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 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 Scheffé'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...