Hotelling's multivariate version of the 1 sample t-test for Euclidean data {mvhtests}

Hotelling's multivariate version of the 1 sample t-test for Euclidean data

Description

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

Usage

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

The hypothesis test is that a mean vector is equal to some specified vector H_0:\pmb{\mu}=\pmb{\mu}_0. We assume that \pmb{\Sigma} is unknown. The first approach to this hypothesis test is parametrically, using the Hotelling's T^2 test Mardia, Bibby and Kent (1979, pg. 125-126). The test statistic is given by

T^2=\frac{\left(n-p\right)n}{\left(n-1\right)p}\left(\bar{{\bf X}}-\pmb{\mu}\right)^T{\bf S}^{-1}\left(\bar{{\bf X}}-\pmb{\mu} \right).

Under the null hypothesis, the above test statistic follows the F_{p,n-p} distribution. The bootstrap version of the one-sample multivariate generalization of the simple t-test is also included in the function. An extra argument (R) indicates whether bootstrap calibration should be used or not. If R=1, then the asymptotic theory applies, if R>1, then the bootstrap p-value will be applied and the number of re-samples is equal to R.

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 [e-mail].

References

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

See Also

eel.test1, el.test1, james, hotel2T2, maov, el.test2

Examples

x <- matrix( rnorm( 100 * 4), ncol = 4)
hotel1T2(x, numeric(4), R = 1)
hotel1T2(x, numeric(4), R = 999, graph = TRUE)