An Introduction to Statistical Methods and Data Analysis

PART 1: INTRODUCTION. 1. Statistics and the Scientific Method. Introduction. Why Study Statistics? Some Current Applications of Statistics. A Note to the Student. Summary. Exercises. PART 2: COLLECTING DATA. 2. Using Surveys and Scientific Studies to Collect Data. Introduction and Abstract of Research Study. Observational Studies. Sampling Designs for Surveys. Experimental Studies. Designs for Experimental Studies. Research Study: Exit Polls versus Election Results. Summary. Exercises. PART 3: SUMMARIZING DATA. 3. Data Description. Introduction and Abstract of Research Study. Calculators, Computers, and Software Systems. 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 Boxplot. Summarizing Data from More Than One Variable: Graphs and Correlation. Research Study: Controlling for Student Background in the Assessment of Teaching. Summary and Key Formulas. Exercises. 4. Probability And Probability Distributions. Introduction and Abstract of Research Study. Finding the Probability of an Event. Basic Event Relations and Probability Laws. Conditional Probability and Independence. Bayes' Formula. Variables: Discrete and Continuous. Probability Distributions for Discrete Random Variables. Two Discrete Random Variables: The Binomial and the Poisson. Probability Distributions for Continuous Random Variables. A Continuous Probability Distribution: The Normal Distribution. Random Sampling. Sampling Distributions. Normal Approximation to the Binomial. Evaluating Whether or Not a Population Distribution Is Normal. Research Study: Inferences about Performance Enhancing Drugs among Athletes. Minitab Instructions. Summary and Key Formulas. Exercises. PART 4: ANALYZING DATA, INTERPRETING THE ANALYSES, AND COMMUNICATING RESULTS. 5. Inferences about Population Central Values. Introduction and Abstract of a Research Study. Estimation of . Choosing the Sample Size for Estimating . A Statistical Test for . Choosing the Sample Size for . The Level of Significance of a Statistical Test. Inferences about for a Normal Population, s Unknown. Inferences about when Population in Nonnormal and n is small: Bootstrap Methods. Inferences about the Median. Research Study: Percent Calories from Fat. Summary and Key Formulas. Exercises. 6. Inferences Comparing Two Population Central Values. Introduction and Abstract of a Research 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. Research Study: Effects of Oil Spill on Plant Growth. Summary. Exercises. 7. Inferences about Population Variances. Introduction and Abstract of a Research Study. Estimation and Tests for a Population Variance. Estimation and Tests for Comparing Two Population Variances. Tests for Comparing t > 2 Population Variances. Research Study: Evaluation of Methods for Detecting E. coli. Summary and Key Formulas. Exercises. 8. Inferences About More Than Two Population Central Values Introduction and Abstract of a Research Study. A Statistical Test About More Than Two Population Means: An Analysis of Variance. The Model for Observations in a Completely Randomized Design. Checking on the AOV Conditions. An Alternative Analysis: Transformations of the Data. A Nonparametric Alternative: The Kruskal-Wallis Test. Research Study: Effect on Timing on the Treatment of Port-Wine Stains with Lasers. Summary and Key Formulas. Exercises. 9. Multiple Comparisons. Introduction and Abstract of Research Study. Linear Contrasts. Which Error Rate Is Controlled? Fisher's Least Significant Difference. Tukey's W Procedure. Student-Neuman-Keuls Procedure. Dunnett's Procedure: Comparison of Treatments to a Control. Scheffe's S Method. A Nonparametric Multiple-Comparison Procedure. Research Study: