Ranking - Ranking in Statistics

Ranking in Statistics

In statistics, "ranking" refers to the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted. For example, the numerical data 3.4, 5.1, 2.6, 7.3 are observed, the ranks of these data items would be 2, 3, 1 and 4 respectively. For example, the ordinal data hot, cold, warm would be replaced by 3, 1, 2. In these examples, the ranks are assigned to values in ascending order. (In some other cases, descending ranks are used.) Ranks are related to the indexed list of order statistics, which consists of the original dataset rearranged into ascending order.

Some kinds of statistical tests employ calculations based on ranks. Examples include:

• Friedman test
• Kruskal-Wallis test
• Rank products
• Spearman's rank correlation coefficient
• Wilcoxon rank-sum test
• Wilcoxon signed-rank test

Some ranks can have non-integer values for tied data values. For example, when there is an even number of copies of the same data value, the above described fractional statistical rank of the tied data ends in ½.