Test whether the mean vector of a single multivariate normal population is equal to a certain value when the population covariance matrix is known or unknown. The null hypothesis is that "H0: mu = mu0".
Arguments
- data
The data matrix which is a matrix or data frame.
- mu0
The mean vector when the null hypothesis is true.
- Sigma0
The population covariance matrix. Default is FALSE which means the covariance matrix is unknown.
- alpha
The significance level. Default is 0.05.
- verbose
A boolean value. Default is TRUE. If TRUE, the null hypothesis will be displayed. If FALSE, the test will be carried out silently.
Value
An object of class "testResult", which is a list with the following elements:
- Conclusion
The conclusion of the test.
- Stat
A data frame containing the statistics, p value and critical value.
- SampMean
The sample mean.
- SampA
The sample deviation.
- Df
The degree of freedom.
References
Huixuan, Gao. Applied Multivariate Statistical Analysis. Peking University Press, 2005: pp.66-68.
Examples
data(iris)
X <- iris[, 1:4]
mu0 <- c(5.8, 3.0, 4.3, 1.3)
# carry out the test
test1 <- meanTest.single(X, mu0)
test2 <- meanTest.single(X, mu0, Sigma0 = diag(1, 4))
test3 <- meanTest.single(X, mu0, verbose = FALSE)
#> H0: mu = (5.8, 3, 4.3, 1.3)' when Sigma is unknown
# get the elements
test1$Stat
#> Value p.value Critical.Value
#> Hotelling T2 244.22150
#> F 59.82607 0 2.43363344771214
test1$SampMean
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 5.843333 3.057333 3.758000 1.199333
test1$SampA
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length 102.168333 -6.322667 189.8730 76.92433
#> Sepal.Width -6.322667 28.306933 -49.1188 -18.12427
#> Petal.Length 189.873000 -49.118800 464.3254 193.04580
#> Petal.Width 76.924333 -18.124267 193.0458 86.56993
test1$Df
#> df
#> Hotelling T2 T2( 4 , 149 )
#> F F( 4 , 146 )