FunChisq (version 2.3.1)

cp.fun.chisq.test: Comparative Chi-Square Test for Non-Parametric Functional Heterogeneity

Description

Comparative functional chi-square tests on two or more contingency tables.

Usage

cp.fun.chisq.test(x, method = "fchisq", log.p = FALSE)

Arguments

x

a list of at least two matrices representing contingency tables of the same dimensionality.

method

a character string to specify the method to compute the functional chi-square statistic and its p-value. The default is "fchisq" (equivalent to "default"). See Details.

log.p

logical; if TRUE, the p-value is given as log(p). Taking the log improves the accuracy when p-value is close to zero. The default is FALSE.

Value

A list with class "htest" containing the following components:

statistic

functional heterogeneity chi-square if method = "fchisq" (equivalent to "default"), or normalized functional chi-square if method = "nfchisq" (equivalent to "normalized").

parameter

degrees of freedom.

p.value

p-value of the comparative functional chi-square test. By default, it is computed by the chi-square distribution. If method = "normalized", it is the p-value of the normalized functional chi-square computed by the standard normal distribution.

Details

The comparative functional chi-square test determines whether the patterns underlying the contingency tables are heterogeneous in a functional way. Specifically, it evaluates whether the column variable is a changed function of the row variable across the contingency tables.

Two methods are provided to compute the functional chi-square statistic and its p-value. When method = "fchisq" (or "default"), the p-value is computed using the chi-square distribution; when method = "nfchisq" (or "normalized") a normalized functional chi-square is obtained by shifting and scaling the original chi-square and a p-value is computed using the standard normal distribution (Box et al., 2005). The normalized test is more conservative on the degrees of freedom.

References

Box, G. E., Hunter, J. S., and Hunter, W. G. (2005). Statistics for Experimenters: Design, Innovation and Discovery, 2nd Edition. Wiley-Interscience, New York.

Zhang, Y. (2014) Nonparametric Statistical Methods for Biological Network Inference. Unpublished doctoral dissertation, Department of Computer Science, New Mexico State University, Las Cruces, USA.

Zhang, Y. and Song, M. (2013) Deciphering interactions in causal networks without parametric assumptions. arXiv Molecular Networks, arXiv:1311.2707. http://arxiv.org/abs/1311.2707

See Also

For comparative chi-square test that does not consider functional dependencies, cp.chisq.test.

Examples

x <- matrix(c(4,0,4,0,4,0,1,0,1), 3)
y <- t(x)
z <- matrix(c(1,0,1,4,0,4,0,4,0), 3)
data <- list(x,y,z)
cp.fun.chisq.test(data)
cp.fun.chisq.test(data, method="nfchisq")