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I have two arrangements(i.e. permutations) of numbers. First one is the target/real arrangement. Second, is the observed arrangement.

e.g.

Target := 1,2,3,4,5,6,7

Observed := 4,1,7,3,2,5,6

Any two elements in an arrangement is not equal. What kind of test should I use?

p.s. I am not good in statistics. I am trying to evaluate a simulation model with real world data. Target arrangement is a sequence of real world events while Observed arrangement is the sequence of events which occurred in a simulation. My hypothesis is that these two are similar.

--EDIT--

Can this be done using Sequence Alignment methods used in Bioinformatics?

--EDIT-- Actually i have 30 samples (30 subjects participated). All target values and observed values for a particular sample are in the same range where range is [1,n] and n ~= 15.

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closed as unclear what you're asking by whuber Jan 9 '14 at 16:00

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ First, your "hypothesis" is non-scientific in that it is vague and undefined and therefore is not subject to statistical testing. Please explain to us how you would quantify "similar." Second, it is (almost) impossible to perform a test based on a single observation: do you have multiple observations of the same type to compare to the target? $\endgroup$ – whuber Dec 12 '13 at 7:27
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    $\begingroup$ I am actually trying to figure out how to measure similarity. I added some info to the question. i have 30 x 4 data which is 120 real world sequences and 120 observed sequences. $\endgroup$ – Deamonpog Dec 12 '13 at 7:30
  • $\begingroup$ Finally in my project, I used Levenshtein Distance and Median Displacement as measures for similarity. This link shows the same question i posted on math exchange, and median displacement is taken from the method suggested by the answer (median of the distribution of displacements). Thanks you Slank for suggesting Levenshtein Distance. $\endgroup$ – Deamonpog Jan 9 '14 at 15:57
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First of all, I would suggest to reconsider the names you chose for your data. In most places 'Observed' is used for the actual observed/measured/real value of your data, so in your case I would expect it to be used for the sequence of real world events.

I would also suggest to switch 'Targeted' for 'predicted' or 'estimated', or anything that signifies that this is coming out of your simulation model.

To attempt to answer what I think you are asking here, can you have a look at this from stackoverflow?

LINK

Levenshtein distance might be what you are looking for.

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  • $\begingroup$ Thank you. I was referring to real world events as "Targeted" and "Observed" for data retrieved form the simulation. I will also try asking in stackoverflow then. There had been no good way for comparing real world with virtual world in Virtual Reality for years. Most research was evaluated by just using user based liket-scales or similar methods. I think this should be another researach. I will look into your link and update this for everyone. :) $\endgroup$ – Deamonpog Dec 12 '13 at 14:52

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