An Introduction to Statistical Methods and Data Analysis

PART I: INTRODUCTION 1. WHAT IS STATISTICS? Introduction / Why Study Statistics? / Some Current Applications of Statistics / What Do Statisticians Do? / Quality and Process Improvement / A Note to the Student / Summary / Supplementary Exercises PART II: COLLECTING THE DATA 2. USING SURVEYS AND SCIENTIFIC STUDIES TO COLLECT DATA Introduction / Surveys / Scientific Studies / Observational Studies / Data Management: Preparing Data for Summarization and Analysis / Summary PART III: SUMMARIZING DATA 3. DATA DESCRIPTION Introduction / Describing Data on a Single Variable: Graphical Methods / Describing Data on a Single Variable: Measures of Central Tendency / Describing Data on a Single Variable: Measures of Variability / The Box Plot / Summarizing Data from More Than One Variable / Calculators, Computers, and Software Systems / Summary / Key Formulas / Supplementary Exercises PART IV: TOOLS AND CONCEPTS 4. PROBABILITY AND PROBABILITY DISTRIBUTIONS How Probability Can Be Used in Making Inferences / Finding the Probability of an Event / Basic Event Relations and Probability Laws / Conditional Probability and Independence / Bayes's Formula / Variables: Discrete and Continuous / Probability Distributions for Discrete Random Variables / A Useful Discrete Random Variable: The Binomial / Probability Distributions for Continuous Random Variables / A Useful Continuous Random Variable: The Normal Distribution / Random Sampling / Sampling Distributions / Normal Approximation to the Binomial / Summary / Key Formulas / Supplementary Exercises PART V: ANALYZING DATA: CENTRAL VALUES, VARIANCES, AND PROPORTIONS 5. INFERENCES ON A POPULATION CENTRAL VALUE Introduction and Case Study / Estimation of / Choosing the Sample Size for Estimating / A Statistical Test for / Choosing the Sample Size for Testing / The Level of Significance of a Statistical Test / Inferences about for Normal Population, s Unknown / Inferences about the Population Median / Summary / Key Formulas / Supplementary Exercises 6. COMPARING TWO POPULATION CENTRAL VALUES Introduction and Case Study / Inferences about 1 - 2: Independent Samples / A Nonparametric Alternative: The Wilcoxon Rank Sum Test / Inferences about 1 - 2: Paired Data / A Nonparametric Alternative: The Wilcoxon Signed-Rank Test / Choosing Sample Sizes for Inferences about 1 - 2 / Summary / Key Formulas / Supplementary Exercises 7. INFERENCES ABOUT POPULATION VARIANCES Introduction and Case Study / Estimation and Tests for a Population Variance / Estimation and Tests for Comparing Two Population Variances / Tests for Comparing k > 2 Population Variances / Summary / Key Formulas / Supplementary Exercises 8. INFERENCES ABOUT POPULATION CENTRAL VALUES Introduction and Case Study / A Statistical Test About More Than Two Population Variances / Checking on the Assumptions / Alternative When Assumptions are Violated: Transformations / A Nonparametric Alternative: The Kruskal-Wallis Test / Summary / Key Formulas / Supplementary Exercises 9. MULTIPLE COMPARISONS Introduction and Case Study / Planned Comparisons Among Treatments: Linear Contrasts / Which Error Rate Is Controlled / Multiple Comparisons with the Best Treatment / Comparison of Treatments to a Control / Pairwise Comparison on All Treatments / Summary / Key Formulas / Supplementary Exercises 10. CATEGORICAL DATA Introduction and Case Study / Inferences about a Population Proportion p / Comparing Two Population Proportions p1 - p2 / Probability Distributions for Discrete Random Variables / The Multinomial Experiment and Chi-Square Goodness-of-Fit Test / The Chi-Square Test of Homogeneity of Proportions / The Chi-Square Test of Independence of Two Nominal Level Variables / Fisher's Exact Test, a Permutation Test / Measures of Association / Combining Sets of Contingency Tables / Summary / Key Formulas / Supplementary Exercises PART VI: ANALYZING DATA: REGRESSION METHODS, MODEL BUILDING 11. SIMPLE LINEAR REGRESSION AND CORRELATION Linear Regression and the Method of Least Squares / Transformations to Linearize Data / Correlation / A Look Ahead: Multiple Regression / Summary of Key Formulas. Supplementary Exercises. 12. INFERENCES RELATED TO LINEAR REGRESSION AND CORRELATION Introduction and Case Study / Diagnostics for Detecting Violations of Model Conditions / Inferences about the Intercept and Slope of the Regression Line / Inferences about the Population Mean for a Specified Value of the Explanatory Variable / Predictions and Prediction Intervals / Examining Lack of Fit in the Model / The Inverse Regression Problem (Calibration): Predicting Values for x for a Specified Value of y / Summary / Key Formulas / Supplementary Exercises 13. MULTIPLE REGRESSION AND THE GENERAL LINEAR MODEL Introduction and Case Study / The General Linear Model / Least Squares Estimates of Parameters in the General Linear Model / Inferences about the Parameters in the General Linear Model / Inferences about the Population Mean and Predictions from the General Linear Model / Comparing the Slope of Several Regression Lines / Logistic Regression / Matrix Formulation of the General Linear Model / Summary / Key Formulas / Supplementary Exercises 14. BUILDING REGRESSION MODELS WITH DIAGNOSTICS Introduction and Case Study / Selecting the Variables (Step 1) / Model Formulation (Step 2) / Checking Model Conditions (Step 3) / Summary / Key Formulas / Supplementary Exercises PART VII: ANALYZING DATA: DESIGN OF EXPERIMENTS AND ANOVA 15. DESIGN CONCEPTS FOR EXPERIMENTS AND STUDIES Experiments, Treatments, Experimental Units, Blocking, Randomization, and Measurement Units / How Many Replications? / Studies for Comparing Means versus Studies for Comparing Variances / Summary / Key Formulas / Supplementary Exercises 16. ANALYSIS OF VARIANCE FOR STANDARD DESIGNS Introduction and Case Study / Completely Randomized Design with Single Factor / Randomized Block Design / Latin Square Design / Factorial Experiments in a Completely Randomized Design / The Estimation of Treatment Differences and Planned Comparisons in the Treatment Means / Checking Model Conditions / Alternative Analyses: Transformation and Friedman's Rank-Based Test / Summary / Key Formulas / Supplementary Exercises 17. ANALYSIS OF COVARIANCE Introduction and Case Study / A Completely Randomized Design with One Covariate / The Extrapolation Problem / Multiple Covariates and More Complicated Designs / Summary / Key Formulas / Supplementary Exercises 18. ANALYSIS OF VARIANCE FOR SOME UNBALANCED DESIGNS Introduction and Case Study / A Randomized Block Design with One or More Missing Observations / A Latin Square Design with Missing Data / Incomplete Block Designs / Summary / Key Formulas / Supplementary Exercises 19. ANALYSIS OF VARIANCE FOR SOME FIXED EFFECTS, RANDOM EFFECTS, AND MIXED EFFECTS MODELS Introduction and Case Study / A One-Factor Experiment with Random Treatment Effects / Extensions of Random-Effects Models / A Mixed Model: Experiments with Both Fixed and Random Treatment Effects / Models with Nested Factors / Rules for Obtaining Expected Mean Squares / Summary / Key Formulas / Supplementary Exercises 20. SPLIT-PLOT DESIGNS AND EXPERIMENTS WITH REPEATED MEASURES Introduction and Case Study / Split-Plot Designs / Single-Factor Experiments with Repeated Measures / Two-Factor Experiments with Repeated Measures on One of the Factors / Crossover Design / Summary / Key Formulas / Supplementary Exercises PART VIII: COMMUNICATING AND DOCUMENTING THE RESULTS OF A STUDY OR EXPERIMENT 21. COMMUNICATING AND DOCUMENTING THE RESULTS OF A STUDY OR EXPERIMENT Introduction / The Difficulty of Good Communication / Communication Hurdles: Graphical Distortions / Communication Hurdles: Biased Samples / Communication Hurdles: Sample Size / The Statistical Report / Documentation and Storage of Results / Summary / Supplementary Exercises