# hcf.aov: Analysis of variance for (hyper-)spherical data In Directional: A Collection of Functions for Directional Data Analysis

## Description

Analysis of variance for (hyper-)spherical data.

## Usage

 ```1 2 3 4 5``` ```hcf.aov(x, ina, fc = TRUE) hclr.aov(x, ina) lr.aov(x, ina) embed.aov(x, ina) het.aov(x, ina) ```

## Arguments

 `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.

## Details

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

## Value

A vector with two or three elements, the test statistic, the p-value and the common concentration parameter kappa based on all the data.

## Author(s)

Michail Tsagris.

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

## References

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.

```hcf.boot, spherconc.test, conc.test, hclr.circaov, ```
 ```1 2 3 4 5 6 7``` ```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) ```