The null distribution of the Wilcoxon signed-rank statistic T+ is determined from the fact that under the null hypothesis of a symmetric distribution about zero, each of the ranks 1, 2, . . . , n is equally likely to be associated with a positive sign or a negative sign. Moreover, the signs are independent of the ranks.
(a) Considering the case n = 3, identify all 23 = 8 possible associations of signs with the ranks 1, 2, and 3, and determine the value of T+ for each association.
(b) Assigning the equal probability of g to each case, obtain the distribution of T+ and verify that the tail probabilities agree with the tabulated values.