**Fundamentals of Modern Statistical Methods 2nd Edition by Rand R. Wilcox, ISBN-13: 978-1441955241**

[PDF eBook eTextbook]

- Publisher: Springer; 2nd ed. 2010 edition (March 18, 2010)
- Language: English
- 265 pages
- ISBN-10: 1441955240
- ISBN-13: 978-1441955241

Conventional statistical methods have a very serious flaw. They routinely miss differences among groups or associations among variables that are detected by more modern techniques, even under very small departures from normality. Hundreds of journal articles have described the reasons standard techniques can be unsatisfactory, but simple, intuitive explanations are generally unavailable. Situations arise where even highly nonsignificant results become significant when analyzed with more modern methods.

Without assuming the reader has any prior training in statistics, Part I of this book describes basic statistical principles from a point of view that makes their shortcomings intuitive and easy to understand. The emphasis is on verbal and graphical descriptions of concepts. Part II describes modern methods that address the problems covered in Part I. Using data from actual studies, many examples are included to illustrate the practical problems with conventional procedures and how more modern methods can make a substantial difference in the conclusions reached in many areas of statistical research.

The * second edition* of this book includes a number of advances and insights that have occurred since the first edition appeared. Included are new results relevant to medians, regression, measures of association, strategies for comparing dependent groups, methods for dealing with heteroscedasticity, and measures of effect size.

**Table of Contents:**

Introduction

1(10)

A Brief History of the Normal Curve

2(3)

Empirical Studies Regarding Normality

5(1)

Inferential Methods

6(5)

Getting Started

11(18)

Probability Curves

11(1)

The Mean

12(4)

The Median

16(2)

A Weighted Mean

18(1)

Variance

19(1)

Measuring Error

20(2)

Fitting a Straight Line to Data

22(5)

Two Views of the Computations

25(2)

A Summary of Key Points

27(2)

The Normal Curve And Outlier Detection

29(18)

The Normal Curve

29(3)

Detecting Outliers

32(2)

The Boxplot

34(1)

The Central Limit Theorem

35(9)

Normality and the Median

40(4)

Three Points Worth Stressing

44(1)

A Summary of Key Points

45(2)

Accuracy And Inference

47(16)

Some Optimal Properties of the Mean

47(2)

The Median Versus the Mean

49(3)

Regression

52(3)

Confidence Intervals

55(2)

Confidence Intervals for the Population Mean

57(1)

Confidence Interval for the Slope

58(4)

A Summary of Key Points

62(1)

Hypothesis Testing And Small Sample Sizes

63(24)

Hypothesis Testing

63(5)

The One-Sample T Test

68(4)

Some Practical Problems With Student’s T

72(5)

The Two-Sample Case

77(2)

The Good News About Student’s T

79(1)

The Bad News About Student’s T

79(2)

What Does Rejecting With Student’s T Tell Us?

81(2)

Comparing Multiple Groups

83(1)

Comparing Medians

83(1)

A Summary of Key Points

84(1)

Bibliographic Notes

85(2)

The Bootstrap

87(22)

Two Bootstrap Methods for Means

88(8)

The Percentile Method

88(4)

The Bootstrap t Method

92(4)

Testing Hypotheses

96(2)

Why Does the Bootstrap t Perform Well Compared to Student’s T?

96(2)

Comparing Two Independent Groups

98(1)

Hypothesis Testing

98(1)

Comparing Medians

99(1)

Regression

99(4)

A Modified Percentile Bootstrap Method

100(2)

The Wild Bootstrap

102(1)

Correlation And Tests of Independence

103(4)

A Summary of Key Points

107(1)

Bibliographic Notes

108(1)

A Fundamental Problem

109(20)

Power

112(2)

Another Look at Accuracy

114(1)

The Graphical Interpretation of Variance

115(1)

Outlier Detection

115(2)

Measuring Effect Size

117(3)

How Extreme Can the Mean Be?

120(1)

Regression

120(3)

Pearson’s Correlation

123(2)

More About Outlier Detection

125(1)

A Summary of Key Points

125(1)

Bibliographic Notes

126(3)

Robust Measures of Location

129(18)

The Trimmed Mean

131(7)

The Population Trimmed Mean

136(2)

M-Estimators

138(3)

Computing a One-Step M-Estimator of Location

141(3)

A Summary of Key Points

144(1)

Bibliographic Notes

145(2)

Inferences About Robust Measures of Location

147(22)

Estimating the Variance of the Trimmed Mean

147(6)

Inferences About the Population Trimmed Mean

153(3)

The Relative Merits of Using a Trimmed Mean Versus Mean

156(1)

The Two-Sample Case

157(2)

Power Using Trimmed Means Versus Means

159(1)

Inferences Based On M-Estimators

160(1)

The Two-Sample Case Using an M-Estimator

161(1)

Comparing Medians

161(1)

Robust Measures of Effect Size

162(1)

Some Remaining Issues

163(2)

Comparing Dependent Groups

165(1)

A Summary of Key Points

166(1)

Bibliographic Notes

167(2)

Measures of Association

169(24)

What Does Pearson’s Correlation Tell Us?

169(3)

Other Ways Pearson’s Correlation Is Used

172(3)

The Winsorized Correlation

175(3)

Spearman’s RHO

178(1)

Kendall’s Tau

179(1)

Methods Related to M-Estimators

180(1)

A Possible Problem

180(3)

Global Measures of Association

183(4)

Minimum Volume Ellipsoid Estimator

183(1)

Minimum Covariance Determinant Estimator

184(3)

Other Global Measures of Association

187(1)

Curvature

187(4)

Measuring the Strength of an Association Based on a Smoother

190(1)

A Summary of Key Points

191(1)

Bibliographic Notes

192(1)

Robust Regression

193(24)

Theil – Sen Estimator

194(3)

Regression Via Robust Correlation And Variances

197(1)

L1 Regression

198(2)

Least Trimmed Squares

200(3)

Least Trimmed Absolute Value

203(1)

Least Median of Squares

203(1)

Regression Outliers And Leverage Points

203(3)

M-Estimators

206(2)

The Deepest Regression Line

208(1)

Relative Merits And Extensions to Multiple Predictors

209(1)

Correlation Based on Robust Regression

210(1)

Robust Smoothers

210(1)

Comparing Regression Lines: Modern Improvements on Ancova

211(2)

Choosing a Regression Method

213(2)

A Summary of Key Points

215(1)

Bibliographic Notes

215(2)

Alternative Strategies And Software

217(20)

Ranked-Based Methods for Comparing Two Groups

217(6)

Empirical Likelihood

223(1)

Permutation Tests

224(2)

Plots for Comparing Two Groups

226(3)

Comparing More Than Two Groups

229(3)

Rank-Based Methods for Comparing Multiple Groups

232(1)

Regression Based on Ranked Residuals

233(1)

Software

233(2)

A Summary of Key Points

235(1)

Bibliographic Notes

236(1)

Appendix A

237(2)

References

239

* Rand Wilcox* is a professor of psychology at the University of Southern California. He is a fellow of the Royal Statistical Society and the Association for Psychological Science. Dr. Wilcox currently serves as an associate editor of Computational Statistics & Data Analysis, Communications in Statistics: Theory and Methods, Communications in Statistics: Simulation and Computation, and Psychometrika. He has published more than 280 articles in a wide range of statistical journals and he is the author of six other books on statistics.

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