Statistics All-in-One For Dummies

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