204 More than success or failure 205 Trials are not independent 205 Probability of success (p) changes 205 Finding Binomial Probabilities Using a Formula 207 Finding Probabilities Using the Binomial Table 210 Finding probabilities for specific values of X 210 Finding probabilities for X greater-than, less-than, or between two values 211 Checking Out the Mean and Standard Deviation of the Binomial 212 Practice Questions Answers and Explanations 214 Whaddya Know? Chapter 9 Quiz 216 Answers to Chapter 9 Quiz 217 Chapter 10: The Normal Distribution 219 Exploring the Basics of the Normal Distribution 219 Meeting the Standard Normal (Z-) Distribution 223 Checking out Z 223 Standardizing from X to Z 223 Finding probabilities for Z with the Z-table 225 Finding Probabilities for a Normal Distribution 227 Knowing Where You Stand with Percentiles 230 Finding X When You Know the Percent 232 Figuring out a percentile for a normal distribution 232 Translating tricky wording in percentile problems 234 Normal Approximation to the Binomial 236 Practice Questions Answers and Explanations 239 Whaddya Know? Chapter 10 Quiz 248 Answers to Chapter 10 Quiz 249 Chapter 11: The t-Distribution 251 Basics of the t-Distribution 251 Comparing the t- and Z-distributions 251 Discovering the effect of variability on t-distributions 252 Using the t-Table 253 Finding probabilities with the t-table 253 Figuring percentiles for the t-distribution 256 Picking out t*-values for confidence intervals 257 Studying Behavior Using the t-Table 258 Practice Questions Answers and Explanations 259 Whaddya Know? Chapter 11 Quiz 260 Answers to Chapter 11 Quiz 261 Chapter 12: Sampling Distributions and the Central Limit Theorem 263 Defining a Sampling Distribution 264 The Mean of a Sampling Distribution 265 Measuring Standard Error 266 Sample size and standard error 266 Population standard deviation and standard error 267 Looking at the Shape of a Sampling Distribution 269 Case 1: The distribution of X is normal 269 Case 2: The distribution of X is not normal — Enter the Central Limit Theorem 269 Finding Probabilities for the Sample Mean 273 The Sampling Distribution of the Sample Proportion 275 Finding Probabilities for the Sample Proportion 278 Practice Questions Answers and Explanations 280 Whaddya Know? Chapter 12 Quiz 283 Answers to Chapter 12 Quiz 284 Unit 4: Guesstimating and Hypothesizing with Confidence 285 Chapter 13: Leaving Room for a Margin of Error 287 Seeing the Importance of that Plus or Minus 287 Finding the Margin of Error: A General Formula 289 Measuring sample variability 289 Calculating margin of error for a sample proportion 291 Reporting results 293 Calculating margin of error for a sample mean 293 Being confident you’re right 294 Determining the Impact of Sample Size 296 Sample size and margin of error 296 Bigger isn’t always (that much) better! 297 Keeping margin of error in perspective 297 Practice Questions Answers and Explanations 300 Whaddya Know? Chapter 13 Quiz 303 Answers to Chapter 13 Quiz 304 Chapter 14: Confidence Intervals: Making Your Best Guesstimate 305 Not All Estimates Are Created Equal 306 Linking a Statistic to a Parameter 306 Getting with the Jargon 307 Interpreting Results with Confidence 308 Zooming In on Width 310 Choosing a Confidence Level 310 Factoring In the Sample Size 312 Counting On Population Variability 313 Calculating a Confidence Interval for a Population Mean 315 Case 1: Population standard deviation is known 315 Case 2: Population standard deviation is unknown and/or n is small 316 Figuring Out What Sample Size You Need 318 Determining the Confidence Interval for One Population Proportion 319 Creating a Confidence Interval for the Difference of Two Means 322 Case 1: Population standard deviations are known 322 Case 2: Population standard deviations are unknown and/or sample sizes are small 323 Estimating the Difference of Two Proportions 326 Spotting Misleading Confidence Intervals 329 Practice Questions Answers and Explanations 330 Whaddya Know? Chapter 14 Quiz 337 Answers to Chapter 14 Quiz 339 Chapter 15: Claims, Tests, and Conclusions 341 Setting Up the Hypotheses 342 Defining the null 342 What’s the alternative? 343 Gathering Good Evidence (Data) 343 Compiling the Evidence: The Test Statistic 344 Gathering sample statistics 344 Measuring variability using standard errors 344 Understanding standard scores 345 Calculating and interpreting the test statistic 345 Weighing the Evidence and Making Decisions: p-Values 346 Connecting test statistics and p-values 346 Defining a p-value 347 Calculating a p-value 347 Making Conclusions 349 Setting boundaries for rejecting H0 350 Testing varicose veins 350 Assessing the Chance of a Wrong Decision 352 Making a false alarm: Type I errors 353 Missing out on a detection: Type II errors 353 Practice Questions Answers and Explanations 356 Whaddya Know? Chapter 15 Quiz 359 Answers to Chapter 15 Quiz 360 Chapter 16: Commonly Used Hypothesis Tests: Formulas and Examples 361 Testing One Population Mean 362 Handling Small Samples and Unknown Standard Deviations: The t-Test 363 Putting the t-test to work 364 Relating t to Z 365 Handling negative t-values 365 Examining the not-equal-to alternative 365 Drawing conclusions using the critical value 366 Testing One Population Proportion 368 Comparing Two (Independent) Population Averages 371 Case 1: Difference of two population means when population standard deviations are known 371 Case 2: Difference of two population means when population standard deviations are unknown 374 Testing for an Average Difference (The Paired t-Test) 375 Comparing Two Population Proportions 378 Practice Questions Answers and Explanations 382 Whaddya Know? Chapter 16 Quiz 387 Answers to Chapter 16 Quiz 388 Unit 5: Statistical Studies and the Hunt for a Meaningful Relationship 389 Chapter 17: Polls, Polls, and More Polls 391 Recognizing the Impact of Polls 392 Getting to the source 392 Surveying what’s hot 393 Impacting lives 394 Behind the Scenes: The Ins and Outs of Surveys 395 Planning and designing a survey 396 Selecting the sample 399 Carrying out a survey 402 Interpreting results and finding problems 405 Practice Questions Answers and Explanations 408 Whaddya Know? Chapter 17 Quiz 411 Answers to Chapter 17 Quiz 412 Chapter 18: Experiments and Observational Studies: Medical Breakthroughs or Misleading Results? 413 Boiling Down the Basics of Studies 414 Looking at the lingo of studies 414 Observing observational studies 415 Examining experiments 415 Designing a Good Experiment 417 Designing the experiment to make comparisons 417 Selecting the sample size 419 Choosing the subjects 421 Making random assignments 421 Controlling for confounding variables 422 Respecting ethical issues 423 Collecting good data 424 Analyzing the data properly 425 Interpreting Experiment Results 428 Making appropriate conclusions 428 Making informed decisions 429 Practice Questions Answers and Explanations 431 Whaddya Know? Chapter 18 Quiz 433 Answers to Chapter 18 Quiz 434 Chapter 19: Looking for Links: Correlation and Regression 435 Picturing a Relationship with a Scatterplot 436 Making a scatterplot 436 Interpreting a scatterplot 437 Quantifying Linear Relationships Using the Correlation 440 Calculating the correlation 440 Interpreting the correlation 441 Examining properties of the correlation 443 Working with Linear Regression 445 Figuring out which variable is X and which is Y 445 Checking the conditions 446 Calculating the regression line 446 Interpreting the regression line 449 Putting it all together: The regression line for the crickets 451 Making Proper Predictions 453 Checking the conditions 453 Staying in-bounds 454 Regression Analysis: Understanding the Output 456 Residing with Residuals 457 Explaining the Relationship: Correlation versus Cause and Effect 458 Practice Questions Answers and Explanations 460 Whaddya Know? Chapter 19 Quiz 465 Answers to Chapter 19 Quiz 466 Chapter 20: Two-Way Tables and Independence 467 Organizing a Two-Way Table 468 Setting up the cells 469 Figuring the totals 469 Interpreting Two-Way Tables 472 Singling out variables with marginal distributions 472 Examining all groups — a joint distribution 476 Comparing groups with conditional distributions 478 Checking Independence and Describing Dependence 483 Checking for independence 484 Describing a dependent relationship 486 Cautiously Interpreting Results 489 Checking for legitimate cause and effect 489 Projecting from sample to population 490 Making prudent predictions 491 Resisting the urge to jump to conclusions 491 Practice Questions Answers and Explanations 492 Whaddya Know? Chapter 20 Quiz 498 Answers to Chapter 20 Quiz 500 Appendix: Tables for Reference 503 The Z-Table 503 The t-Table 506 The Binomial Table 508 Index 513