aov.circular: Analysis of Variance for circular data

Description Usage Arguments Details Value Author(s) References Examples

View source: R/aov.circular.R

Description

One Critrion Analysis of Variance for circular data

Usage

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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 folowing 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

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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")

Example output

Attaching package: 'circular'

The following objects are masked from 'package:stats':

    sd, var


Call:
aov.circular(x = x, group = group)


 Circular Analysis of Variance: High Concentration F-Test 
 
         df     SS     MS     F         p
Between   1  5.148 5.1482 27.75 4.775e-07
Within  148 31.750 0.2145    NA        NA
Total   149 36.898 0.2476    NA        NA

 

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


 Circular Analysis of Variance: Likelihood Ratio Test 
 
 df:      1 
 ChiSq:   24.63 
 p.value: 6.959e-07 
 

circular documentation built on May 1, 2019, 7:57 p.m.