ConDis.matrix: Calculation and display of concordant and discordant pairs

In asbio: A Collection of Statistical Tools for Biologists

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 Y1.

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

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

asbio documentation built on May 29, 2024, 5:57 a.m.