Modern Statistics for the Social and Behavioral Sciences: A Practical Introduction

INTRODUCTION Samples versus Populations Software R Basics NUMERICAL AND GRAPHICAL SUMMARIES OF DATA Basic Summation Notation Measures of Location Measures of Variation or Scale Detecting Outliers Histograms Kernel Density Estimators Stem-and-Leaf Displays Skewness Choosing a Measure of Location Covariance and Pearson's Correlation Exercises PROBABILITY AND RELATED CONCEPTS Basic Probability Expected Values Conditional Probability and Independence Population Variance The Binomial Probability Function Continuous Variables and the Normal Curve Understanding the Effects of Non-normality Pearson's Correlation and the Population Covariance Some Rules About Expected Values Chi-Squared Distributions Exercises SAMPLING DISTRIBUTIONS AND CONFIDENCE INTERVALS Random Sampling Sampling Distributions A Confidence Interval for the Population Mean Judging Location Estimators Based on Their Sampling Distribution An Approach to Non-normality: The Central Limit Theorem Student's t and Non-normality Confidence Intervals for the Trimmed Mean Transforming Data Confidence Interval for the Population Median A Remark About MOM and M-Estimators Confidence Intervals for the Probability of Success Exercises HYPOTHESIS TESTING The Basics of Hypothesis Testing Power and Type II Errors Testing Hypotheses about the Mean When sigma Is Not Known Controlling Power and Determining n Practical Problems with Student's T Test Hypothesis Testing Based on a Trimmed Mean Testing Hypotheses About the Population Median Making Decisions About Which Measure of Location To Use Exercises REGRESSION AND CORRELATION The Least Squares Principle Confidence Intervals and Hypothesis Testing Standardized Regression Practical Concerns About Least Squares Regression and How They Might Be Addressed Pearson's Correlation and the Coefficient of Determination Testing H0: rho = 0 A Regression Method for Estimating the Median of Y and Other Quantiles Detecting Heteroscedasticity Concluding Remarks Exercises BOOTSTRAP METHODS Bootstrap-t Method The Percentile Bootstrap Method Inferences About Robust Measures of Location Estimating PowerWhen Testing Hypotheses About a Trimmed Mean A Bootstrap Estimate of Standard Errors Inferences about Pearson's Correlation: Dealing with Heteroscedasticity Bootstrap Methods for Least Squares Regression Detecting Associations Even When There Is Curvature Quantile Regression Regression: Which Predictors are Best? Comparing Correlations Empirical Likelihood Exercises COMPARING TWO INDEPENDENT GROUPS Student's T Test Relative Merits of Student's T Test Welch's Heteroscedastic Method for Means Methods for Comparing Medians and Trimmed Means Percentile Bootstrap Methods for Comparing Measures of Location Bootstrap-t Methods for Comparing Measures of Location Permutation Tests Rank-Based and Nonparametric Methods Graphical Methods for Comparing Groups Comparing Measures of Scale Methods for Comparing Measures of Variation Measuring Effect Size Comparing Correlations and Regression Slopes Comparing Two Binomials Making Decisions About Which Method To Use Exercises COMPARING TWO DEPENDENT GROUPS The Paired T Test Comparing Robust Measures of Location Handling Missing Values A Different Perspective When Using Robust Measures of Location R Functions loc2dif and l2drmci The Sign Test Wilcoxon Signed Rank Test Comparing Variances Comparing Robust Measures of Scale Comparing All Quantiles Plots for Dependent Groups Exercises ONE-WAY ANOVA Analysis of Variance for Independent Groups Dealing with Unequal Variances Judging Sample Sizes and Controlling Power When Data Are Available Trimmed Means Bootstrap Methods Random Effects Model Rank-Based Methods R Function kruskal.test Exercises TWO-WAY AND THREE-WAY DESIGNS Basics of a Two-Way ANOVA Design Testing Hypotheses About Main Effects and Interactions Heteroscedastic Methods for Trimmed Means, Including Means Bootstrap Methods Testing Hypotheses Based on Medians A Rank-Based Method For a Two-Way Design Three-Way ANOVA Exercises COMPARING MORE THAN TWO DEPENDENT GROUPS Comparing Means in a One-Way Design Comparing Trimmed Means When Dealing with a One-Way Design Percentile Bootstrap Methods for a One-Way Design Rank-Based Methods for a One-Way Design Comments on Which Method to Use Between-by-Within Designs Within-by-Within Design Three-Way Designs Exercises MULTIPLE COMPARISONS One-Way ANOVA, Independent Groups SOME MULTIVARIATE METHODS Location, Scatter, and Detecting Outliers One-Sample Hypothesis Testing Two-Sample Case MANOVA A Multivariate Extension of the Wilcoxon-Mann-Whitney Test Rank-Based Multivariate Methods Multivariate Regression Principal Components Exercises ROBUST REGRESSION AND MEASURES OF ASSOCIATION Robust Regression Estimators Comments on Choosing a Regression Estimator Testing Hypotheses When Using Robust Regression Estimators Dealing with Curvature: Smoothers Some Robust Correlations and Tests of Independence Measuring the Strength of an Association Based on a Robust Fit Comparing the Slopes of Two Independent Groups Tests for Linearity Identifying the Best Predictors Detecting Interactions and Moderator Analysis ANCOVA Exercises BASICMETHODS FOR ANALYZING CATEGORICAL DATA Goodness of Fit A Test of Independence Detecting Differences in the Marginal Probabilities6 Measures of Association Logistic Regression Exercises ANSWERS TO SELECTED EXERCISES TABLES BASIC MATRIX ALGEBRA REFERENCES Index