Statistical Hypothesis Testing with SAS and R

A comprehensive guide to statistical hypothesis testing with examples in SAS and R

When analyzing datasets the following questions often arise:

Is there a short hand procedure for a statistical test available in SAS or R?
If so, how do I use it?
If not, how do I program the test myself?

This book answers these questions and provides an overview of the most common
statistical test problems in a comprehensive way, making it easy to find and perform
an appropriate statistical test.

A general summary of statistical test theory is presented, along with a basic
description for each test, including the necessary prerequisites, assumptions, the
formal test problem and the test statistic. Examples in both SAS and R are provided,
along with program code to perform the test, resulting output and remarks
explaining the necessary program parameters.

Key features:
• Provides examples in both SAS and R for each test presented.
• Looks at the most common statistical tests, displayed in a clear and easy to follow way.
• Supported by a supplementary website http://www.d-taeger.de featuring example
program code.

Academics, practitioners and SAS and R programmers will find this book a valuable
resource. Students using SAS and R will also find it an excellent choice for reference
and data analysis.

Dirk Taeger, Institute for Prevention and Occupational Medicine of the German Social
Accident Insurance, Institute of the Ruhr-Universität Bochum (IPA), Bochum, Germany

Sonja Kuhnt, Department of Computer Science, Dortmund University of Applied Sciences
and Arts, Dortmund, Germany

Preface

Part One Introduction

1 Statistical Hypothesis Testing

1.1 Theory of Statistical Hypothesis Testing

1.2 Testing Statistical Hypothesis with SAS and R

1.2.1 Programming Philosophy of SAS and R

1.2.2 Testing in SAS and R - An Example

1.2.3 Calculating P-Values

1.3 Presentation of the Statistical Tests

References

Part Two Normal Distribution

2 Tests on the Mean

2.1 One-Sample Tests

2.1.1 Z-Test

2.1.2 T-Test

2.2 Two-Sample Tests

2.2.1 Two-Sample Z-Test

2.2.2 Two-Sample Pooled T-Test

2.2.3 Welch-Test

2.2.4 Paired Z-Test

2.2.5 Paired T-Test

References

3 Tests on the Variance

3.1 One-Sample Tests

3.1.1 _2-Test on the Variance (Mean Known)

3.1.2 _2-Test on the Variance (Mean Unknown)

3.2 Two-Sample Tests

3.2.1 Two-sample F-test on Two Populations Variances

3.2.2 T-Test on Variances of Two Dependent Populations

References

Part Three Binomial Distribution

4 Tests on Proportions

4.1 One-Sample Tests

4.1.1 Binomial Test

4.2 Two-Sample Tests

4.2.1 Z-Test for the Difference of Two Proportions (Unpooled Variances)

4.2.2 Z-Test for the Equality between Two Proportions (Pooled Variances)

4.3 K-Sample Tests

4.3.1 K-Sample Binomial Test

References

Part Four Other Distributions

5 Poisson Distribution

5.1 Tests on Poisson parameter

5.1.1 Z-Test on Poisson Parameter

5.1.2 Exact Test on Poisson Parameter

5.1.3 Z-Test on the Difference of Two Poisson Parameters

References

6 Exponential Distribution

6.1 Test on the Parameter of an Exponential Distribution

6.1.1 Z-Test on the Parameter of an Exponential Distribution

References

Part Five Correlation

7 Tests on Association

7.1 One-Sample Tests

7.1.1 Pearson’s Product Moment Correlation Coefficient

7.1.2 Spearman’s Rank Correlation Coefficient

7.1.3 Partial Correlation

7.2 Two-Sample Tests

7.2.1 Z-Test for Two Correlation Coefficients (Independent Populations)

References

Part Six Nonparametric Tests

8 Tests on Location

8.1 One-Sample Tests

8.1.1 Sign Test

8.1.2 Wilcoxon Signed Rank Test

8.2 Two-Sample Tests

8.2.1 Wilcoxon Rank-Sum Test (Mann-Whitney U test)

8.2.2 Wilcoxon Matched-Pairs Signed-Ranks Test

8.3 K-Sample Tests

8.3.1 Kruskal-Wallis Test

References

9 Tests on Scale Difference

9.1 Two-Sample Tests

9.1.1 Siegel-Tukey Test

9.1.2 Ansari-Bradley Test

9.1.3 Mood Test

References

10 Other Tests

10.1 Two-Sample Tests

10.1.1 Kolmogorov-Smirnov Two Sample Test (Smirnov Test)

References

Part Seven Goodness-of-Fit Tests

11 Tests on Normality

11.1 Tests based on the EDF

11.1.1 Kolmogorov-Smirnov Test (Lilliefors test for normality)

11.1.2 Anderson-Darling Test

11.1.3 Cram´er-von Mises Test

11.2 Tests based not on the EDF

11.2.1 Shapiro-Wilk Test

11.2.2 Jarque-Bera Test

References

12 Tests on other Distributions

12.1 Tests based on the EDF

12.1.1 Kolmogorov-Smirnov Test

12.1.2 Anderson-Darling Test

12.1.3 Cram´er-von Mises Test

12.2 Tests based not on the EDF

12.2.1 _2 Goodness-of-fit test

References

Part Eight Tests on Randomness

13 Tests on Randomness

13.1 Run Tests

13.1.1 Wald-Wolfowitz Runs Test

13.1.2 Runs Up and Down Test

13.2 Successive Difference Tests

13.2.1 von Neumann Test

13.2.2 von Neumann Rank Test (Bartels Test)

References

Part Nine Tests on Contingency Tables

14 Tests on Contingency Tables

14.1 Tests on Independence and Homogeneity

14.1.1 Fisher’s Exact Test

14.1.2 Pearson’s Chi-Square Test

14.1.3 Likelihood-Ratio Chi-Square Test

14.2 Tests on Agreement and Symmetry

14.2.1 Test on Cohen’s kappa

14.2.2 McNemar’s Test

14.2.3 Bowker’s Test for Symmetry

14.3 Test on Risk Measures

14.3.1 Large Sample Test on the Odds Ratio

14.3.2 Large Sample Test on the Relative Risk

References

Part Ten Tests on Outliers

15 Tests on Outliers

15.1 Outliers Tests for Gaussian Null Distribution

15.1.1 Grubbs’ Test

15.1.2 David-Hartley-Pearson Test

15.1.3 Dixon’s Tests

15.2 Outlier Tests for Other Null Distributions

15.2.1 Test on Outliers for Exponential Null Distributions

15.2.2 Test on Outliers for Uniform Null Distribution

References

Part Eleven Tests in Regression Analysis

16 Tests in Regression Analysis

16.1 Simple Linear Regression

16.1.1 Test on the Slope

16.1.2 Test on the Intercept

16.2 Multiple Linear Regression

16.2.1 Test on an Individual Regression Coefficient

16.2.2 Test for Significance of Regression

17 Tests in Variance Analysis

17.1 Analysis of Variance (ANOVA)

17.1.1 One-Way ANOVA

17.1.2 Two-Way ANOVA

17.2 Tests for Homogeneity of Variances

17.2.1 Bartlett Test

17.2.2 Levene Test

References

Appendix A Datasets

Appendix B

Glossary

Index

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