# [R] Sample all possible contingency tables both margin fixed

David L Carlson dcarlson at tamu.edu
Tue Jun 24 20:18:47 CEST 2014

```Since a 2x2 table with fixed row and column margins has only one degree of freedom, it is pretty easy to enumerate them:

A    B
A  a    c    M
B  b    d    M
M M   N

Create a vector of the margins:
M <- c(a+b, c+d, a+c, b+d)

The number of possible tables is min(M[c(1, 3)])+1 since a cannot be larger than the first column margin or the first row margin. The +1 recognizes that a can be 0.

Given any vector M of marginal values, the 2x2 tables are as follows:

M <- c(8, 9, 9, 8) # For example
M+M==M+M # Check to make sure these are valid margins
TRUE
all.2x2s <- t(sapply(0:min(M[c(1,3)]), function(i) c(a=i, b=M - i,
c=M - i, d=M - M + i)))
all.2x2s
a b c d
[1,] 0 8 9 0
[2,] 1 7 8 1
[3,] 2 6 7 2
[4,] 3 5 6 3
[5,] 4 4 5 4
[6,] 5 3 4 5
[7,] 6 2 3 6
[8,] 7 1 2 7
[9,] 8 0 1 8

-------------------------------------
David L Carlson
Department of Anthropology
Texas A&M University
College Station, TX 77840-4352

----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Gabor Grothendieck
Sent: Tuesday, June 24, 2014 12:07 PM
To: Tahira Jamil
Cc: r-help at r-project.org
Subject: Re: [R] Sample all possible contingency tables both margin fixed

On Tue, Jun 24, 2014 at 10:41 AM, Tahira Jamil <tahjamil at gmail.com> wrote:
> Hi,
>
> I am interested in generating all possible contingency table (2 by 2) with fixed row margins and column margins. Can anyone help me.
>

If the reason you want this is to sample them then r2dtable can do
that directly.

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