Statistical Hypothesis Testing with SAS and R

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  • Format: Hardcover
  • Copyright: 2014-03-24
  • Publisher: Wiley

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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.

Table of Contents


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


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


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


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



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


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


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)


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


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


10 Other Tests

10.1 Two-Sample Tests

10.1.1 Kolmogorov-Smirnov Two Sample Test (Smirnov Test)


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


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


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)


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


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


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


Appendix A Datasets

Appendix B



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