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Ranking (statistics)
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Ranking (statistics)
In statistics, ranking is the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted.
For example, the ranks of the numerical data 3.4, 5.1, 2.6, 7.3 are 2, 3, 1, 4.
As another 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, although descending ranks can also be 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:
The distribution of values in decreasing order of rank is often of interest when values vary widely in scale; this is the rank-size distribution (or rank-frequency distribution), for example for city sizes or word frequencies. These often follow a power law.
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 fractional statistical rank of the tied data ends in ½. Percentile rank is another type of statistical ranking.
Microsoft Excel provides two ranking functions, the Rank.EQ function which assigns competition ranks in the case of ties, and the Rank.AVG function which assigns fractional ranks to ties. For example, if the data being ranked was ("5, 7, 7, 10"), then Rank.EQ would return ("1, 2, 2, 4"), whereas Rank.AVG would return ("1, 2.5, 2.5, 4"). Note that Rank.AVG preserves rank sums in the case of ties, whereas Rank.EQ does not. This makes the latter undesirable in many statistical applications. The functions have the order argument, which is by default is set to descending, i.e. the largest number will have a rank 1. This is generally uncommon for statistics where the ranking is usually in ascending order, where the smallest number has a rank 1.
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Ranking (statistics)
In statistics, ranking is the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted.
For example, the ranks of the numerical data 3.4, 5.1, 2.6, 7.3 are 2, 3, 1, 4.
As another 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, although descending ranks can also be 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:
The distribution of values in decreasing order of rank is often of interest when values vary widely in scale; this is the rank-size distribution (or rank-frequency distribution), for example for city sizes or word frequencies. These often follow a power law.
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 fractional statistical rank of the tied data ends in ½. Percentile rank is another type of statistical ranking.
Microsoft Excel provides two ranking functions, the Rank.EQ function which assigns competition ranks in the case of ties, and the Rank.AVG function which assigns fractional ranks to ties. For example, if the data being ranked was ("5, 7, 7, 10"), then Rank.EQ would return ("1, 2, 2, 4"), whereas Rank.AVG would return ("1, 2.5, 2.5, 4"). Note that Rank.AVG preserves rank sums in the case of ties, whereas Rank.EQ does not. This makes the latter undesirable in many statistical applications. The functions have the order argument, which is by default is set to descending, i.e. the largest number will have a rank 1. This is generally uncommon for statistics where the ranking is usually in ascending order, where the smallest number has a rank 1.