# Association Plots

### Description

Produce a Cohen-Friendly association plot indicating deviations from independence of rows and columns in a 2-dimensional contingency table.

### Usage

1 2 |

### Arguments

`x` |
a two-dimensional contingency table in matrix form. |

`col` |
a character vector of length two giving the colors used for drawing positive and negative Pearson residuals, respectively. |

`space` |
the amount of space (as a fraction of the average rectangle width and height) left between each rectangle. |

`main` |
overall title for the plot. |

`xlab` |
a label for the x axis. Defaults to the name (if any) of
the row dimension in |

`ylab` |
a label for the y axis. Defaults to the name (if any) of
the column dimension in |

### Details

For a two-way contingency table, the signed contribution to Pearson's
*chi^2* for cell *i, j* is *d_{ij} = (f_{ij} - e_{ij}) / sqrt(e_{ij})*,
where *f_{ij}* and *e_{ij}* are the observed and expected
counts corresponding to the cell. In the Cohen-Friendly association
plot, each cell is represented by a rectangle that has (signed) height
proportional to *d_{ij}* and width proportional to
*sqrt(e_{ij})*, so that the area of the box is
proportional to the difference in observed and expected frequencies.
The rectangles in each row are positioned relative to a baseline
indicating independence (*d_{ij} = 0*). If the observed frequency
of a cell is greater than the expected one, the box rises above the
baseline and is shaded in the color specified by the first element of
`col`

, which defaults to black; otherwise, the box falls below
the baseline and is shaded in the color specified by the second
element of `col`

, which defaults to red.

A more flexible and extensible implementation of association plots
written in the grid graphics system is provided in the function
`assoc`

in the contributed package \CRANpkgvcd
(Meyer, Zeileis and Hornik, 2005).

### References

Cohen, A. (1980),
On the graphical display of the significant components in a two-way
contingency table.
*Communications in Statistics—Theory and Methods*, **A9**,
1025–1041.

Friendly, M. (1992),
Graphical methods for categorical data.
*SAS User Group International Conference Proceedings*, **17**,
190–200.
http://www.math.yorku.ca/SCS/sugi/sugi17-paper.html

Meyer, D., Zeileis, A., and Hornik, K. (2005)
The strucplot framework: Visualizing multi-way contingency tables with vcd.
*Report 22*, Department of Statistics and Mathematics,
Wirtschaftsuniversität Wien, Research Report Series.
http://epub.wu.ac.at/dyn/openURL?id=oai:epub.wu-wien.ac.at:epub-wu-01_8a1

### See Also

`mosaicplot`

, `chisq.test`

.

### Examples

1 2 3 4 | ```
## Aggregate over sex:
x <- margin.table(HairEyeColor, c(1, 2))
x
assocplot(x, main = "Relation between hair and eye color")
``` |