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The problem is the following:

I have multiple datasets for which I want to calculate a ranking for each. All observations contained in the datasets can be arbitrarily permuted, so they are unpaired, to speak in the words of statisticians.

Example datasets are:

dataset1 = [0.6487500071525574, 0.6499999761581421, 0.6412500143051147, 0.6662499904632568, 0.6225000023841858, 0.6324999928474426, 0.637499988079071, 0.6287500262260437, 0.6412500143051147, 0.6212499737739563]

dataset2 = [0.6075000166893005, 0.6287500262260437, 0.6312500238418579, 0.6162499785423279, 0.6012499928474426, 0.6150000095367432, 0.6387500166893005, 0.6200000047683716, 0.5950000286102295, 0.5849999785423279]
 
dataset3 =[0.6237499713897705, 0.612500011920929, 0.6075000166893005, 0.6162499785423279,  0.6187499761581421, 0.6287500262260437, 0.6200000047683716, 0.6237499713897705, 0.5824999809265137, 0.5787500143051147]

I understand for datasets with paired observation, one would simply rank each observation column-wise and simply average over the average each observation has in each dataset. Example:

ranks_dataset2 = [3, 2, 2, 2.5, 3, 3, 1, 3, 2, 3]
=> Avg.Rank: 2.45

But how would I do this for unpaired observations?

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1 Answer 1

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I think I figured out a nice way on how to rank the datasets:

Ranking formula

The rank r(D) of dataset D is calculated by subtracting from the total number of datasets N_D the sum of the number of wins W_i of each observation i in D averaged over the total number of observations |D| in respect to the complete set of observations without |D|, which is N - |D|, multiplied the number of remaining datasets N_D - 1. So if all observations in D have N-|D| wins, the rank of the dataset |D| is 1. If all observations have no wins (they are 0), the rank of the dataset |D| is simply N_D.

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