Re: [R] How do you test for "consecutivity"?

From: Charles C. Berry <cberry_at_tajo.ucsd.edu>
Date: Tue, 29 Apr 2008 09:34:53 -0700

On Tue, 29 Apr 2008, Anthony28 wrote:

>
> I need to use R to model a large number of experiments (say, 1000). Each
> experiment involves the random selection of 5 numbers (without replacement)
> from a pool of numbers ranging between 1 and 30.
>
> What I need to know is what *proportion* of those experiments contains two
> or more numbers that are consecutive. So, for instance, an experiment that
> yielded the numbers 2, 28, 31, 4, 27 would be considered a "consecutive =
> true" experiment since 28 and 27 are two consecutive numbers, even though
> they are not side-by-side.
>
> I am quite new to R, so really am puzzled as to how to go about this. I've
> tried sorting each experiment, and then subtracting adjacent pairs of
> numbers to see if the difference is plus or minus 1. I'm also unsure about
> whether to use an array to store all the data first.
>
> Any assistance would be much appreciated.

Are the numbers 1:30 equiprobable??

If so, you can find the probability by direct enumeration.

> mat <- combn(30,5) # each column happens to be in order
> tab <- table( mat[2:5,]-mat[1:4,]==1, col(mat[1:4,]) )
> table(tab[2,])

     0 1 2 3 4
65780 59800 15600 1300 26
> prop.table( table(tab[2,] != 0 ) )

     FALSE TRUE
0.4615946 0.5384054
>

If the numbers are not equiprobable, you will need to weight the values of tab[2,] according to the probability of each column of mat.

HTH, Chuck

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Charles C. Berry                            (858) 534-2098
                                             Dept of Family/Preventive Medicine
E mailto:cberry_at_tajo.ucsd.edu	            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego 92093-0901

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