Statistics II For Dummies

Deborah J. Rumsey, PhD, is a Statistics Education Specialist and Associated Professor in the Department of Statistics at The Ohio State University. She is also a Fellow of the American Statistical Association and has received the Presidential Teaching Award from Kansas State University. Dr. Rumsey has published numerous papers and given many professional presentations on the subject of statistics education.

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