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

Requiring no prior training, Modern Statistics for the Social and Behavioral Sciences provides a two-semester, graduate-level introduction to basic statistical techniques that takes into account recent advances and insights that are typically ignored in an introductory course. Hundreds of journal articles make it clear that basic techniques, routinely taught and used, can perform poorly when dealing with skewed distributions, outliers, heteroscedasticity (unequal variances) and curvature. Methods for dealing with these concerns have been derived and can provide a deeper, more accurate and more nuanced understanding of data. A conceptual basis is provided for understanding when and why standard methods can have poor power and yield misleading measures of effect size. Modern techniques for dealing with known concerns are described and illustrated. Features: Presents an in-depth description of both classic and modern methods Explains and illustrates why recent advances can provide more power and a deeper understanding of data Provides numerous illustrations using the software R Includes an R package with over 1300 functions Includes a solution manual giving detailed answers to all of the exercises This second edition describes many recent advances relevant to basic techniques. For example, a vast array of new and improved methods is now available for dealing with regression, including substantially improved ANCOVA techniques. The coverage of multiple comparison procedures has been expanded and new ANOVA techniques are described. Rand Wilcox is a professor of psychology at the University of Southern California. He is the author of 13 other statistics books and the creator of the R package WRS. He currently serves as an associate editor for five statistics journals. He is a fellow of the Association for Psychological Science and an elected member of the International Statistical Institute.

Table of Contents:
Table of Contents INTRODUCTION SAMPLES VERSUS POPULATIONS SOFTWARE R BASICS Entering Data R Functions and Packages Data Sets Arithmetic Operations NUMERICAL AND GRAPHICAL SUMMARIES OF DATA BASIC SUMMATION NOTATION MEASURES OF LOCATION The Sample Mean R Function Mean The Sample Median R Function for the Median A CRITICISM OF THE MEDIAN: IT MIGHT TRIM TOO MANY VALUES R Function for the Tr R Function winmean What is a Measure of Location? MEASURES OF VARIATION OR SCALE Sample Variance and Standard Deviation R Functions var and sd The Interquartile Range R Functions idealf and ideafIQR Winsorized Variance R Function winvar Median Absolute Deviation R Function mad Average Absolute Distance from the Median Other Robust Measures of Variation R Functions bivar, pbvar, tauvar, and tbs DETECTING OUTLIERS A Method Based on the Mean and Variance A Better Outlier Detection Rule: The MAD-Median Rule R Function out The Boxplot R Function boxplot Modifications of the Boxplot Rule for Detecting Outliers R Function outbox Other Measures of Location R Functions mom and onestep HISTOGRAMS R Functions hist and splot KERNEL DENSITY ESTIMATORS R Functions kdplot and akerd STEM-AND-LEAF DISPLAYS R Function stem SKEWNESS Transforming Data CHOOSING A MEASURE OF LOCATION EXERCISES PROBABILITY AND RELATED CONCEPTS BASIC PROBABILITY EXPECTED VALUES CONDITIONAL PROBABILITY AND INDEPENDENCE POPULATION VARIANCE THE BINOMIAL PROBABILITY FUNCTION R Functions dbinom and pbinom CONTINUOUS VARIABLES AND THE NORMAL CURVE Computing Probabilities Associated with Normal Curves R Function pnorm R Function pnorm R Function pnorm UNDERSTANDING THE EFFECTS OF NON-NORMALITY Skewness PEARSON’S CORRELATION AND THE POPULATION COVARIANCE (OPTIONAL) Computing the Population Covariance and Pearson’s Correlation SOME RULES ABOUT EXPECTED VALUES CHI-SQUARED DISTRIBUTIONS EXERCISES SAMPLING DISTRIBUTIONS AND CONFIDENCE INTERVALS RANDOM SAMPLING SAMPLING DISTRIBUTIONS Sampling Distribution of the Sample Mean Computing Probabilities Associated with the Sample Mean A CONFIDENCE INTERVAL FOR THE POPULATION MEAN Known Variance Confidence Intervals When _ Is Not Known R Functions pt and qt Confidence Interval for the Population Mean Using Student’s t R Function t.test JUDGING LOCATION ESTIMATORS BASED ON THEIR SAMPLING DISTRIBUTION Trimming and Accuracy: Another Perspective AN APPROACH TO NON-NORMALITY: THE CENTRAL LIMIT THEOREM STUDENT’S T AND NON-NORMALITY CONFIDENCE INTERVALS FOR THE TRIMMED MEAN Estimating the Standard Error of a Trimmed Mean Function trimse A Confidence Interval for the Population Trimmed Mean R Function trimci TRANSFORMING DATA CONFIDENCE INTERVAL FOR THE POPULATION MEDIAN R Function sint Estimating the Standard Error of the Sample Median R Function msmedse More Concerns About Tied Values A REMARK ABOUT MOM AND M-ESTIMATORS CONFIDENCE INTERVALS FOR THE PROBABILITY OF SUCCESS R Functions binomci, acbinomci and and binomLCO BAYESIAN METHODS EXERCISES HYPOTHESIS TESTING THE BASICS OF HYPOTHESIS TESTING P-Value or Significance Level Criticisms of Two-Sided Hypothesis Testing and P-Values Summary and Generalization POWER AND TYPE II ERRORS Understanding How n, _, and _ Are Related to Power TESTING HYPOTHESES ABOUT THE MEAN WHEN _ IS NOT KNOWN R Function t.test CONTROLLING POWER AND DETERMINING THE SAMPLE SIZE Choosing n Prior to Collecting Data R Function power.t.test Stein’s Method: Judging the Sample Size When Data Are Available R Functions stein1 and stein2 PRACTICAL PROBLEMS WITH STUDENT’S T TEST HYPOTHESIS TESTING BASED ON A TRIMMED MEAN R Function trimci R Functions stein1.tr and stein2.tr TESTING HYPOTHESES ABOUT THE POPULATION MEDIAN R Function sintv2 MAKING DECISIONS ABOUT WHICH MEASURE OF LOCATION TO USE BOOTSTRAP METHODS BOOTSTRAP-T METHOD Symmetric Confidence Intervals Exact Nonparametric Confidence Intervals for Means Are Impossible THE PERCENTILE BOOTSTRAP METHOD INFERENCES ABOUT ROBUST MEASURES OF LOCATION Using the Percentile Method R Functions onesampb, momci and trimpb The Bootstrap-t Method Based on Trimmed Means R Function trimcibt ESTIMATING POWER WHEN TESTING HYPOTHESES ABOUT A TRIMMED MEAN R Functions powt1est and powt1an A BOOTSTRAP ESTIMATE OF STANDARD ERRORS R Function bootse EXERCISES REGRESSION AND CORRELATION THE LEAST SQUARES PRINCIPLE CONFIDENCE INTERVALS AND HYPOTHESIS TESTING Classic Inferential Techniques Multiple Regression R Functions ols and lm STANDARDIZED REGRESSION PRACTICAL CONCERNS ABOUT LEAST SQUARES REGRESSION AND HOW THEY MIGHT BE ADDRESSED The Effect of Outliers on Least Squares Regression Beware of Bad Leverage Points Beware of Discarding Outliers Among the Y Values Do Not Assume Homoscedasticity or that the Regression Line is Straight Violating Assumptions When Testing Hypotheses Dealing with Heteroscedasticity: The HC4 Method R Functions olshc4 and hc4test Interval Estimation of the Mean Response R Function olshc4band PEARSON’S CORRELATION AND THE COEFFICIENT OF DETERMINATION A Closer Look at Interpreting r TESTING H0: _ = 0 R Function cor.test R Function pwr.r.test Testing H0: _ = 0 When There is Heteroscedasticity R Function pcorhc4 When Is It Safe to Conclude that Two Variables Are Independent? A REGRESSION METHOD FOR ESTIMATING THE MEDIAN OF Y AND OTHER QUANTILES R Function rqfit DETECTING HETEROSCEDASTICITY R Function khomreg INFERENCES ABOUT PEARSON’S CORRELATION: DEALING WITH HETEROSCEDASTICITY R Function pcorb BOOTSTRAP METHODS FOR LEAST SQUARES REGRESSION R Functions hc4wtest, olswbtest and lsfitci DETECTING ASSOCIATIONS EVEN WHEN THERE IS CURVATURE R Functions indt and medind QUANTILE REGRESSION R Functions qregci and rqtest A Test for Homoscedasticity Using a Quantile Regression Approach R Function qhomt REGRESSION: WHICH PREDICTORS ARE BEST? The 0.632 Bootstrap Method R function regpre Least Angle Regression R Function larsR COMPARING CORRELATIONS R Functions TWOpov and TWOpNOV CONCLUDING REMARKS EXERCISES COMPARING TWO INDEPENDENT GROUPS STUDENT’S T TEST Choosing the Sample Sizes R Function power.t.test RELATIVE MERITS OF STUDENT’S T WELCH’S HETEROSCEDASTIC METHOD FOR MEANS R function t.test Tukey’s Three-Decision Rule Non-normality and Welch’s Method Three Modern Insights Regarding Methods for Comparing Means METHODS FOR COMPARING MEDIANS AND TRIMMED MEANS Yuen’s Method for Trimmed Means R Functions yuen and fac2list Comparing Medians R Function msmed PERCENTILE BOOTSTRAP METHODS FOR COMPARING MEASURES OF LOCATION Using Other Measures of Location Comparing Medians R Function medpb2 Some Guidelines on When To Use the Percentile Bootstrap Method R Functions trimpb2, med2g and pb2gen BOOTSTRAP-T METHODS FOR COMPARING MEASURES OF LOCATION Comparing Means Bootstrap-t Method When Comparing Trimmed Means R Functions yuenbt and yhbt Estimating Power and Judging the Sample Sizes R Functions powest and pow2an PERMUTATION TESTS RANK-BASED AND NONPARAMETRIC METHODS Wilcoxon-Mann-Whitney Test Handling Tied Values and Heteroscedasticity Cliff’s Method R functions cid and cidv2 The Brunner–Munzel Method R function bmp The Kolmogorov–Smirnov Test R Function ks Comparing All Quantiles Simultaneously: An Extension of the Kolmogorov–Smirnov Test R Function sband GRAPHICAL METHODS FOR COMPARING GROUPS Error Bars R Functions ebarplot and ebarplot.med Plotting the Shift Function Plotting the Distributions R Function sumplot2g Other Approaches COMPARING MEASURES OF VARIATION R Function comvar2 Brown-Forsythe Method Comparing Robust Measures of Variation MEASURING EFFECT SIZE R Functions yuenv2 and akp.effect COMPARING CORRELATIONS AND REGRESSION SLOPES R Functions twopcor, twolsreg, and tworegwb COMPARING TWO BINOMIALS Storer–Kim Method Beal’s Method R Functions twobinom, twobici, bi2KMSv2 and power.prop.test Comparing Two Discrete Distributions R Function disc2com MAKING DECISIONS ABOUT WHICH METHOD TO USE EXERCISES COMPARING TWO DEPENDENT GROUPS THE PAIRED T TEST When Does the Paired T Test Perform Well? R Function t.test COMPARING ROBUST MEASURES OF LOCATION R Functions yuend, ydbt and dmedpb Comparing Marginal M-Estimators R Function rmmest Measuring Effect Size R Function D.akp.effect HANDLING MISSING VALUES R Functions rm2miss and rmmismcp A DIFFERENT PERSPECTIVE WHEN USING ROBUST MEASURES OF LOCATION R Functions loc2dif and l2drmci THE SIGN TEST WILCOXON SIGNED RANK TEST R Function wilcox.test COMPARING VARIANCES R Function comdvar COMPARING ROBUST MEASURES OF SCALE R Function rmrvar COMPARING ALL QUANTILES R Functions lband PLOTS FOR DEPENDENT GROUPS R Function g2plotdifxy EXERCISES ONE-WAY ANOVA ANALYSIS OF VARIANCE FOR INDEPENDENT GROUPS A Conceptual Overview 345 ANOVA via Least Squares Regression and Dummy Coding R Functions anova, anova1, aov, and fac2list Controlling Power and Choosing the Sample Sizes R Functions power.anova.test and anova.power DEALING WITH UNEQUAL VARIANCES 356 Welch’s Test JUDGING SAMPLE SIZES AND CONTROLLING POWER WHEN DATA ARE AVAILABLE R Functions bdanova1 and bdanova2 TRIMMED MEANS R Functions t1way, t1wayv2, t1wayF and g5plot Comparing Groups Based on Medians R Function med1way BOOTSTRAP METHODS A Bootstrap-t Method R Functions t1waybt and BFBANOVA Two Percentile Bootstrap Methods R Functions b1way, pbadepth and Qanova Choosing a Method RANDOM EFFECTS MODEL A Measure of Effect Size A Heteroscedastic Method A Method Based on Trimmed Means R Function rananova RANK-BASED METHODS The Kruskall-Wallis Test R Function kruskal.test Method BDM R Functions bdm and bdmP EXERCISES TWO-WAY AND THREE-WAY DESIGNS BASICS OF A TWO-WAY ANOVA DESIGN Interactions R Functions interaction.plot and interplot Interactions When There Are More Than Two Levels TESTING HYPOTHESES ABOUT MAIN EFFECTS AND INTERACTIONS R function anova Inferences About Disordinal Interactions The Two-Way ANOVA Model HETEROSCEDASTIC METHODS FOR TRIMMED MEANS, INCLUDING MEANS R Function t2way BOOTSTRAP METHODS R Functions pbad2way and t2waybt TESTING HYPOTHESES BASED ON MEDIANS R Function m2way A RANK-BASED METHOD FOR A TWO-WAY DESIGN R Function bdm2way The Patel–Hoel Approach to Interactions THREE-WAY ANOVA R Functions anova and t3way EXERCISES COMPARING MORE THAN TWO DEPENDENT GROUPS COMPARING MEANS IN A ONE-WAY DESIGN R Function aov COMPARING TRIMMED MEANS WHEN DEALING WITH A ONE-WAY DESIGN R Functions rmanova and rmdat2mat A Bootstrap-t Method for Trimmed Means R Function rmanovab PERCENTILE BOOTSTRAP METHODS FOR A ONE-WAY DESIGN Method Based on Marginal Measures of Location R Function bd1way Inferences Based on Difference Scores R Function rmdzero RANK-BASED METHODS FOR A ONE-WAY DESIGN Friedman’s Test R Function friedman.test Method BPRM R Function bprm COMMENTS ON WHICH METHOD TO USE BETWEEN-BY-WITHIN DESIGNS Method for Trimmed Means R Function bwtrim and bw2list A Bootstrap-t Method R Function tsplitbt Inferences Based on M-estimators and Other Robust Measures of Location R Functions sppba, sppbb, and sppbi A Rank-Based Test R Function bwrank WITHIN-BY-WITHIN DESIGN R Function wwtrim THREE-WAY DESIGNS R Functions bbwtrim, bwwtrim and wwwtrim Data Management: R Functions bw2list and bbw2list EXERCISES MULTIPLE COMPARISONS ONE-WAY ANOVA AND RELATED SITUATIONS, INDEPENDENT GROUPS Fisher’s Least Significant Difference Method The Tukey-Kramer Method R Function TukeyHSD Tukey-Kramer and the ANOVA F Test Step-Down Methods Dunnett’s T3 Games-Howell Method Comparing Trimmed Means R Functions lincon, stepmcp and twoKlin Alternative Methods for Controlling FWE Percentile Bootstrap Methods for Comparing Trimmed Means, Medians, and M-estimators R Functions medpb, tmcppb, pbmcp and p.adjust A Bootstrap-t Method R Function linconbt Rank-Based Methods R Functions cidmul, cidmulv2, and bmpmul Comparing the Individual Probabilities of Two Discrete Distributions R Functions binband, splotg2, cumrelf and cumrelfT Comparing the Quantliles of Two Independent Groups R Functions qcomhd and qcomhdMC Multiple Comparisons for Binomial and Categorical Data R Functions skmcp and discmcp TWO-WAY, BETWEEN-BY-BETWEEN DESIGN Scheff'e’s Homoscedastic Method Heteroscedastic Methods Extension of Welch-˘Sid'ak and Kaiser–Bowden Methods to Trimmed Means R Function kbcon R Functions con2way and conCON Linear Contrasts Based on Medians R Functions msmed and mcp2med Bootstrap Methods R Functions mcp2a, and bbmcppb The Patel-Hoel Rank-Based Interaction Method R Function rimul JUDGING SAMPLE SIZES Tamhane’s Procedure R Function tamhane Hochberg’s Procedure R Function hochberg METHODS FOR DEPENDENT GROUPS Linear Contrasts Based on Trimmed Means R Function rmmcp Comparing M-estimators R Functions rmmcppb, dmedpb, dtrimpb and boxdif Bootstrap-t Method R Function bptd Comparing the Quantiles of the Marginal Distributions R Function Dqcomhd BETWEEN-BY-WITHIN DESIGNS R Functions bwmcp, bwamcp, bwbmcp, bwimcp, spmcpa, spmcpb, spmcpi, and bwmcppb WITHIN-BY-WITHIN DESIGNS Three-Way Designs R Functions con3way, mcp3atm, and rm3mcp Bootstrap Methods for Three-Way Designs R Functions bbwmcp, bwwmcp, bwwmcppb, bbbmcppb, bbwmcppb, bwwmcppb, and wwwmcppb EXERCISES SOME MULTIVARIATE METHODS LOCATION, SCATTER, AND DETECTING OUTLIERS Detecting Outliers Via Robust Measures of Location and Scatter R Functions cov.mve and cov.mcd More Measures of Location and Covariance R Functions rmba, tbs, and ogk R Function out A Projection-Type Outlier Detection Method R Functions outpro, outproMC, outproad, outproadMC, and out3d Skipped Estimators of Location R Function smean ONE-SAMPLE HYPOTHESIS TESTING Comparing Dependent Groups R Functions smeancrv2, hotel1, and rmdzeroOP TWO-SAMPLE CASE R Functions smean2, mat2grp, matsplit and mat2list R functions matsplit, mat2grp and mat2list MANOVA R Function manova Robust MANOVA Based on Trimmed Means R Functions MULtr.anova and MULAOVp A MULTIVARIATE EXTENSION OF THE WILCOXON–MANN–WHITNEY TEST Explanatory Measure of Effect Size: A Projection-Type Generalization R Function mulwmwv2 RANK-BASED MULTIVARIATE METHODS The Munzel–Brunner Method R Function mulrank The Choi–Marden Multivariate Rank Test R Function cmanova MULTIVARIATE REGRESSION Multivariate Regression Using R Robust Multivariate Regression R Function mlrreg and mopreg PRINCIPAL COMPONENTS R Functions prcomp and regpca Robust Principal Components 545 R Functions outpca, robpca, robpcaS, Ppca, and Ppca.summary EXERCISES ROBUST REGRESSION AND MEASURES OF ASSOCIATION ROBUST REGRESSION ESTIMATORS The Theil–Sen Estimator R Functions tsreg, tshdreg and regplot Least Median of Squares Least Trimmed Squares and Least Trimmed Absolute Value Estimators R Functions lmsreg, ltsreg, and ltareg M-Estimators R Function chreg Deepest Regression Line R Function mdepreg Skipped Estimators R Functions opreg and opregMC S-estimators and an E-Type Estimator R Function tstsreg COMMENTS ON CHOOSING A REGRESSION ESTIMATOR INFERENCES BASED ON ROBUST REGRESSION ESTIMATORS Testing Hypotheses About the Slopes Inferences About the Typical Value of Y Given X R Functions regtest, regtestMC, regci, regciMC, regYci and regYband Comparing Measures of Location via Dummy Coding DEALING WITH CURVATURE: SMOOTHERS Cleveland’s Smoother R Functions lowess, lplot, lplot.pred and lplotCI Smoothers Based on Robust Measures of Location R Functions rplot, rplotCIS, rplotCI, rplotCIv2, rplotCIM, rplot.pred, qhdsm and qhdsm.pred Prediction When X Is Discrete: The R Function rundis Seeing Curvature with More than Two Predictors R Function prplot Some Alternative Methods Detecting Heteroscedasticity Using a Smoother R Function rhom SOME ROBUST CORRELATIONS AND TESTS OF INDEPENDENCE Kendall’s tau Spearman’s rho Winsorized Correlation R Function wincor OP or Skipped Correlation R Function scor Inferences about Robust Correlations: Dealing with Heteroscedasticity R Functions corb and scorci MEASURING THE STRENGTH OF AN ASSOCIATION BASED ON A ROBUST FIT COMPARING THE SLOPES OF TWO INDEPENDENT GROUPS R Function reg2ci TESTS FOR LINEARITY R Functions lintest, lintestMC, and linchk IDENTIFYING THE BEST PREDICTORS Inferences Based on Independent Variables Taken in Isolation R Functions regpord, ts2str, and sm2strv7 585 Inferences When Independent Variables Ares Taken Together R Function regIVcom INTERACTIONS AND MODERATOR ANALYSES R Functions olshc4.inter, ols.plot.inter, regci.inter, reg.plot.inter and adtest Graphical Methods for Assessing Interactions R Functions kercon, runsm2g, regi 1ANCOVA Classic ANCOVA Robust ANCOVA Methods Based on a Parametric Regression Model R Functions ancJN, ancJNmp, anclin, reg2plot and reg2g.p2plot ANCOVA Based on the running-interval Smoother R Functions ancsm, Qancsm, ancova, ancovaWMW, ancpb, ancovaUB, ancboot, ancdet, runmean2g, qhdsm2g and l2plot R Functions Dancts, Dancols, Dancova, Dancovapb, DancovaUB and Dancdet EXERCISES BASIC METHODS FOR ANALYZING CATEGORICAL DATA GOODNESS OF FIT R Functions chisq.test and pwr.chisq.test TEST OF INDEPENDENCE R Function chi.test.ind DETECTING DIFFERENCES IN THE MARGINAL PROBABILITIES R Functions contab and mcnemar.test MEASURES OF ASSOCIATION The Proportion of Agreement Kappa Weighted Kappa R Function Ckappa LOGISTIC REGRESSION R Functions glm and logreg A Confidence Interval for the Odds Ratio R Function ODDSR.CI Smoothers for Logistic Regression R Functions logrsm, rplot.bin, and logSM EXERCISES Appendix A _ ANSWERS TO SELECTED EXERCISES Appendix B _ TABLES Appendix C _ BASIC MATRIX ALGEBRA Index

About the Author :
Rand Wilcox has been a Professor of Psychology at the University of Southern California since 1987. He received his Ph.D. from the University of California, Santa Barbara in 1976. His research interests are statistical methods, particularly robust methods for comparing groups and studying associations. He also collaborates with researchers in occupational therapy, gerontology, biology and psychology. He is the author of four books.