| Relationship between Hotelling's T2 test and James' MANOVA {mvhtests} | R Documentation |
Relationship between Hotelling's T^2 test and James' MANOVA
Description
Relationship between Hotelling's T^2 test and James' MANOVA.
Usage
maovjames.hotel(x, ina)
Arguments
x |
A matrix containing the Euclidean data of the first group. |
ina |
A numerical or factor variable indicating the groups of the data. |
Details
The relationship for the James two sample test (see the function james.hotel) is true for the case of the MANOVA. The estimate of the common mean, \pmb{mu}_c (see the function james for the expression of \pmb{\mu}_c), is in general, for g groups, each of sample size n_i, written as
\hat{\pmb{\mu}}_c = \left(\sum_{i=1}^gn_i{\bf S}_i^{-1}\right)^{-1}\sum_{i=1}^gn_i{\bf S}_i^{-1}\bar{{\bf X}}_i.
The function is just a proof of the mathematics you will find in Emerson (2009, pg. 76–81) and is again intended for educational purposes.
Value
A list including:
test |
The value of the test statistic, the sum of the two Hotelling's test statistic using the common mean. |
mc |
The common mean. |
Author(s)
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
References
Emerson S. (2009). Small sample performance and calibration of the Empirical Likelihood method. PhD thesis, Stanford university.
James G.S. (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.
See Also
hotel2T2, maovjames, el.test2, eel.test2
Examples
maovjames.hotel( as.matrix(iris[, 1:4]), iris[, 5] )
maovjames( as.matrix(iris[, 1:4]), iris[, 5] )