Signs, Ranks, and Signed Ranks

The following are used in testing non-parametric statistics.

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.
    Source: Statistics II for Dummies