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# Tests on location

In this chapter we present nonparametric tests for the location parameter. The simplest one is the sign test, with the only assumption that the data are sampled from a continuous distribution. This test has its foundation in the early eighteenth century (Arbuthnot 1710). Some of the tests presented here find their parametric analogs in the one- and two-sample t-tests. So, these tests are good alternatives if the Gaussian distribution assumption appears to be violated. We show how to perform one-, two-, and -sample nonparametric tests on the location parameter in SAS and R. Tables of critical values can be found, for example, in Owen (1962) and in Hollander and Wolfe (1999) as well as in many other textbooks.

# 8.1 One-sample tests

In this section we deal with the question if the median of a population differs from a predefined value. The most straightforward test is the sign test. However, if a symmetric distribution can be assumed the Wilcoxon signed-rank test is a better alternative.

## 8.1.1 Sign test

 Description: Tests if the location (median ) of a population differs from a specific value . Assumptions: Data are measured at least on an ordinal scale. ...

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