Statistics II for dummies

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Statistics II for dummies

by Deborah J. Rumsey

（--For dummies）

John Wiley & Sons, c2022

2nd ed

  • : pbk

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Statistics two for dummies

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Includes index

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Description

Continue your statistics journey with this all-encompassing reference Completed Statistics through standard deviations, confidence intervals, and hypothesis testing? Then you're ready for the next step: Statistics II. And there's no better way to tackle this challenging subject than with Statistics II For Dummies! Get a brief overview of Statistics I in case you need to brush up on earlier topics, and then dive into a full explanation of all Statistic II concepts, including multiple regression, analysis of variance (ANOVA), Chi-square tests, nonparametric procedures, and analyzing large data sets. By the end of the book, you'll know how to use all the statistics tools together to create a great story about your data. For each Statistics II technique in the book, you get an overview of when and why it's used, how to know when you need it, step-by-step directions on how to do it, and tips and tricks for working through the solution. You also find: What makes each technique distinct and what the results say How to apply techniques in real life An interpretation of the computer output for data analysis purposes Instructions for using Minitab to work through many of the calculations Practice with a lot of examples With Statistics II For Dummies, you will find even more techniques to analyze a set of data. Get a head start on your Statistics II class, or use this in conjunction with your textbook to help you thrive in statistics!

Table of Contents

Introduction 1 About This Book 1 Foolish Assumptions 3 Icons Used in This Book 3 Beyond the Book 4 Where to Go from Here 4 Part 1: Tackling Data Analysis and Model-Building Basics 7 Chapter 1: Beyond Number Crunching: The Art and Science of Data Analysis 9 Data Analysis: Looking before You Crunch 9 Nothing (not even a straight line) lasts forever 10 Data snooping isn't cool 11 No (data) fishing allowed 12 Getting the Big Picture: An Overview of Stats II 13 Population parameter 13 Sample statistic 13 Confidence interval 14 Hypothesis test 14 Analysis of variance (ANOVA) 15 Multiple comparisons 15 Interaction effects 16 Correlation 16 Linear regression 17 Chi-square tests 18 Chapter 2: Finding the Right Analysis for the Job 21 Categorical versus Quantitative Variables 22 Statistics for Categorical Variables 23 Estimating a proportion 23 Comparing proportions 24 Looking for relationships between categorical variables 25 Building models to make predictions 26 Statistics for Quantitative Variables 27 Making estimates 27 Making comparisons 28 Exploring relationships 28 Predicting y using x 30 Avoiding Bias 31 Measuring Precision with Margin of Error 33 Knowing Your Limitations 35 Chapter 3: Having the Normal and Sampling Distributions in Your Back Pocket 37 Recognizing the VIP Distribution - the Normal 38 Characterizing the normal 38 Standardizing to the standard normal (Z-) distribution 38 Using the normal table 40 Finding probabilities for the normal distribution 41 Finally Getting Comfortable with Sampling Distributions 42 The mean and standard error of a sampling distribution 42 Sampling distribution of X 43 Sampling distribution of p 44 Heads Up! Building Confidence Intervals and Hypothesis Tests 45 Confidence interval for the population mean 45 Confidence interval for the population proportion 46 Hypothesis test for population mean 46 Hypothesis test for the population proportion 47 Chapter 4: Reviewing Confidence Intervals and Hypothesis Tests 49 Estimating Parameters by Using Confidence Intervals 50 Getting the basics: The general form of a confidence interval 50 Finding the confidence interval for a population mean 51 What changes the margin of error? 52 Interpreting a confidence interval 55 What's the Hype about Hypothesis Tests? 56 What Ho and Ha really represent 56 Gathering your evidence into a test statistic 57 Determining strength of evidence with a p-value 57 False alarms and missed opportunities: Type I and II errors 58 The power of a hypothesis test 60 Part 2: Using Different Types of Regression to Make Predictions 65 Chapter 5: Getting in Line with Simple Linear Regression 67 Exploring Relationships with Scatterplots and Correlations 68 Using scatterplots to explore relationships 69 Collating the information by using the correlation coefficient 70 Building a Simple Linear Regression Model 71 Finding the best-fitting line to model your data 72 The y-intercept of the regression line 73 The slope of the regression line 74 Making point estimates by using the regression line 75 No Conclusion Left Behind: Tests and Confidence Intervals for Regression 75 Scrutinizing the slope 76 Inspecting the y-intercept 78 Building confidence intervals for the average response 80 Making the band with prediction intervals 81 Checking the Model's Fit (The Data, Not the Clothes!) 83 Defining the conditions 84 Finding and exploring the residuals 85 Using r2 to measure model fit 89 Scoping for outliers 90 Knowing the Limitations of Your Regression Analysis 92 Avoiding slipping into cause-and-effect mode 92 Extrapolation: The ultimate no-no 93 Sometimes you need more than one variable 94 Chapter 6: Multiple Regression with Two X Variables 95 Getting to Know the Multiple Regression Model 96 Discovering the uses of multiple regression 96 Looking at the general form of the multiple regression model 96 Stepping through the analysis 97 Looking at x's and y's 97 Collecting the Data 98 Pinpointing Possible Relationships 100 Making scatterplots 100 Correlations: Examining the bond 101 Checking for Multicolinearity 104 Finding the Best-Fitting Model for Two x Variables 105 Getting the multiple regression coefficients 106 Interpreting the coefficients 107 Testing the coefficients 108 Predicting y by Using the x Variables 110 Checking the Fit of the Multiple Regression Model 111 Noting the conditions 112 Plotting a plan to check the conditions 112 Checking the three conditions 114 Chapter 7: How Can I Miss You If You Won't Leave? Regression Model Selection 117 Getting a Kick out of Estimating Punt Distance 118 Brainstorming variables and collecting data 118 Examining scatterplots and correlations 120 Just Like Buying Shoes: The Model Looks Nice, But Does It Fit? 123 Assessing the fit of multiple regression models 124 Model selection procedures 125 Chapter 8: Getting Ahead of the Learning Curve with Nonlinear Regression 129 Anticipating Nonlinear Regression 130 Starting Out with Scatterplots 131 Handling Curves in the Road with Polynomials 133 Bringing back polynomials 134 Searching for the best polynomial model 136 Using a second-degree polynomial to pass the quiz 138 Assessing the fit of a polynomial model 141 Making predictions 143 Going Up? Going Down? Go Exponential! 145 Recollecting exponential models 145 Searching for the best exponential model 146 Spreading secrets at an exponential rate 148 Chapter 9: Yes, No, Maybe So: Making Predictions by Using Logistic Regression 153 Understanding a Logistic Regression Model 154 How is logistic regression different from other regressions? 154 Using an S-curve to estimate probabilities 155 Interpreting the coefficients of the logistic regression model 156 The logistic regression model in action 157 Carrying Out a Logistic Regression Analysis 158 Running the analysis in Minitab 158 Finding the coefficients and making the model 160 Estimating p 161 Checking the fit of the model 162 Fitting the movie model 162 Part 3: Analyzing Variance with Anova 167 Chapter 10: Testing Lots of Means? Come On Over to ANOVA! 169 Comparing Two Means with a t-Test 170 Evaluating More Means with ANOVA 171 Spitting seeds: A situation just waiting for ANOVA 172 Walking through the steps of ANOVA 173 Checking the Conditions 174 Verifying independence 174 Looking for what's normal 174 Taking note of spread 176 Setting Up the Hypotheses 178 Doing the F-Test 179 Running ANOVA in Minitab 180 Breaking down the variance into sums of squares 180 Locating those mean sums of squares 182 Figuring the F-statistic 183 Making conclusions from ANOVA 184 What's next? 186 Checking the Fit of the ANOVA Model 186 Chapter 11: Sorting Out the Means with Multiple Comparisons 189 Following Up after ANOVA 190 Comparing cellphone minutes: An example 190 Setting the stage for multiple comparison procedures 192 Pinpointing Differing Means with Fisher and Tukey .193 Fishing for differences with Fisher's LSD 194 Separating the turkeys with Tukey's test 197 Examining the Output to Determine the Analysis 198 So Many Other Procedures, So Little Time! 199 Controlling for baloney with the Bonferroni adjustment 200 Comparing combinations by using Scheffe's method 201 Finding out whodunit with Dunnett's test 202 Staying cool with Student Newman-Keuls 202 Duncan's multiple range test 202 Chapter 12: Finding Your Way through Two-Way ANOVA 205 Setting Up the Two-Way ANOVA Model 206 Determining the treatments 206 Stepping through the sums of squares 207 Understanding Interaction Effects 209 What is interaction, anyway? 209 Interacting with interaction plots 210 Testing the Terms in Two-Way ANOVA .213 Running the Two-Way ANOVA Table 214 Interpreting the results: Numbers and graphs 214 Are Whites Whiter in Hot Water? Two-Way ANOVA Investigates 217 Chapter 13: Regression and ANOVA: Surprise Relatives! 221 Seeing Regression through the Eyes of Variation 222 Spotting variability and finding an "x-planation" 222 Getting results with regression 223 Assessing the fit of the regression model 225 Regression and ANOVA: A Meeting of the Models 226 Comparing sums of squares 226 Dividing up the degrees of freedom 228 Bringing regression to the ANOVA table 229 Relating the F- and t-statistics: The final frontier 230 Part 4: Building Strong Connections with Chi-Square Tests and Nonparametrics 233 Chapter 14: Forming Associations with Two-Way Tables 235 Breaking Down a Two-Way Table 236 Organizing data into a two-way table 236 Filling in the cell counts 237 Making marginal totals 238 Breaking Down the Probabilities 239 Marginal probabilities 239 Joint probabilities 241 Conditional probabilities 242 Trying To Be Independent 247 Checking for independence between two categories 247 Checking for independence between two variables 249 Demystifying Simpson's Paradox 250 Experiencing Simpson's Paradox 250 Figuring out why Simpson's Paradox occurs 253 Keeping one eye open for Simpson's Paradox 254 Chapter 15: Being Independent Enough for the Chi-Square Test 257 The Chi-Square Test for Independence 258 Collecting and organizing the data 259 Determining the hypotheses 261 Figuring expected cell counts 261 Checking the conditions for the test 262 Calculating the Chi-square test statistic 263 Finding your results on the Chi-square table 266 Drawing your conclusions 269 Putting the Chi-square to the test 271 Comparing Two Tests for Comparing Two Proportions 272 Getting reacquainted with the Z-test for two population proportions 273 Equating Chi-square tests and Z-tests for a two-by-two table 274 Chapter 16: Using Chi-Square Tests for Goodness-of-Fit (Your Data, Not Your Jeans) 279 Finding the Goodness-of-Fit Statistic 280 What's observed versus what's expected 280 Calculating the goodness-of-fit statistic 282 Interpreting the Goodness-of-Fit Statistic Using a Chi-Square 284 Checking the conditions before you start 285 The steps of the Chi-square goodness-of-fit test 286 Chapter 17: Rebels Without a Distribution - Nonparametric Procedures 291 Arguing for Nonparametric Statistics 292 No need to fret if conditions aren't met 292 The median's in the spotlight for a change 293 So, what's the catch? 295 Mastering the Basics of Nonparametric Statistics 296 Sign 296 Chapter 18: All Signs Point to the Sign Test 299 Reading the Signs: The Sign Test 300 Testing the median in real estate 302 Estimating the median 304 Testing matched pairs 306 Part 5: Putting it all Together: Multi-Stage Analysis of A Large Data Set 309 Chapter 19: Conducting a Multi-Stage Analysis of a Large Data Set 311 Steps Involved in Working with a Large Data Set 311 Wrangling Data 313 Discovery 313 Structuring 314 Cleaning 315 Enriching 315 Validating 316 Publishing 317 Visualizing Data 317 Exploring the Data 319 Looking for Relationships 319 Building Models and Making Inferences 320 Sharing the Story 321 Who is the audience? 322 Make an outline 322 Include an executive summary 323 Check your writing 323 Chapter 20: A Statistician Watches the Movies 325 Examining the Movie Variables and Asking Questions 326 Visualizing the Movie Data 327 Categorical movie variables 328 Quantitative movie variables 329 Doing Descriptive Dirty Work 332 Looking for Relationships 333 Relationships between quantitative movie variables 333 Relationships between two categorical variables 337 Relationships between quantitative and categorical variables 338 Building a Model for Predicting U.S Revenue 340 Writing It Up 343 Chapter 21: Looking Inside the Refrigerator 347 Refrigerator Data - The Variables 348 Exploring the Data 348 Analyzing the Data 350 Writing It Up 358 Part 6: The Part of Tens 361 Chapter 22: Ten Common Errors in Statistical Conclusions 363 Claiming These Statistics Prove 363 It's Not Technically Statistically Significant, But 364 Concluding That x Causes y 365 Assuming the Data Was Normal 366 Only Reporting "Important" Results 366 Assuming a Bigger Sample Is Always Better 367 It's Not Technically Random, But 369 Assuming That 1,000 Responses Is 1,000 Responses 369 Of Course the Results Apply to the General Population 371 Deciding Just to Leave It Out 372 Chapter 23: Ten Ways to Get Ahead by Knowing Statistics 375 Asking the Right Questions 375 Being Skeptical 376 Collecting and Analyzing Data Correctly 377 Calling for Help 378 Retracing Someone Else's Steps 379 Putting the Pieces Together 379 Checking Your Answers 380 Explaining the Output 381 Making Convincing Recommendations 382 Establishing Yourself as the Statistics Go-To Person 383 Chapter 24: Ten Cool Jobs That Use Statistics 385 Pollster 386 Data Scientist 387 Ornithologist (Bird Watcher) 387 Sportscaster or Sportswriter 388 Journalist 390 Crime Fighter 390 Medical Professional 391 Marketing Executive 392 Lawyer 393 Appendix A: Reference Tables 395 Index 409

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