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# (Fisher signed deviation statistic) Suppose that(x 1 ……..x n ) is a sample from an absolutely…

(Fisher signed deviation statistic) Suppose that(x1……..xn ) is a sample from an absolutely continuous distribution on R1 with density that is symmetrical about its median. Suppose we want to assess the hypothesis

One possibility for this is to use the Fisher signed deviation test based on the statistic S+. The observed value of + is given  We then assess H0 by comparing S+ o with the conditional distribution of S given the absolute deviations  If a value S+ o occurs near the smallest or largest possible value for Sunder this conditional distribution, then we assert that we have evidence against H0We measure this by computing the P-value given by the conditional probability of obtaining a value as far, or farther, from the center of the conditional distribution of S+  using the conditional mean as the center. This is an example of a randomization test, as the distribution for the test statistic is determined by randomly modifying the observed data (in this case, by randomly changing the signs of the deviations of the xi from x0).