Which statement describes how the Wilcoxon signed-rank test differs from the sign test?

Which statement describes how the Wilcoxon signed-rank test differs from the sign test?

• A. It ignores the magnitude of differences.
• B. It uses the ranks of the differences, incorporating magnitude information.
• C. It is identical to the sign test for all data.
• D. It can only be used with ordinal data.

Answer: (B)

The Wilcoxon signed-rank test differs from the sign test by using the magnitude of differences as well as their direction. It takes the absolute differences between paired observations, ranks those magnitudes, and then applies the sign of each difference to its rank. This means the test incorporates information about how large each change is, not just whether it occurred in the positive or negative direction. The sign test, by contrast, only counts how many pairs show a positive difference versus a negative difference and ignores how big the differences are. So the best description is that it uses the ranks of the differences, incorporating magnitude information. It can be used with interval or ratio data as long as the differences can be ranked, not just with ordinal data.

The Wilcoxon signed-rank test differs from the sign test by using the magnitude of differences as well as their direction. It takes the absolute differences between paired observations, ranks those magnitudes, and then applies the sign of each difference to its rank. This means the test incorporates information about how large each change is, not just whether it occurred in the positive or negative direction. The sign test, by contrast, only counts how many pairs show a positive difference versus a negative difference and ignores how big the differences are. So the best description is that it uses the ranks of the differences, incorporating magnitude information. It can be used with interval or ratio data as long as the differences can be ranked, not just with ordinal data.