aov.circular: Analysis of Variance for circular data

In circular: Circular Statistics

Analysis of Variance for circular data

Description

One Critrion Analysis of Variance for circular data

Usage

aov.circular(x, group, kappa = NULL,
    method = c("F.test", "LRT"), F.mod = TRUE, control.circular=list())
## S3 method for class 'aov.circular'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

x	a vector of class circular.
group	a vector identifying the groups or samples.
kappa	the common value of the concentration parameter. Used when method is "LRT". If left unspecified (by default) the maximum likelihood estimate of kappa is computed and used in the test statistic.
method	the test statistic to use; either a high-concentration F-test or a likelihood ratio test.
F.mod	logical; if TRUE, the AOV F-statistic is modified by a factor of 1+3/8k to improve its approximate F distribution. Default is TRUE.
control.circular	the coordinate system used in the output for the objects mu and mu.all. See circular for details.
digits	the number of digits to be printed.
...	additional arguments.

Details

The samples are assumed to have been drawn from von Mises populations with equal concentration parameter, kappa. The null hypothesis being tested is that all populations also have the same mean direction.

If method is "F.test" a high concentration F-test makes use of a decomposition of total sample variation into between groups and within groups variation, analogous to the one-way classification analysis of variance for linear data. Stephens (1972) presented an improved modification to the F-test derived from this decomposition. This is implemented when F.mod is TRUE.

A likelihood ratio test is performed when method is "LRT". This function uses the test statistic presented by Cordeiro, Paula, and Botter (1994) which has an approximate chi-squared distribution. If the common concentration parameter is known, it can be specified and used in the computation of the test statistic. Otherwise, the maximum likelihood estimate of the common concentration parameter is used.

Value

An object of class aov.circular with the following components:

mu	mean direction for each sample with class circular.
mu.all	mean direction of all samples combined with class circular.
kappa	concentration parameter for each sample.
kappa.all	concentration parameter for all samples combined.
rho	mean resultant length for each sample.
rho.all	mean resultant length for all samples combined.
method	the test statistic used.
df	degrees of freedom.
statistic	the value of the test statistic.
p.value	the p.value of the test statistic.
call	the match.call result.

If the method is "F.test" then the object contains also:

SSE	Sum of squares used in F-test.
MSE	Mean squares used in F-test.

Author(s)

Claudio Agostinelli and Ulric Lund

References

Cordeiro, G., Paula, G. and Botter, D. (1994). Improved likelihood ratio tests for dispersion models. International Statistical Review, 62, 257-274.

Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, Section 5.3, World Scientific Press, Singapore.

Mardia, K. and Jupp, P. (1999). Directional Statistics, Section 7.4, John Wiley and Sons, England.

Stephens, M. (1972). Multi-sample tests for the von Mises distribution. Technical Report 190, Department of Statistics, Stanford University.

Examples

x <- c(rvonmises(50, circular(0), 1), rvonmises(100, circular(pi/3), 10))
group <- c(rep(0, 50), rep(1, 100))

aov.circular(x, group)
aov.circular(x, group, method="LRT")

circular documentation built on Sept. 11, 2024, 8:21 p.m.