## Montecarlo-statistics on R x C matrices

### Compares R x C table with randomized tables of same row
and column totals.

### Methods, References and Acknowledgements

Method described in:

* Nico Blüthgen, Florian Menzel and Nils Blüthgen: Measuring specialization in species interaction networks,BMC Ecology 2006, 6:9* (pdf)

RxC randomization algorithm based on:

*Patefield, W.M. (1981) An efficient method of generating random RxC
tables with given row and column totals. Applied Statistics 30: 91-97.*

The StatLib of the Royal
Statistical Society
is acknowledged for permission.

Test statistic T=sum( f(r,c) * log f(r,c) ) or H=-sum( p(r,c) * log p(r,c) )

Minimum percentage of random matrices with T below or
above observed matrix taken as signficance level
of difference between given matrix and random matrices,
see:

*Manley, B.F.J. (1997) Randomization, bootstrap and Monte Carlo methods in
biology. Chapman & Hall, London, 399 pp.*

### Contact

Please contact
Nils Blüthgen (nils.bluethgen AT charite.de)
or Nico
Blüthgen (bluethgen AT biozentrum.uni-wuerzburg.de) for further information.

### Changes

26.09.10 Changed input form (number rows and cols automatically determined)

26.09.10 Fixed bugs in obtaining maximum H

12.12.05 Calculation of H, H', d and d' included

20.07.05 Calculation of Tmin, Tmax and S included

13.02.02 Changed input-buffer to allow bigger matrices

05.09.02 Output is now stddev and not variance