chi.plot {asbio} | R Documentation |

## Chi plots for diagnosing multivariate independence.

### Description

Chi-plots (Fisher and Switzer 1983, 2001) provide a method to diagnose multivariate
non-independence among *Y* variables.

### Usage

```
chi.plot(Y1, Y2, ...)
```

### Arguments

`Y1` |
A |

`Y2` |
A second |

`...` |
Additional arguments from |

### Details

The method relies on calculating all possible pairwise differences within **y**`_1`

and within **y**`_2`

. Let pairwise differences associated with the first observation in **y**`_1`

that are greater than zero be transformed to ones and all other differences be zeros. Take the sum of the transformed values, and let this sum divided by (1 - *n*) be be the first element in the 1 x *n* vector **z**.
Find the rest of the elements (2,..,*n*) in **z** using the same process.

Perform the same transformation for the pairwise differences associated with the first observation in **y**`_2`

. Let pairwise differences associated with the first observation in **y**`_2`

that are greater than zero be transformed to ones and all other differences be zeros. Take the sum of the transformed values, and let this sum divided by (1 - *n*) be be the first element in the 1 x *n* vector **g**.
Find the rest of the elements (2,..,*n*) in **g** using the same process.

Let pairwise differences associated with the first observation in **y**`_1`

and the first observation in `\bold{y}_2`

that are both greater than zero be transformed to ones and all other differences be zeros. Take the sum of the transformed values, and let this sum divided by (1 - *n*) be be the first element in the 1 x *n* vector **h**. Find the rest of the elements (2,..,*n*) in **h** using the same process. We let:

`S = sign((\bold{z} - 0.5)(\bold{g} - 0.5))`

`\chi =(\bold{h} - \bold{z} \times \bold{g})/\sqrt{\bold{z} \times (1 - \bold{z}) \times \bold{g} \times (1 - \bold{g})}`

`\lambda = 4 \times S \times max[(\bold{z} - 0.5)^2,(\bold{g} - 0.5)^2]`

We plot the resulting paired `\chi`

and `\lambda`

values for values of `\lambda`

less than `4(1/(n - 1) - 0.5)^2`

. Values outside of `\frac{1.78}{\sqrt{n}}`

can be considered non-independent.

### Value

Returns a chi-plot.

### Author(s)

Ken Aho and Tom Taverner (Tom provided modified original code to eliminate looping)

### References

Everitt, B. (2006) *R and S-plus Companion to Multivariate Analysis*. Springer.

Fisher, N. I, and Switzer, P. (1985) Chi-plots for assessing dependence. *Biometrika*, 72:
253-265.

Fisher, N. I., and Switzer, P. (2001) Graphical assessment of dependence: is a picture worth 100 tests?
*The American Statistician*, 55: 233-239.

### See Also

### Examples

```
Y1<-rnorm(100, 15, 2)
Y2<-rnorm(100, 18, 3.2)
chi.plot(Y1, Y2)
```

*asbio*version 1.9-7 Index]