Anova for (hyper-)spherical data | R Documentation |

Analysis of variance for (hyper-)spherical data.

```
hcf.aov(x, ina, fc = TRUE)
hclr.aov(x, ina)
lr.aov(x, ina)
embed.aov(x, ina)
het.aov(x, ina)
```

`x` |
A matrix with the data in Euclidean coordinates, i.e. unit vectors. |

`ina` |
A numerical variable or a factor indicating the group of each vector. |

`fc` |
A boolean that indicates whether a corrected F test should be used or not. |

The high concentration (hcf.aov), high concentration log-likelihood ratio (hclr.aov), log-likelihood ratio (lr.aov), embedding approach (embed.aov) or the non equal concentration parameters approach (het.aov) is used.

This is an "htest"class object. Thus it returns a list including:

`statistic` |
The test statistic value. |

`parameter` |
The degree(s) of freedom of the test. |

`p.value` |
The p-value of the test. |

`alternative` |
A character with the alternative hypothesis. |

`method` |
A character with the test used. |

`data.name` |
A character vector with two elements. |

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Giorgos Athineou <gioathineou@gmail.com>.

Mardia K. V. and Jupp P. E. (2000). Directional statistics. Chicester: John Wiley & Sons.

Rumcheva P. and Presnell B. (2017). An improved test of equality of mean directions for the Langevin-von Mises-Fisher distribution. Australian & New Zealand Journal of Statistics, 59(1): 119–135.

Tsagris M. and Alenazi A. (2022). An investigation of hypothesis testing procedures for circular and spherical mean vectors. Communications in Statistics-Simulation and Computation (Accepted for publication).

```
hcf.boot, hcfboot, hclr.circaov,
```

```
x <- rvmf(60, rnorm(3), 15)
ina <- rep(1:3, each = 20)
hcf.aov(x, ina)
hcf.aov(x, ina, fc = FALSE)
lr.aov(x, ina)
embed.aov(x, ina)
het.aov(x, ina)
```

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