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.
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Famous quotes containing the words ranking and/or statistics:
“Falsity cannot keep an idea from being beautiful; there are certain errors of such ingenuity that one could regret their not ranking among the achievements of the human mind.”
—Jean Rostand (1894–1977)
“O for a man who is a man, and, as my neighbor says, has a bone in his back which you cannot pass your hand through! Our statistics are at fault: the population has been returned too large. How many men are there to a square thousand miles in this country? Hardly one.”
—Henry David Thoreau (1817–1862)