ConDis.matrix {asbio} | R Documentation |

## Calculation and display of concordant and discordant pairs

### Description

Calculates whether pairs of observations from two vectors are concordant discordant or neither. These are displayed in the lower diagonal of a symmetric output matrix as 1, -1 or 0.

### Usage

```
ConDis.matrix(Y1, Y2)
```

### Arguments

`Y1` |
A vector of quantitative data. |

`Y2` |
A vector of quantitative data. Observations are assumed to be paired
with respective observations from |

### Details

Consider all possible combinations of `(Y_{1i}, Y_{ij})`

and `(Y_{2i}, Y_{ij})`

where `1<=i<j<=n`

. A pair is concordant if `Y_{1i} > Y_{1j}`

and `Y_{2i} > Y_{2j}`

or if `Y_{1i} < Y_{1j}`

and `Y_{2i} < Y_{2j}`

. Conversely, a pair is discordant if `Y_{1i} < Y_{1j}`

and `Y_{2i} > Y_{2j}`

or if `Y_{1i} > Y_{1j}`

and `Y_2i < Y_2j`

. This information has a number of important uses including calculation of Kendall's `\tau`

.

### Value

A matrix is returned. Elements in the lower triangle indicate whether observations are concordant (element = `1`

), discordant (element = `-1`

) or neither (element = `0`

).

### Author(s)

Ken Aho

### References

Hollander, M., and Wolfe, D. A. (1999) *Nonparametric statistical methods*. New York: John Wiley & Sons.

Liebetrau, A. M. (1983) *Measures of association*. Sage Publications, Newbury Park, CA.

Sokal, R. R., and Rohlf, F. J. (1995) *Biometry*. W. H. Freeman and Co., New York.

### See Also

### Examples

```
#Crab data from Sokal and Rohlf (1998)
crab<-data.frame(gill.wt=c(159,179,100,45,384,230,100,320,80,220,320,210),
body.wt=c(14.4,15.2,11.3,2.5,22.7,14.9,1.41,15.81,4.19,15.39,17.25,9.52))
attach(crab)
crabm<-ConDis.matrix(gill.wt,body.wt)
crabm
```

*asbio*version 1.9-7 Index]