Signs, Ranks, and Signed Ranks

What is a sign?

• a value $\in \{0, 1\}$ assigned to each member of a data-set
• If the data-member is greater than the test-value, it's assigned a 1. Otherwise it gets a 0.

What is a rank?

• The number representing a data points' place in the ordered set (1-based index)
• If multiple points have the same value each is reassigned the mean of their original Ranks.

What is an absolute rank?

• Each point is reassigned its absolute value
• Then the set is Ranked

What is a signed rank?

1. Assign a 1 to each data point greater than the test-value.
2. Assign a 0 to the remaining points.
3. Find the absolute rank.
4. For each point, assign it a signed rank:
   \[SignedRank = Sign \times AbsoluteRank\]

What is a rank sum?

• the sum of all the ranks for a data-set.