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Modern Statistics for the Social and Behavioral Sciences

A Practical Introduction

By Rand Wilcox

CRC Press – 2011 – 862 pages

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  • Add to CartHardback: $98.95
    978-1-43-983456-5
    August 5th 2011

Description

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.

Reviews

Relative advantages/disadvantages of various techniques are presented so that the reader can be helped to understand the choices they make on using the techniques. … A considerable number of illustrations are included and the book focuses on using R for its computer software application. … A useful text for … postgraduate students in the social science disciplines.

—Susan Starkings, International Statistical Review, 2012

This is an interesting and valuable book … By gathering a mass of results on that topic into a single volume with references, alternative procedures, and supporting software, the author has provided a valuable service to those interested in these issues, which should probably include anyone teaching the techniques covered in this book. … Recommended to those with a solid background in traditional statistical inference who want a highly competent and comprehensive statement of the cases against traditional statistical inference techniques.

—Robert W. Hayden, MAA Reviews, March 2012

Contents

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 σ 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: ρ = 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

Name: Modern Statistics for the Social and Behavioral Sciences: A Practical Introduction (Hardback)CRC Press 
Description: By Rand Wilcox. 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...
Categories: Quantitative Methods, Statistics & Probability, Statistical Theory & Methods, Regression Analysis and Multivariate Statistics