Rankit
A rankit is an order statistic. It reflects the expected value of a given rank in a set of observations.
Contents
Description
Consider a set of 20 observations drawn from a normal distribution, and then sort them low to high. (For simplicity, assume standard normal.) These observations are now ranked 1 to 20.
For a given ordered position i, there is an expected value p calculated as:
This gives the rankit for position i. The rankits for a sample of 20 are:
- -1.96
- -1.44
- -1.15
- -0.93
- -0.76
- -0.60
- -0.45
- -0.32
- -0.19
- -0.06
- -0.06
- 0.19
- 0.32
- 0.45
- 0.60
- 0.76
- 0.93
- 1.15
- 1.44
- 1.96
More generally, the set of observations does not need to be sorted, only ranked. Furthermore, the formula can be abstracted to alternative constants as a (thereby requiring adjustments to the denominator as well). For observation i, the rank is ri and the rankit is pi:
General guidance for a:
for n ≤ 10, use 3/8
for n > 10, use 0.5
Note that 1 - 2a cancels out in this case