Rank Order

Rank order refers to a property of a set of scores such that the scores are ordered from lowest to highest, or, alternatively, from highest to lowest. The scores 15, 14, 8, 11, 12 can be placed into rank order by ordering them from lowest to highest as 8, 11, 12, 14, 15. These scores can be rank ordered from highest to lowest by putting them in the order 15, 14, 12, 11, 8. Stated more formally, a set of scores is rank ordered from lowest to highest if, for any given score Xj, it is always the case that Xj−1 ≤ Xj ≤ Xj+1. Scores are rank ordered from highest to lowest if, for any given score Xj, it is always the case that Xj−1 ≥ Xj ≥ Xj+1.

Sometimes, scores are assigned a rank based on their rank order. Ranks are consecutive, ordered numbers (usually integers) in which the number reflects the relative position of a score in a set of scores that is in rank order. For example, the scores 8, 11, 12, 14, and 15 might be assigned the following ranks:

A rank of 3 means that the score is the third highest score relative to the lowest score when scores are assigned ranks where the lowest score receives a rank of 1. A rank of 4 means the score is the fourth highest score relative to the lowest score. Sometimes, scores are assigned ranks whereby the highest score has a rank of 1 and the lowest score has a rank of N, where N is the number of scores being ranked.

The same score may appear twice in a set of scores, such as 8, 11, 15, 14, 8, 12. These scores can still be rank ordered from lowest to highest as 8, 8, 11, 12, 14, 15, or from highest to lowest as 15, 14, 12, 11, 8, 8. When assigning ranks to duplicate scores, the tradition is to assign a rank value that is the average of the ranks, as follows:

where the rank assigned to the two values of 8 is based on(1 + 2)/2 = 1.5.