# RayleighTest3D: Rayleigh Test. Formal test of uniformity. In VecStatGraphs3D: Vector analysis using graphical and analytical methods in 3D

## Description

This function performs the Rayleigh test of uniformity.

## Usage

 `1` ```RayleighTest3D(coord, Alpha = 0.05) ```

## Arguments

 `coord` Matrix containing the values of the coordinates `Alpha` Value used to obtain the Rayleigh Value from the chi-square table. The values can be 0.05, 0.025, 0.01, 0.005, 0.001, 0.0005. The default is 0.05.

## Details

This test detects a single modal direction in a sample of angles when the mean angles is unspecified. The hypothesis of uniformity is rejected if the mean module is very large. This test assumes that a larger mean module implies a more concentration around the mean, and therefore less probability that the data is uniformly distributed.

One way to get a set of coordinates X, Y and Z of the origin position and end position (coordinates X, Y and Z of the vector) or of the colatitude and longitude, it is using the `LoadData3D` function.

## Value

Returns the probability value, and indicates whether or not to accept the hypothesis of uniformity.

## Author(s)

Ruiz-Cuetos, J.C., [email protected], Polo, M.E., [email protected], Rodriguez, P.G. [email protected]

## References

Fisher N.I. , Lewis T. , Embleton, B.J.J. (1987) Statistical analysis of spherical data. Cambridge. Cambridge University Press.

`AllAngleStatistics`, `AllModuleStatistics3D`.
 ```1 2 3 4``` ``` FileName<-system.file("data/XYZcoor.txt", package="VecStatGraphs3D") dat<-LoadData3D(FileName, Type=1) coordinates<-dat[,4:6] RayleighTest3D(coordinates, Alpha = 0.05) ```