kendall.w {synchrony}

Kendall's W

Description

Compute Kendall's coefficient of concordance (W)

Usage

kendall.w (data, nrands = 0, type = 1, quiet = FALSE)

Arguments

data

matrix in wide format where each row represents a different sample and each column represents a different variable.

nrands

Number of randomizations to perform to determine significance. Default is 0.

type

Randomization method. The type=1 method randomly shuffles each column of the data matrix, thus destroying both the autocorrelation structure of each column and the cross-correlation between columns. The type=2 method shifts each column of the data matrix by a random amount, thus preserving the autocorrelation structure of each column but destroying the cross-correlation between columns (Purves and Law 2002). Default is type=1

quiet

Suppress progress bar when set to TRUE. Default is FALSE

Details

Kendall's W is a non-parametric statistic that ranges from 0 to 1 and measures the level of agreement between multiple variables. When the number of observations n>10, its significance can be determined by using a \chi^2 distribution with df=n-1. Legendre (2005) shows that the \chi^2 test is always too conservative (low power) compared to the randomization test. Hence, both tests have been made available in this function. The Monte Carlo randomizations are performed by shuffling the columns of the community matrix independently (Legendre 2005).

Value

Returns a named list containing:

w.uncorrected

Kendall's W uncorrected for tied ranks

w.corrected

Kendall's W corrected for tied ranks

pval

p-value of Kendall's W

spearman.corr

Spearman's ranked correlation

pval.rand

p-value of Kendall's W based on randomization test. This variable is only returned if nrands > 0

rands

randomizations. This variable is only returned if nrands > 0

Author(s)

Tarik C. Gouhier ([e-mail])

References

Buonaccorsi, J. P., J. S. Elkinton, S. R. Evans, and A. M. Liebhold. 2001. Measuring and testing for spatial synchrony. Ecology 82:1668-1679.

Gouhier, T. C., and F. Guichard. 2007. Local disturbance cycles and the maintenance of spatial heterogeneity across scales in marine metapopulations. Ecology 88:647-657.

Gouhier, T. C., F. Guichard, and A. Gonzalez. 2010. Synchrony and stability of food webs in metacommunities. The American Naturalist 175:E16-E34.

Legendre, P. 2005. Species associations: the Kendall coefficient of concordance revisited. Journal of Agricultural, Biological, and Environmental Statistics 10:226-245.

Purves, D. W., and R. Law. 2002. Fine-scale spatial structure in a grassland community: quantifying the plant's eye view. Journal of Ecology 90:121-129.

Zar, J. H. 1999. Biostatistical Analysis, Fourth edition. Prentice-Hall, Inc., Upper Saddle River, NJ.

Examples

data(bird.traits)
(w=kendall.w(bird.traits))