Suppose we have evidence that points to a symmetric population distribution. Then a Wilcoxon signed rank test for the median is in order. Additionally, with the population distribution symmetric, this test for the median is “equivalent to a test for the mean.” To execute the Wilcoxon signed rank test, let us extract a random sample of size n with values X1, X2, . . ., Xn from a continuous symmetric population and test the following hypotheses pertaining to the population median MED:
|Case 1||Case 2||Case 3|
|H0: MED = MEDo||H0: MED = MEDo||H0: MED = MEDo|
|H1: MED ≠ MEDo||H1: MED > MEDo||H1: MED < MEDo|
where MEDo is the null value of MED.
To perform the Wilcoxon signed rank test, let us consider the following sequence of steps:
Let us specify our test statistic as
the sum of the ...