like X= [1,3,3,5,1,7], the rank values would be [1,2,2,3,1,4] if tied ranks get the same rank value.

But the ranks can be transformed to [0.5, 2.5, 2.5,3, .5, 4] if ties are replaced by the mean of tied ranks.

Here is Python code to compute ranks based on raw scores according to four strategies published in the reference.

""" File scores2ranks.py Author Ernesto Adorio, PhD. UPDEPP at Clarkfield, Pampanga ernesto.adorio@gmail.com Desc Conversion of raw scores to ranks using various strategies. Version 0.0.1 October 1, 2011 License Educational use only with proper attribution for research purposes. Reference http://en.wikipedia.org/wiki/Ranking """ def scores2ranks(X, ztol = 1.0e-1, breakties = 1): """ Converts raw scores to ranks, returning an array of ranks. Args X - scores to convert to ranks ztol - equality comparison tolerance breakties- strategy: 0 - None. 1234 ordinal ranking 1 - replace ties by mean of tied ranks.1 2.5, 2.5, 4 fractional ranking. 2 - (competition rank) 1224 standard competition ranking. 3 - replace ties by highest tied rank. 1334 modified competition ranking. 4 - replace rank after ties in sequence 1223 dense ranking. References: For conversion of matrix scores to ranks using fractional ranking: http://my-other-life-as-programmer.blogspot.com/2011/02/python-converting-raw-scores-to-ranks.html """ Z = [(x, i) for i, x in enumerate(X)] Z.sort() n = len(Z) Rx = [0] * n for j, (x,i) in enumerate(Z): Rx[i] = j+1 if breakties == 0: return Rx s = 1 # sum of ties. start = end = 0 # starting and ending marks. for i in range(1, n): if abs(Z[i][0] -Z[i-1][0]) < ztol and i != n-1: pos = Z[i][1] s+= Rx[pos] end = i else: #end of similar x values. if breakties == 1: tiedRank = float(s)/(end-start+1) for j in range(start, end+1): Rx[Z[j][1]] = tiedRank if breakties == 2 or breakties == 4: tiedRank = Rx[Z[start][1]] for j in range(start, end+1): Rx[Z[j][1]] = tiedRank if breakties == 3: tiedRank = Rx[Z[end][1]] for j in range(start, end+1): Rx[Z[j][1]] = tiedRank start = end = i s = Rx[Z[i][1]] if breakties == 4: #ensure that the ranks are in sequence! for i, x in enumerate(sorted(list(set(Rx[:])))): for j, y in enumerate(Rx): if y == x: Rx[j] = i+1 return Rx if __name__ == "__main__": X= [1,3,3,5, 1, 7] print "X = ", X print scores2ranks(X, breakties = 4)When the above code is run, it outputs

$ python scores2ranks.py X = [1, 3, 3, 5, 1, 7] strategy 0 : [1, 3, 4, 5, 2, 6] strategy 1 : [1.5, 3.5, 3.5, 5.0, 1.5, 6] strategy 2 : [1, 3, 3, 5, 1, 6] strategy 3 : [2, 4, 4, 5, 2, 6] strategy 4 : [1, 2, 2, 3, 1, 4]

I will be grateful if readers will discover any mistake.

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ReplyDeleteif you take an Array [2,4,4,4]

ReplyDeletethen the rank returned is [1,2,2,3]

but it must have returned [1,2,2,2].Do we have a way to fix this?