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 fi nd this book a valuable resource. Students using SAS and R will also fi nd it an excellent choice for reference and data analysis.

Preface xiii Part I INTRODUCTION 1 1 Statistical hypothesis testing 3 1.1 Theory of statistical hypothesis testing 3 1.2 Testing statistical hypothesis with SAS and R 4 1.3 Presentation of the statistical tests 13 References 15 Part II NORMAL DISTRIBUTION 17 2 Tests on the mean 19 2.1 One–sample tests 19 2.2 Two–sample tests 23 References 35 3 Tests on the variance 36 3.1 One–sample tests 36 3.2 Two–sample tests 41 References 47 Part III BINOMIAL DISTRIBUTION 49 4 Tests on proportions 51 4.1 One–sample tests 51 4.2 Two–sample tests 55 4.3 K–sample tests 62 References 64 Part IV OTHER DISTRIBUTIONS 65 5 Poisson distribution 67 5.1 Tests on the Poisson parameter 67 References 75 6 Exponential distribution 76 6.1 Test on the parameter of an exponential distribution 76 Reference 78 Part V CORRELATION 79 7 Tests on association 81 7.1 One–sample tests 81 7.2 Two–sample tests 94 References 98 Part VI NONPARAMETRIC TESTS 99 8 Tests on location 101 8.1 One–sample tests 101 8.2 Two–sample tests 110 8.3 K–sample tests 116 References 118 9 Tests on scale difference 120 9.1 Two–sample tests 120 References 131 10 Other tests 132 10.1 Two–sample tests 132 References 135 Part VII GOODNESS–OF–FIT TESTS 137 11 Tests on normality 139 11.1 Tests based on the EDF 139 11.2 Tests not based on the EDF 148 References 152 12 Tests on other distributions 154 12.1 Tests based on the EDF 154 12.2 Tests not based on the EDF 164 References 166 Part VIII TESTS ON RANDOMNESS 167 13 Tests on randomness 169 13.1 Run tests 169 13.2 Successive difference tests 178 References 185 Part IX TESTS ON CONTINGENCY TABLES 187 14 Tests on contingency tables 189 14.1 Tests on independence and homogeneity 189 14.2 Tests on agreement and symmetry 197 14.3 Test on risk measures 205 References 214 Part X TESTS ON OUTLIERS 217 15 Tests on outliers 219 15.1 Outliers tests for Gaussian null distribution 219 15.2 Outlier tests for other null distributions 229 References 235 Part XI TESTS IN REGRESSION ANALYSIS 237 16 Tests in regression analysis 239 16.1 Simple linear regression 239 16.2 Multiple linear regression 246 References 252 17 Tests in variance analysis 253 17.1 Analysis of variance 253 17.2 Tests for homogeneity of variances 258 References 263 Appendix A Datasets 264 Appendix B Tables 271 Glossary 284 Index 287

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