# Hypothesis testing for equivalence of two arrangements [closed]

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.

## 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.

• 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? – whuber Dec 12 '13 at 7:27
• 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. – Deamonpog Dec 12 '13 at 7:30
• 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. – Deamonpog Jan 9 '14 at 15:57