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The odds-on best way to master stats.
Statistics All-in-One For Dummies is packed with lessons, examples, and practice problems to help you slay your stats course. Develop confidence and understanding in statistics with easy-to-understand (even fun) explanations of key concepts. Plus, you’ll get access to online chapter quizzes and other resources that will turn you into a stats master. This book teaches you how to interpret graphs, determine probability, critique data, and so much more. Written by an expert author and serious statistics nerd, Statistics AIO For Dummies explains everything in terms anyone can understand.
Statistics All-in-One For Dummies follows the curriculum of intro college statistics courses (including AP Stats!) so you can learn everything you need to know to get the grade you need—the Dummies way.
Deborah Rumsey, PhD, is a Professor of Statistics and Statistics Education Specialist at The Ohio State University. She is the author of Statistics For Dummies, Statistics Workbook For Dummies, Statistics II For Dummies, and Probability 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
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