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Modern statistics for the social and behavioral sciences: a practical introduction
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Varies, see individual formats and editions
Publication Date
2012.
Language
English
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Embry Riddle Aero University - CIRCCOLL - Circulating Collection
HA29.W513 2012
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HA29.W513 2012
1 available
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ISBN
9781439834565
9781466503236
9781466503236
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Table of Contents
From the Book - Regular Print
1. Introduction
Samples versus populations
Software
R Basics
Entering data
R functions and packages
Data sets
Arithmetic operations
2. 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 trimmed mean
A Winsorized mean
R function winmean
What is a measure of location?
Measures or variation of scale
Sample variance and standard deviation
R functions for the variance and standard deviation
The interquartile range
R function idealf
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 function kdplot and akerd
Stem-and-leaf displays
R function stem
Skewness
Transforming data
Choosing a measure of location
Covariance and Pearson's correlation
Exercises
3. Probability and related concepts
Basic probability
Expected values
Conditional probability and independence
Population variance
The binomial probability function
Continuous variables and the normal curve
Computing probabilities associated with normal distributions
R function pnorm
Understanding the effects of non-normality
Skewness
Pearson's correlation and the population covariance
Computing the population covariance and Pearson's correlation
Some rules about expected values
Chi-squared distributions
Exercises.
4. 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 ơ is not known
R function 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
R 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 about MOM and M-estimators
Confidence intervals for the probability of success
R functions binomci and acbinomci
Exercises
5. Hypothesis testing
The basics of hypothesis testing
P-value or significance level
R function t. test
Criticisms of two-sided hypothesis testing and p-values
Summary and generalization
Power and type II errors
Understanding how n, [symbol] and ơ are related to power
Testing hypotheses about the mean when ơ is not known
Controlling power and determining n
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
Exercises
6. Regression and correlation
The least squares principle
Confidence intervals and hypothesis testing
Classic inferential techniques
Multiple regression
R functions ols, lm, and olsplot
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
Pearson's correlation and the coefficient of determination
A closer look at interpreting r
Testing H₀: p = 0
R functions cor.test and pwr.t.test
R function pwr.r.test
Testing H₀: p = 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
Concluding remarks
Exercises
7. 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 function powt1est and powt1an
A bootstrap estimate of standard errors
R function bootse
Inferences about Pearson's correlation : dealing with heteroscedasticity
R function pcorb
Bootstrap methods for least squares regression
R functions hc4wtest, olswbtest, 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?
R function regpre
Least angle regression
R function larsR
Comparing correlations
R functions TWOpov and TWOpNOV
Empirical likelihood
Exercises
8. 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 function trimpb2 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 function powest and pow2an
Permutation tests
R function permg
Rank-based and nonparametric methods
Wilcoxon-Mann-Whitney test
R functions wmw and wilcox.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 function ebarplot
Plotting the shift function
Plotting the distributions
R function sumplot2g
Other approaches
Comparing measures of scale
Methods for 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, and power.prop.test
Making decisions about which method to use
Exercises
9. 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
Handling missing values
R functions rm2miss and rmmismcp
A different perspective when using robust measures of location
R function loc2dif and l2drmci
The sign test
R function signt
Wilcoxon signed rank test
R function wilcox.test
Comparing variances
Comparing robust measures of scale
R function rmrvar
Comparing all quantiles
R function lband
Plots for dependent groups
R function g2plotdifxy
Exercises
10. One-way ANOVA
Analysis of variance for independent groups
A conceptual overview
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
Welch's test
Judging sample sizes and controlling power when data are available
R functions bdanova1 and bdanova2
Trimmed means
R functions t1way, t1wayv2, and t1wayF
Comparing groups based on medians
R functions med1way
Bootstrap methods
A bootstrap-t method
R function t1waybt
Two percentile bootstrap methods
R functions b1way and pbadepth
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 Kruskal-Wallis test
R function kruskal.test
Method BDM
R function bdm
Exercises
11. 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 function 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
12. 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 from 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
13. Multiple comparisons
One-way ANOVA, independent groups
Fisher's least significant difference method
The Tukey-Kramer method
R function TukeyHSD
Tukey-Kramer and the ANOVA F test
A step-down method
Dunnett's T3
Games-Howell method
Comparing trimmed means
R function lincon
Alternative methods for controlling FWE
Percentile bootstrap methods for comparing trimmed means, medians, and M-estimators
R functions medpb, tmcppb, pbmcp, and mcppb20
A bootstrap-t method
R function linconb
Rank-based methods
R functions cidmul, cidmulv2, and bmpmul
Two-way, between-by-between design
Scheffé's homoscedastic method
Heteroscedastic methods
Extension of Welch-S̆idák and Kaiser-Bowden methods to trimmed means
R function kbcon
R function con2way
Linear contrasts based on medians
R functions msmed and mcp2med
Bootstrap methods
R functions linconb, 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, and dtrimpb
Bootstrap-t method
R function bptd
Between-by-within designs
R functions bwmcp, bwamcp, bwbmcp, bwimcp, spmcpa, spmcpb, 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, bbbmcppb, bbwmcppb, bwwmcppb, and wwwmcppb
Exercises
14. Some multivariate methods
Location, scatter, and detecting outliers
Detecting outliers via robust measures of location and scatter
R functions cov.mve and com.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 functions smean
One-sample hypothesis testing
Comparing dependent groups
R functions smeancrv2, hotel1, and rmdzeroOP
Two-sample case
R functions smean2, mat2grp, and matsplit
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
R function outpca, robpca, robpcaS, Ppca, and Ppca.summary
Exercises
15. Robust regression and measures of association
Robust regression estimators
The Theil-Sen estimator
R functions tsreg 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 tsts
Comments on choosing a regression estimator
Testing hypotheses when using robust regression estimators
R functions regtest, regtestMC, regci, and regciMC
Comparing measures of location via dummy coding
Dealing with curvature : smoothers
Cleveland's smoother
R functions lowess and lplot
Smoothers based on robust measures of location
R functions rplot and rplotsm
More smoothers.
R functions kerreg, runpd, and qsmcobs
Prediction when X is discrete : the R function rundis
Seeing curvature with more than two predictors
R function prplot
Some alternative methods
Some robust correlations and tests of independence
Kendall's tau
Spearman's rho
Winsorized correlation
R function wincor
OP correlation
R function scor
Inferences about robust correlations : dealing with heteroscedasticity
R function corb
Measuring the strength of an association based on a robust fit
Comparing the slopes of two independent groups
R functions reg2ci, runmean2g, and l2plot
Tests for linearity
R functions lintest, lintestMC, and linchk
Identifying the best predictors
R functions regpord, ts2str, and sm2strv7
Detecting interactions and moderator analysis
R functions adtest
Graphical methods for assessing interactions
R functions kercon, runsm2g, regi, ols.polt.inter, and reg.plot.inter
ANCOVA
Classic ANCOVA
Some modern ANCOVA methods
R functions ancsm, Qancsm, ancova, ancpb, ancbbpb, and ancboot
Exercises
16. Basic methods for analyzing categorical data
Goodness of fit
R functions chisq.test and pwr.chisq.test
A 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
Appendix D: References.
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