Question

How does the Wilcoxon signed-rank test improve on the sign test?

Answer 1

Wilcoxon test improve on the Sign test:

1) The Wilcoxon test takes into account both the direction of the differences (signs) and magnitude of the differences (rank) while the sign consider only the direction of the difference. As such the Wilcoxon test will be more efficient than the sign test.

2) Both the tests are useful generally for the same type of problem, but only the Wilcoxon test is suitable for a test of symmetry as well.

3) The assumptions required are not very restricted for the sign test, independence of observations and continuity at population median are required and for the Wilcoxon test continuity everywhere, independence and symmetry are the underlying assumptions.