# hotel2T2: Hotelling's multivariate version of the 2 sample t-test for... In Compositional: Compositional Data Analysis

## Description

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

## Usage

 `1` ```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 <[email protected]> and Giorgos Athineou <[email protected]>

## References

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

```james, maov, el.test2, comp.test ```

## Examples

 ```1 2 3 4``` ```hotel2T2( as.matrix(iris[1:25, 1:4]), as.matrix(iris[26:50, 1:4]) ) hotel2T2( as.matrix(iris[1:25, 1:4]), as.matrix(iris[26:50, 1:4]), R = 1 ) james( as.matrix(iris[1:25, 1:4]), as.matrix(iris[26:50, 1:4]) ) james( as.matrix(iris[1:25, 1:4]), as.matrix(iris[26:50, 1:4]), R = 1 ) ```

### Example output

```\$mesoi
Sepal.Length Sepal.Width Petal.Length Petal.Width
Sample 1        5.028       3.480        1.460       0.248
Sample 2        4.984       3.376        1.464       0.244

\$pvalue
[1] 0.883

\$mesoi
Sepal.Length Sepal.Width Petal.Length Petal.Width
Sample 1        5.028       3.480        1.460       0.248
Sample 2        4.984       3.376        1.464       0.244

\$info
test    p-value   critical   numer df   denom df
0.2693994  0.8961307  2.5787392  4.0000000 45.0000000

\$note
[1] "Bootstrap calibration"

\$mesoi
Sepal.Length Sepal.Width Petal.Length Petal.Width
Sample 1        5.028       3.480        1.460       0.248
Sample 2        4.984       3.376        1.464       0.244

\$pvalue
[1] 0.906

\$runtime
user  system elapsed
0.133   0.003   0.138

\$note
[1] "James test"

\$mesoi
Sepal.Length Sepal.Width Petal.Length Petal.Width
Sample 1        5.028       3.480        1.460       0.248
Sample 2        4.984       3.376        1.464       0.244

\$info
test            p-value         correction corrected.critical
1.1494375          0.9119979          1.1664380         11.0668476
```

Compositional documentation built on Jan. 13, 2019, 5:04 p.m.