Description Usage Arguments Details Value Author(s) References Examples

One Critrion Analysis of Variance for circular data

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`x` |
a vector of class |

`group` |
a vector identifying the groups or samples. |

`kappa` |
the common value of the concentration parameter. Used
when |

`method` |
the test statistic to use; either a high-concentration F-test or a likelihood ratio test. |

`F.mod` |
logical; if |

`control.circular` |
the coordinate system used in the output for the objects |

`digits` |
the number of digits to be printed. |

`...` |
additional arguments. |

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.

An object of class `aov.circular`

with the folowing components:

`mu` |
mean direction for each sample with class |

`mu.all` |
mean direction of all samples combined with class |

`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 |

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. |

Claudio Agostinelli and Ulric Lund

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.

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```
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
```

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