[R] (Fisher) Randomization Test for Matched Pairs: Permutation Data Setup Based on Signs

[Petr Savicky]

On Thu, Mar 08, 2012 at 09:49:20PM -0800, Ghandalf wrote:
> Hi,
> 
> I am currently attempting to write a small program for a randomization test
> (based on rank/combination) for matched pairs. If you will please allow me
> to introduce you to some background information regarding the test prior to
> my question at hand, or you may skip down to the bold portion for my issue. 
> 
> There are two sample sizes; the data, as I am sure you guessed, is matched
> into pairs and each pair's difference is denoted by Di. 
> 
> The test statistic =*T* = Sum(Di) (only for those Di > 0). 
> 
> The issue I am having is based on the method required to use in R to setup
> the data into the proper structure. I am to consider the absolute value of
> Di, without regard to their sign. There are 2^n ways of assigning + or -
> signs to the set of absolute differences obtained, where n = the number of
> Dis. That is, we can assign + signs to all n of the |Di|, or we might assign
> + to |D1| but - signs to |D2| to |Dn|, and so forth.
> 
>  So, for example, if I have *D1=-16, D2=-4, D3=-7, D4=-3, D5=-5, D6=+1, and
> D7=-10 and n=7. *
> I need to consider the 2^7 ways of assigning signs that result in the lowest
> sum of the "positive" absolute difference. To exemplify further, we have
> *
> -16, -4, -7, -3, -5, -1, -10            T = 0
> -16, -4, -7, -3, -5, +1, -10           T = 1
> -16, -4, -7, +3, -5, -1, -10           T = 3
> -16, -4, -7, +3, -5, +1, -10          T = 4 *
> ... and so on. 

Hi.

The minimum sum of "positive" absolute differencies is always
zero and is achieved for every sign combination, which
assigns -1 to all nonzero abs(Di) and any sign to zero abs(Di).
In particular, the combination rep(-1, times=7) is a solution.

I am not sure, whether this is, what you are asking for.
Can you give more detail?

Petr Savicky.