Statistics for Dummies
Biographical Note: 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. Jacket Description/Back: Grasp statistical ideas, formulas, and calculations Interpret graphs and polls and determine probability Analyze data using many techniques The simple way to study statistics Stymied by statistics? Fear not! In easy-to-understand terms, this guide shows you how to make sense of statistics. From collecting, graphing, and critiquing data to calculating confidence intervals and hypothesis tests, you'll have everything you need to analyze data with confidence. In no time, you'll be deciphering binomial, normal, t-, and sampling distributions; tackling regression and two-way tables; and much more. Inside... Plain-English definitions Understanding and critiquing polls Information on organizing data Explanations of random variables Facts about the Central Limit Theorem Data analysis tools Table of Contents: Introduction 1 Part 1: Vital Statistics about Statistics 7 Chapter 1: Statistics in a Nutshell 9 Chapter 2: The Statistics of Everyday Life 23 Chapter 3: Taking Control: So Many Numbers, So Little Time 35 Chapter 4: Tools of the Trade 47 Part 2: Number-Crunching Basics 69 Chapter 5: Means, Medians, and More 71 Chapter 6: Getting the Picture: Graphing Categorical Data 95 Chapter 7: Going by the Numbers: Graphing Numerical Data 107 Part 3: Distributions and the Central Limit Theorem 133 Chapter 8: Random Variables and the Binomial Distribution 135 Chapter 9: The Normal Distribution 149 Chapter 10: The t-Distribution 165 Chapter 11: Sampling Distributions and the Central Limit Theorem 171 Part 4: Guesstimating and Hypothesizing with Confidence 187 Chapter 12: Leaving Room for a Margin of Error 189 Chapter 13: Confidence Intervals: Making Your Best Guesstimate 201 Chapter 14: Claims, Tests, and Conclusions 223 Chapter 15: Commonly Used Hypothesis Tests: Formulas and Examples 237 Part 5: Statistical Studies and the Hunt for a Meaningful Relationship 255 Chapter 16: Polls, Polls, and More Polls 257 Chapter 17: Experiments: Medical Breakthroughs or Misleading Results? 275 Chapter 18: Looking for Links: Correlation and Regression 293 Chapter 19: Two-Way Tables and Independence 311 Part 6: The Part of Tens 333 Chapter 20: Ten Tips for the Statistically Savvy Sleuth 335 Chapter 21: Ten Surefire Exam Score Boosters 349 Appendix: Tables for Reference 365 Index 375 0002730987.indd III May 5, 2016 4:00 Pm 0002730987.indd IV May 5, 2016 4:00 Pm Table of Contents 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 Table of Contents v 0002730987.indd V May 5, 2016 4:00 Pm 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 vi Statistics for Dummies 0002730987.indd VI May 5, 2016 4:00 Pm 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 Table of Contents vii 0002730987.indd VII May 5, 2016 4:00 Pm 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 viii Statistics for Dummies 0002730987.indd VIII May 5, 2016 4:00 Pm 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 Table of Contents ix 0002730987.indd IX May 5, 2016 4:00 Pm 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 H o 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 x Statistics for Dummies 0002730987.indd X May 5, 2016 4:00 Pm 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 Table of Contents xi 0002730987.indd XI May 5, 2016 4:00 Pm 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 xii Statistics for Dummies 0002730987.indd XII May 5, 2016 4:00 Pm 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 Table of Contents xiii 0002730987.indd XIII May 5, 2016 4:00 Pm 0002730987.INDD xiv May 5, 2016 4:00 PM Author: Rumsey, Deborah JPublisher: For DummiesBinding: PaperbackPub Date: 2016-06-07BISAC: Mathematics / Probability & Statistics / Multivariate Analysis|Education / Teaching / Subjects - Mathematics|Education / Statistics|Business & Economics / StatisticsSubjects: StatisticsWeight: 1.2 lbsISBN: 9781119293521ASIN: -SKU: SP-9781119293521
