Compositional (version 1.5)

James multivariate version of the t-test: 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.

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.

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 corected chi-square distribution, whereas the modified version uses an F distribution.

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

See Also

hotel2T2, maovjames, el, comp.test

Examples

james( iris[1:25, 1:4], iris[26:50, 1:4], R = 1 )
james( iris[1:25, 1:4], iris[26:50, 1:4], R = 2 )
james( iris[1:25, 1:4], iris[26:50, 1:4] )
hotel2T2( iris[1:25, 1:4], iris[26:50, 1:4] )