Tests for Trend and Association

In this chapter, we consider additional applications of the smooth model paradigm described earlier in Chapter 4 We begin by considering tests for trend. We then proceed with the study of the one-sample test for a randomized block design. We obtain a different proof of the asymptotic distribution of Friedman’s statistic based on Alvo (2016) who developed a likelihood function approach for the analysis of ranking data. Further, we derive a test statistic for the two-sample problem as well as for problems involving various two-way experimental designs. We exploit the parametric paradigm further by introducing the use of penalized likelihood in order to gain further insight into the data. Specifically, if judges provide rankings of t objects, penalized likelihood enables us to focus on those objects which exhibit the greatest differences.

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