Sign Test vs. Wilcoxon Signed-Ranks Test Using the data in Exercise 1, we can test for no difference between September weights and April weights by using the sign test or the Wilcoxon signed-ranks test. In what sense does the Wilcoxon signed-ranks test incorporate and use more information than the sign test?
Sign test only uses the sign of paired difference, while the Wilcoxon signed rank test uses magnitude and sign of the paired difference ranks. The sign test uses only the signs of the differences. By using ranks instead of signs, the Wilcoxon signed ranks test takes the magnitude of the differences into account, so it includes and uses more information than the sign test and therefore reflects true nature of the data.