Modern statistics for the social and behavioral sciences : a practical introduction

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Modern statistics for the social and behavioral sciences : a practical introduction

Rand Wilcox

CRC Press, c2012

  • : hardback

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内容説明

In addition to learning how to apply classic statistical methods, students need to understand when these methods perform well, and when and why they can be highly unsatisfactory. Modern Statistics for the Social and Behavioral Sciences illustrates how to use R to apply both standard and modern methods to correct known problems with classic techniques. Numerous illustrations provide a conceptual basis for understanding why practical problems with classic methods were missed for so many years, and why modern techniques have practical value. Designed for a two-semester, introductory course for graduate students in the social sciences, this text introduces three major advances in the field: Early studies seemed to suggest that normality can be assumed with relatively small sample sizes due to the central limit theorem. However, crucial issues were missed. Vastly improved methods are now available for dealing with non-normality. The impact of outliers and heavy-tailed distributions on power and our ability to obtain an accurate assessment of how groups differ and variables are related is a practical concern when using standard techniques, regardless of how large the sample size might be. Methods for dealing with this insight are described. The deleterious effects of heteroscedasticity on conventional ANOVA and regression methods are much more serious than once thought. Effective techniques for dealing heteroscedasticity are described and illustrated. Requiring no prior training in statistics, Modern Statistics for the Social and Behavioral Sciences provides a graduate-level introduction to basic, routinely used statistical techniques relevant to the social and behavioral sciences. It describes and illustrates methods developed during the last half century that deal with known problems associated with classic techniques. Espousing the view that no single method is always best, it imparts a general understanding of the relative merits of various techniques so that the choice of method can be made in an informed manner.

目次

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 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: = 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

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