# ait.test: Aitchison's test for two mean vectors and/or covariance... In Compositional: Compositional Data Analysis

 Aitchison's test for two mean vectors and/or covariance matrices R Documentation

## Aitchison's test for two mean vectors and/or covariance matrices

### Description

Aitchison's test for two mean vectors and/or covariance matrices.

### Usage

```ait.test(x1, x2, type = 1, alpha = 0.05)
```

### Arguments

 `x1` A matrix containing the compositional data of the first sample. Zeros are not allowed. `x2` A matrix containing the compositional data of the second sample. Zeros are not allowed. `type` The type of hypothesis test to perform. Type=1 refers to testing the equality of the mean vectors and the covariance matrices. Type=2 refers to testing the equality of the covariance matrices. Type=2 refers to testing the equality of the mean vectors. `alpha` The significance level, set to 0.05 by default.

### Details

The test is described in Aitchison (2003). See the references for more information.

### Value

A vector with the test statistic, the p-value, the critical value and the degrees of freedom of the chi-square distribution.

### Author(s)

Michail Tsagris.

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

### References

John Aitchison (2003). The Statistical Analysis of Compositional Data, p. 153-157. Blackburn Press.

``` comp.test, maovjames, el.test2, eel.test2, ```

### Examples

```x1 <- as.matrix(iris[1:50, 1:4])
x1 <- x1 / rowSums(x1)
x2 <- as.matrix(iris[51:100, 1:4])
x2 <- x2 / rowSums(x2)
ait.test(x1, x2, type = 1)
ait.test(x1, x2, type = 2)
ait.test(x1, x2, type = 3)
```

Compositional documentation built on July 8, 2022, 1:06 a.m.