ABSTRACT
This chapter discusses methods that rely on fewer assumptions than standard analysis. Transformations can be used to get free of assumptions by attempting to conform to those very assumptions. Transformations can improve the behavior of inferential statistics for testing and interval estimation. In the absence of theory or strong empirical evidence for a particular transformation, many researchers turn to rank-based methods, a nonparametric monotone transformation of the data. Many problems with assumptions can be overcome by replacing observations by their ranks. Ranks are most often used in testing hypotheses about differences in the center of distributions. Statistical packages can be used to replace responses by ranks and then use standard analysis of variance methods. Analysis of variance methods are fairly robust to violations of assumptions of equal variance and normality. Markov chain Monte Carlo methods construct a Markov chain which samples from the data likelihood.
