ABSTRACT
All of the hypothesis test discussions in the previous two chapters (Chapter 7: One-Sample Hypothesis Testing and Chapter 8: Two-Sample Hypothesis Testing) have assumed the data follow some probability distribution (normal, binomial). However, it is rarely the case that real data collected in clinical and public health research adhere to these distributional assumptions. Although all data will become approximately normal with a large enough sample size, some studies do not have a sufficient sample size to make the assumptions necessary for parametric (distribution-based) tests. When assumptions cannot be made about the underlying distribution of the data or there are very small sample sizes, nonparametric hypothesis tests can be used. The chapter includes common nonparametric statistical tests such as the sign test (paired data), the Wilcoxon signed-rank test (paired data; nonparametric counterpart of the paired t-test), and the Wilcoxon rank-sum test (independent data; nonparametric counterpart of independent two-sample t-test). Readers will learn when to use and how to calculate each test. Statistical tables are provided in the appendix for the Wilcoxon sign-ranked (Table A.7) and Wilcoxon rank-sum (Table A.8) exact tests when the normal approximation is not appropriate. Use of statistical software (SAS and Stata) to conduct tests is demonstrated.
