scipy.stats.rankdata

scipy.stats.rankdata(a, method='average', *, axis=None)

Assign ranks to data, dealing with ties appropriately.

By default (axis=None), the data array is first flattened, and a flat array of ranks is returned. Separately reshape the rank array to the shape of the data array if desired (see Examples).

Ranks begin at 1. The method argument controls how ranks are assigned to equal values. See [1] for further discussion of ranking methods.

Parameters

aarray_like

The array of values to be ranked.

method{‘average’, ‘min’, ‘max’, ‘dense’, ‘ordinal’}, optional

The method used to assign ranks to tied elements. The following methods are available (default is ‘average’):

• ‘average’: The average of the ranks that would have been assigned to all the tied values is assigned to each value.

• ‘min’: The minimum of the ranks that would have been assigned to all the tied values is assigned to each value. (This is also referred to as “competition” ranking.)

• ‘max’: The maximum of the ranks that would have been assigned to all the tied values is assigned to each value.

• ‘dense’: Like ‘min’, but the rank of the next highest element is assigned the rank immediately after those assigned to the tied elements.

• ‘ordinal’: All values are given a distinct rank, corresponding to the order that the values occur in a.

axis{None, int}, optional

Axis along which to perform the ranking. If None, the data array is first flattened.

Returns

ranksndarray

An array of size equal to the size of a, containing rank scores.

References

1

“Ranking”, https://en.wikipedia.org/wiki/Ranking

Examples

>>> from scipy.stats import rankdata
>>> rankdata([0, 2, 3, 2])
array([ 1. ,  2.5,  4. ,  2.5])
>>> rankdata([0, 2, 3, 2], method='min')
array([ 1,  2,  4,  2])
>>> rankdata([0, 2, 3, 2], method='max')
array([ 1,  3,  4,  3])
>>> rankdata([0, 2, 3, 2], method='dense')
array([ 1,  2,  3,  2])
>>> rankdata([0, 2, 3, 2], method='ordinal')
array([ 1,  2,  4,  3])
>>> rankdata([[0, 2], [3, 2]]).reshape(2,2)
array([[1. , 2.5],
      [4. , 2.5]])
>>> rankdata([[0, 2, 2], [3, 2, 5]], axis=1)
array([[1. , 2.5, 2.5],
       [2. , 1. , 3. ]])