Measure the deviation of a ranking of elements

[Stef7]

Hello there,

I have elements in a table as seen here:

	1st place	2nd place	3rd place	4th place	5th place
Experiment1	Element20	Element23	Element10	Element13	Element0
Experiment2	Element23	Element27	Element10	Element20	Element13
Experiment3	Element23	Element20	Element10	Element13	Element1
Experiment4	Element23	Element13	Element10	Element24	Feature18
Experiment5	Element23	Element13	Element28	Element27	Feature24

As you can see for different experiments the ranking of the elements (1st place, 2nd place, etc.) changes. Also, some new elements might appear in the top 5 places while others can disappear.

I would like to measure the ranking variation/deviation (I am not sure how to properly call it) of each unique element. Roughly what I want is: "how much each element moves in the rankings". I thought of assigning the numbers 1-5 on the places - columns and counting the occurrences of each element at each place for getting the std deviation. For example for Element20 we have the places (1,2,4) -> std deviation = 1.24. But I am not sure whether I should be calculating a sample or population std deviation, or measuring something else completely.

Also is there a way to measure the global ranking deviation (sorry for the bad terming), which would reflect the volatility (or robustness) of the elements on the ranking?

I have not much experience in probability/statistics, so any help on this will be greatly appreciated.

Cheers

 

[Deleted member 4993]

Hello there,

I have elements in a table as seen here:

	1st place	2nd place	3rd place	4th place	5th place
Experiment1	Element20	Element23	Element10	Element13	Element0
Experiment2	Element23	Element27	Element10	Element20	Element13
Experiment3	Element23	Element20	Element10	Element13	Element1
Experiment4	Element23	Element13	Element10	Element24	Feature18
Experiment5	Element23	Element13	Element28	Element27	Feature24

As you can see for different experiments the ranking of the elements (1st place, 2nd place, etc.) changes. Also, some new elements might appear in the top 5 places while others can disappear.

I would like to measure the ranking variation/deviation (I am not sure how to properly call it) of each unique element. Roughly what I want is: "how much each element moves in the rankings". I thought of assigning the numbers 1-5 on the places - columns and counting the occurrences of each element at each place for getting the std deviation. For example for Element20 we have the places (1,2,4) -> std deviation = 1.24. But I am not sure whether I should be calculating a sample or population std deviation, or measuring something else completely.

Also is there a way to measure the global ranking deviation (sorry for the bad terming), which would reflect the volatility (or robustness) of the elements on the ranking?

I have not much experience in probability/statistics, so any help on this will be greatly appreciated.

Cheers

I am assuming this problem is related to your work as opposed to classroom assignment. But we need to know where can we start to explain to you.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[Stef7]

I am assuming this problem is related to your work as opposed to classroom assignment. But we need to know where can we start to explain to you.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

This is part of some research that I am conducting. The table is a result of programming models and outputs that is of no importance. What I want to measure is the robustness of the elements in the way they are ranked. As I mentioned I am interested in the variability for both scenarios (the one being the deviation of each element in the rankings and the other being the global variability/volatility of the elements on the table reflecting the ranking differences). My idea was to use the standard deviation formula for each independent element in order to solve the 1st scenario. But I am not sure if it is a mathematically correct solution for expressing the ranking deviation, since I work with an order of elements instead of values of a population/sample. I am generally stuck due to my lack of creativity and knowledge in descriptive Statistics.