James multivariate version of the t-test {Compositional} R Documentation

## James multivariate version of the t-test

### Description

James test for testing the equality of two population mean vectors without assuming equality of the covariance matrices.

### Usage

```james(y1, y2, a = 0.05, R = 999, graph = FALSE)
```

### Arguments

 `y1` A matrix containing the Euclidean data of the first group. `y2` 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 without assuming equality of the covariance matrices. The p-value can be calculated either asymptotically or via bootstrap. The James test (1954) or a modification proposed by Krishnamoorthy and Yanping (2006) is implemented. The James test uses a corrected chi-square distribution, whereas the modified version uses an F distribution.

### Value

A list including:

 `note` A message informing the user about the test used. `mesoi` The two mean vectors. `info` The test statistic, the p-value, the correction factor and the corrected critical value of the chi-square distribution if the James test has been used or, the test statistic, the p-value, the critical value and the degrees of freedom (numerator and denominator) of the F distribution if the modified James test has been used. `pvalue` The bootstrap p-value if bootstrap is employed. `runtime` The runtime of the bootstrap calibration.

### Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Giorgos Athineou <gioathineou@gmail.com>.

### References

G.S. James (1954). Tests of Linear Hypothese in Univariate and Multivariate Analysis when the Ratios of the Population Variances are Unknown. Biometrika, 41(1/2): 19-43.

Krishnamoorthy K. and Yanping Xia. On Selecting Tests for Equality of Two Normal Mean Vectors (2006). Multivariate Behavioral Research 41(4): 533-548.

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