E-Book, Englisch, 754 Seiten
Wilcox Modern Statistics for the Social and Behavioral Sciences
2. Auflage 2017
ISBN: 978-1-4987-9679-8
Verlag: CRC Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
A Practical Introduction, Second Edition
E-Book, Englisch, 754 Seiten
ISBN: 978-1-4987-9679-8
Verlag: CRC Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
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.
Autoren/Hrsg.
Weitere Infos & Material
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
