Hotelling's multivariate version of the 2 sample t-test for Euclidean data {Compositional} R Documentation

## Hotelling's multivariate version of the 2 sample t-test for Euclidean data

### Description

Hotelling's test for testing the equality of two Euclidean population mean vectors.

### Usage

```hotel2T2(x1, x2, a = 0.05, R = 999, graph = FALSE)
```

### Arguments

 `x1` A matrix containing the Euclidean data of the first group. `x2` A matrix containing the Euclidean data of the second group. `a` The significance level, set to 0.05 by default. `R` If R is 1 no bootstrap calibration is performed and the classical p-value via the F distribution is returned. If R is greater than 1, the bootstrap p-value is returned. `graph` A boolean variable which is taken into consideration only when bootstrap calibration is performed. IF TRUE the histogram of the bootstrap test statistic values is plotted.

### Details

Multivariate analysis of variance assuming equality of the covariance matrices. The p-value can be calculated either asymptotically or via bootstrap.

### Value

A list including:

 `mesoi` The two mean vectors. `info` The test statistic, the p-value, the critical value and the degrees of freedom of the F distribution (numerator and denominator). This is given if no bootstrap calibration is employed. `pvalue` The bootstrap p-value is bootstrap is employed. `note` A message informing the user that bootstrap calibration has been employed. `runtime` The runtime of the bootstrap calibration.

### Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

### References

Everitt B. (2005). An R and S-Plus Companion to Multivariate Analysis p. 139-140. Springer.

```james, maov, el.test2, eel.test2, comp.test ```
```hotel2T2( as.matrix(iris[1:25, 1:4]), as.matrix(iris[26:50, 1:4]) )