# homogen.test {prabclus}

### Description

Classical distance-based test for homogeneity against clustering. Test statistics is number of isolated vertices in the graph of smallest distances. The homogeneity model is a random graph model where `ne`

edges are drawn from all possible edges.

### Usage

homogen.test(distmat, ne = ncol(distmat), testdist = "erdos")

### Arguments

- distmat
- numeric symmetric distance matrix.
- ne
- integer. Number of edges in the data graph, corresponding to smallest distances.
- testdist
- string. If
`testdist="erdos"`

, the test distribution is a Poisson asymptotic distibution as given by Erdos and Renyi (1960). If`testdist="ling"`

, the test distribution is exact as given by Ling (1973), which needs much more computing time.

### Details

The "ling"-test is one-sided (rejection if the number of isolated vertices is too large), the "erdos"-test computes a one-sided as well as a two-sided p-value.

### Values

A list with components

- p
- p-value for one-sided test.
- p.twoside
- p-value for two-sided test, only if
`testdist="erdos"`

. - iv
- number of isolated vertices in the data.
- lambda
- parameter of the Poisson test distribution, only if
`testdist="erdos"`

. - distcut
- largest distance value for which an edge has been drawn.
- ne
- see above.

### References

Erdos, P. and Renyi, A. (1960) On the evolution of random graphs. *Publications of the Mathematical Institute of the Hungarian Academy of Sciences* 5, 17-61.

Godehardt, E. and Horsch, A. (1995) Graph-Theoretic Models for Testing the Homogeneity of Data. In Gaul, W. and Pfeifer, D. (Eds.) *From Data to Knowledge*, Springer, Berlin, 167-176. Ling, R. F. (1973) A probability theory of cluster analysis. *Journal of the American Statistical Association* 68, 159-164.

### See Also

`prabtest`

### Examples

Documentation reproduced from package prabclus, version 2.2-6. License: GPL