mercredi 21 août 2019

Maximum number of triplets two sequences have in common

I have two questions related to the same topic. I ran a simulation of 16000 sequences of 100 elements without repetitions with numbers between 1-4, for example: 124232143214223142314... These simulations were done to see what was the longest sequence in common between the sequences randomly generated and the pre-defined sequence. Participants were also asked to do this, to generate the sequence that they had previously learned without awareness.

I want now to do two things:

1) Determine what would constitute chance level. I was thinking about 
finding the 95th percentile as these scores would be 
highly unlikely. Hence if participant's scores were equal or above that, 
we could assume that they had knowledge. However, the random distribution 
is non-normal (rightly skewed). What would be the best approach?


2) Also, I want to find all the triplets in common between both sequences. 
So if we have sequence A: 12342134213421313242... and sequence B: 
21342134123214. It would have to count all the triplets in common 
including repetitions: 213, 134, 342, 213, etc.

I have looked at Chebyshev’s Theorem, but I am not sure if my data is adequate for it as mean = 5.42, SD = 1.05, kurtosis = 1.76 and skewness = 0.97.




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