We can see here that the decision for the related-samples sign test is based on comparing the number of concordant pairs (pairs with the same sign) to the total number of pairs.
We can deduce that in a related-samples sign test, the researcher examines the differences between paired observations (in this case, positive and negative ranks) to assess if there's a systematic difference between the two conditions.
Given:
- Number of positive ranks (n₁) = 13
- Number of negative ranks (n₂) = 4
- Total number of pairs (n) = 17
To conduct the related-samples sign test, the null hypothesis assumes that there's no difference between the two conditions, i.e., the number of positive and negative ranks are equally likely. The alternative hypothesis assumes that there's a systematic difference.