One Critrion Analysis of Variance for circular data
aov.circular(x, group, kappa = NULL,
method = c("F.test", "LRT"), F.mod = TRUE, control.circular=list())
# S3 method for aov.circular
print(x, digits = max(3, getOption("digits") - 3), ...)An object of class aov.circular with the following components:
mean direction for each sample with class circular.
mean direction of all samples combined with class circular.
concentration parameter for each sample.
concentration parameter for all samples combined.
mean resultant length for each sample.
mean resultant length for all samples combined.
the test statistic used.
degrees of freedom.
the value of the test statistic.
the p.value of the test statistic.
the match.call result.
If the method is "F.test" then the object contains also:
Sum of squares used in F-test.
Mean squares used in F-test.
a vector of class circular.
a vector identifying the groups or samples.
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.
the test statistic to use; either a high-concentration F-test or a likelihood ratio test.
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.
the coordinate system used in the output for the objects mu and mu.all. See circular for details.
the number of digits to be printed.
additional arguments.
Claudio Agostinelli and Ulric Lund
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.
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.
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")
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