Order statistics are based on the rank order of data, ignoring their absolute values. Order statistics are used particularly in nonparametric statistics such as Mann-Whitney test.
As an example consider the following sets of error counts after using some software
novice users: 17, 12, 7, 8
experts: 5, 0, 9, 2
We first sort the scores: (0,2,5,7,8,9,12,17), then map the values to their rank order giving:
novice users: 8, 7, 4, 5
experts: 3, 1, 6, 2
These values are then used to calculate tests, such as the Wilcoxon rank sum test.
novice users: 17, 12, 7, 8
experts: 5, 0, 9, 2
We first sort the scores: (0,2,5,7,8,9,12,17), then map the values to their rank order giving:
novice users: 8, 7, 4, 5
experts: 3, 1, 6, 2
These values are then used to calculate tests, such as the Wilcoxon rank sum test.
If several values are the same they are usually all given the average of the relevant ranks, for example, the data values:
3, 7, 8, 8, 12, 15, 15, 15, 20
would map to ranks
1, 2, 3.5, 3.5, 5, 7, 7, 7, 9
3, 7, 8, 8, 12, 15, 15, 15, 20
would map to ranks
1, 2, 3.5, 3.5, 5, 7, 7, 7, 9
Used in Chap. 13: page 150
Also used in hcistats2e: Chap. 4: page 58; Chap. 10: pages 111, 114
Used in glossary entries: Mann-Whitney test, nonparametric statistics, Wilcoxon rank sum test