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. Cover......Page 1 Title Page......Page 5 Copyright......Page 6 Contents......Page 9 Preface......Page 15 Part I Introduction......Page 17 1.1 Theory of statistical hypothesis testing......Page 19 1.2 Testing statistical hypothesis with SAS and R......Page 20 1.2.1 Programming philosophy of SAS and R......Page 21 1.2.2 Testing in SAS and R-An example......Page 22 1.2.3 Calculating p-values......Page 27 1.3 Presentation of the statistical tests......Page 29 References......Page 31 Part II Normal Distribution......Page 33 2.1.1 z-test......Page 35 2.1.2 t-test......Page 38 2.2.1 Two-sample z-test......Page 39 2.2.2 Two-sample pooled t-test......Page 42 2.2.3 Welch test......Page 44 2.2.4 Paired z-test......Page 47 2.2.5 Paired t-test......Page 49 References......Page 51 3.1.1 x2-test on the variance (mean known)......Page 52 3.1.2 x2-test on the variance (mean unknown)......Page 55 3.2.1 Two-sample F-test on variances of two populations......Page 57 3.2.2 t-test on variances of two dependent populations......Page 60 References......Page 63 Part III Binomial Distribution......Page 65 4.1.1 Binomial test......Page 67 4.2.1 z-test for the difference of two proportions (unpooled variances)......Page 71 4.2.2 z-test for the equality between two proportions (pooled variances)......Page 75 4.3.1 K-sample binomial test......Page 78 References......Page 80 Part IV Other Distributions......Page 81 5.1.1 z-test on the Poisson parameter......Page 83 5.1.2 Exact test on the Poisson parameter......Page 86 5.1.3 z-test on the difference between two Poisson parameters......Page 88 References......Page 91 6.1.1 z-test on the parameter of an exponential distribution......Page 92 Reference......Page 94 Part V Correlation......Page 95 7.1.1 Pearson's product moment correlation coefficient......Page 97 7.1.2 Spearman's rank correlation coefficient......Page 102 7.1.3 Partial correlation......Page 107 7.2.1 z-test for two correlation coefficients (independent populations)......Page 110 References......Page 114 Part VI Nonparametric Tests......Page 115 8.1.1 Sign test......Page 117 8.1.2 Wilcoxon signed-rank test......Page 121 8.2.1 Wilcoxon rank-sum test (Mann-Whitney U test)......Page 126 8.2.2 Wilcoxon matched-pairs signed-rank test......Page 130 8.3.1 Kruskal-Wallis test......Page 132 References......Page 134 9.1.1 Siegel-Tukey test......Page 136 9.1.2 Ansari-Bradley test......Page 141 9.1.3 Mood test......Page 144 References......Page 147 10.1.1 Kolmogorov-Smirnov two-sample test (Smirnov test)......Page 148 References......Page 151 Part VII Goodness-of-Fit Tests......Page 153 11.1.1 Kolmogorov-Smirnov test (Lilliefors test for normality)......Page 155 11.1.2 Anderson-Darling test......Page 158 11.1.3 Cramér-von Mises test......Page 161 11.2.1 Shapiro-Wilk test......Page 164 11.2.2 Jarque-Bera test......Page 166 References......Page 168 12.1.1 Kolmogorov-Smirnov test......Page 170 12.1.2 Anderson-Darling test......Page 173 12.1.3 Cramér-von Mises test......Page 176 12.2.1 x2-Goodness-of-fit test......Page 180 References......Page 182 Part VIII Tests on Randomness......Page 183 13.1.1 Wald-Wolfowitz runs test......Page 185 13.1.2 Runs up and down test......Page 190 13.2.1 von Neumann test......Page 194 13.2.2 von Neumann rank test (Bartels' test)......Page 197 References......Page 201 Part IX Tests on Contingency Tables......Page 203 14.1.1 Fisher's exact test......Page 205 14.1.2 Pearson's x2-test......Page 208 14.1.3 Likelihood-ratio x2-test......Page 211 14.2.1 Test on Cohen's kappa......Page 213 14.2.2 McNemar's test......Page 216 14.2.3 Bowker's test for symmetry......Page 219 14.3.1 Large sample test on the odds ratio......Page 221 14.3.2 Large sample test on the relative risk......Page 226 References......Page 230 Part X Tests on Outliers......Page 233 15.1.1 Grubbs' test......Page 235 15.1.2 David-Hartley-Pearson test......Page 239 15.1.3 Dixon's tests......Page 241 15.2.1 Test on outliers for exponential null distributions......Page 245 15.2.2 Test on outliers for uniform null distributions......Page 248 References......Page 251 Part XI Tests in Regression Analysis......Page 253 16.1.1 Test on the slope......Page 255 16.1.2 Test on the intercept......Page 259 16.2 Multiple linear regression......Page 262 16.2.1 Test on an individual regression coefficient......Page 263 16.2.2 Test for significance of regression......Page 266 References......Page 268 17.1.1 One-way ANOVA......Page 269 17.1.2 Two-way ANOVA......Page 271 17.2.1 Bartlett test......Page 274 17.2.2 Levene test......Page 276 References......Page 279 Appendix A Datasets......Page 280 Appendix B Tables......Page 287 Glossary......Page 300 Index......Page 303 "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. 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."-- Unedited summary from book "This book provides a reference guide to statistical tests and their application to data using SAS and R.A general summary of statistical test theory is presented, along with a general description for each test, together with necessary prerequisites, assumptions, and the formal test problem. The test statistic is stated together with annotations on its distribution, along with examples in both SAS and R. Each example contains the code to perform the test, the output, and remarks that explain necessary program parameters"-- Provided by publisher