188.8.131.52 Algorithms (One-Sample Wilcoxon Signed Rank Test)
The Wilcoxon Sign Rank test is used to replace the one sample t-test, when the normality is questionable. So it requires looser conditions than the one sample t-test and has a wider use than the t-test.
a) For each , for , the signed difference is found,where is a given test value for the median of the sample.
b) Ignore the cases where . Rank the rest of, use as its rank. Pay attention to that any tied values of are assigned the average of the tied ranks. For example, three? ranked as 7 8 9 are ties, then their rank is (7+8+9) /3=8.?
c) To each rank is affixed the sign of to which it corresponds. Let
d) The sum of the positive-signed ranks is calculated as
Our null hypothesis is that the population median has a specific value . We test the null hypothesis against the two-sided alternative hypothesis that the population does not have a median value . The confidence interval is converted to hypothesis-test form. The test is a one-sample Wilcoxon Sign Rank test, and it is defined as:
For more details of the algorithm, please refer to nag_wilcoxon_test (g08agc)