# [R] ascending permutation within treatment

eugen pircalabelu eugen_pircalabelu at yahoo.com
Thu Mar 4 18:28:28 CET 2010

```Hi R-users,
I have a question related to permutations in R.
I started learning something about the permutation/randomization tests using Edgington and Onghena (2007) and i tried replicating some of the examples in the book (i have seen also the packages from R that concern permutation ), but at some point i got stuck.

If i have 3 treatments, 7 subjects in an experiment, and a 2 of them take treatment A, 2 take treatment B and 3 take treatment C then there are 7!/2!2!3! =210 ways in which they can be assigned. So how can i create sequences in R that are of the form

A     B    C
1 2 | 3 4 | 5 6 7
1 2 | 3 5 | 4 6 7
1 2 | 3 6 | 4 5 7
1 2 | 3 7 | 4 5 6
1 2 | 4 5 | 3 6 7
.........
6 7 | 3 4 | 1 2 5
6 7 | 3 5 | 1 2 4
6 7 | 4 5 | 1 2 3

The list is generated taking into account that in each treatment the sequence is always ascending, and so this way it can be avoided listing 7!=5040, but only 7!/2!2!3! =210 sequences will be listed.

Can anyone  please, offer some guidance, or some advice on how to generate this permutations with this constraint that the order within the treatment is ascending.
My hope is that using only this relevant set can greatly improve the time needed for the computation, when i have a larger sample.

I have seen also the recommendations to sample a lot of permutations, and i have no problem in doing that, everything goes smoothly and fast, but i want also to be able to do this.

Thank you very much and have a great day ahead!

Eugen Pircalabelu
(0032)471 842 140
(0040)727 839 293

```