SciPy

scipy.stats.rankdata

scipy.stats.rankdata(a, method='average')

Assign ranks to data, dealing with ties appropriately.

Ranks begin at 1. The method argument controls how ranks are assigned to equal values. See [R259] for further discussion of ranking methods.

Parameters :

a : array_like

The array of values to be ranked. The array is first flattened.

method : str, optional

The method used to assign ranks to tied elements. The options are ‘average’, ‘min’, ‘max’, ‘dense’ and ‘ordinal’.

‘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.

The default is ‘average’.

Returns :

ranks : ndarray

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

Notes

All floating point types are converted to numpy.float64 before ranking. This may result in spurious ties if an input array of floats has a wider data type than numpy.float64 (e.g. numpy.float128).

References

[R259](1, 2) “Ranking”, http://en.wikipedia.org/wiki/Ranking

Examples

>>> 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.])

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