# hotel1T2: Hotelling's multivariate version of the 1 sample t-test for... In Compositional: Compositional Data Analysis

## Description

Hotelling's test for testing one Euclidean population mean vector.

## Usage

 `1` ```hotel1T2(x, M, a = 0.05, R = 999, graph = FALSE) ```

## Arguments

 `x` A matrix containing Euclidean data. `a` The significance level, set to 0.05 by default. `M` The hypothesized mean vector. `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 hypothesis test for a one sample mean vector. This is the multivariate analogue of the one sample t-test. The p-value can be calculated either asymptotically or via bootstrap.

## Value

A list including:

 `m` The sample mean vector. `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. `runtime` The runtime of the bootstrap calibration.

## Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris <[email protected]> and Giorgos Athineou <[email protected]>

## References

K.V. Mardia, J.T. Kent and J.M. Bibby (1979). Multivariate analysis.

```eel.test1, el.test1, james, hotel2T2, maov, el.test2, comp.test ```
 ```1 2 3``` ```x <- Rfast::rmvnorm(100, numeric(10), diag( rexp(10,0.5) ) ) hotel1T2(x, numeric(10), R = 1) hotel1T2(x, numeric(10), R = 999, graph = TRUE) ```