asbio (version 1.9-7)

ConDis.matrix: 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)

Value

A matrix is returned. Elements in the lower triangle indicate whether observations are concordant (element = 1), discordant (element = -1) or neither (element = 0).

Arguments

Y1

A vector of quantitative data.

Y2

A vector of quantitative data. Observations are assumed to be paired with respective observations from Y1.

Author

Ken Aho

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 \(\tau\).

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

cor

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