Test whether the mean vectors of two multivariate normal populations are equal when the covariance matrices are equal or unequal. The null hypothesis is that "H0: mu1 = mu2".
Usage
meanTest.two(
data1,
data2,
alpha = 0.05,
equal = TRUE,
method = c("None", "Coupled", "Transformed"),
verbose = TRUE
)Arguments
- data1
A matrix or data frame of group 1.
- data2
A matrix or data frame of group 2.
- alpha
The significance level. Default is 0.05.
- equal
A boolean value. Default is TRUE. If TRUE, the covariance matrix is equal. If FALSE, the covariance matrix is not equal.
- method
A string value. Default is "None". When equal is FALSE, you must choose a method in "Coupled" or "Transformed". Choose "Coupled" when the sample size of two groups is equal. Choose "Transformed" when the sample size of two groups is not equal.
- 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: Return when the param equal is TRUE.
- Conclusion
The conclusion of the test.
- Stat
A data frame containing the statistics, p value and critical value.
- SampMean1
The sample mean of group 1.
- SampMean2
The sample mean of group 2.
- SampA1
The sample deviation of group 1.
- SampA2
The sample deviation of group 2.
- MixSampA
The mixed sample deviation.
- Df
The degree of freedom.
Return when the param equal is FALSE and method is "Coupled".
- Conclusion
The conclusion of the test.
- Stat
A data frame containing the statistics, p value and critical value.
- SampMeanC
The sample mean of coupled data.
- SampAC
The sample deviation of coupled data.
- Df
The degree of freedom.
- dataC
The coupled data.
Return when the param equal is FALSE and method is "Transformed".
- Conclusion
The conclusion of the test.
- Stat
A data frame containing the statistics, p value and critical value.
- SampMeanT
The sample mean of transformed data.
- SampAT
The sample deviation of transformed data.
- Df
The degree of freedom.
- dataT
The transformed data. Return when the param equal is FALSE and method is "Transformed".
References
Huixuan, Gao. Applied Multivariate Statistical Analysis. Peking University Press, 2005: pp.76-80.
Examples
data(iris)
X <- iris[1:50, 1:4]
Y <- iris[51:100, 1:4]
# carry out the test
test1 <- meanTest.two(X, Y)
test2 <- meanTest.two(X, Y, verbose = TRUE)
test3 <- meanTest.two(X, Y, equal = FALSE, method = "Coupled")
test4 <- meanTest.two(X, Y, equal = FALSE, method = "Transformed")
# get the elements
test1$Stat
#> Value p.value Critical.Value
#> Hotelling T2 2580.8385
#> F 625.4583 0 2.46749362344965
test1$SampMean1
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 5.006 3.428 1.462 0.246
test3$SampMeanC
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> -0.930 0.658 -2.798 -1.080
test4$dataT
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 1 -1.9 0.3 -3.3 -1.2
#> 2 -1.5 -0.2 -3.1 -1.3
#> 3 -2.2 0.1 -3.6 -1.3
#> 4 -0.9 0.8 -2.5 -1.1
#> 5 -1.5 0.8 -3.2 -1.3
#> 6 -0.3 1.1 -2.8 -0.9
#> 7 -1.7 0.1 -3.3 -1.3
#> 8 0.1 1.0 -1.8 -0.8
#> 9 -2.2 0.0 -3.2 -1.1
#> 10 -0.3 0.4 -2.4 -1.3
#> 11 0.4 1.7 -2.0 -0.8
#> 12 -1.1 0.4 -2.6 -1.3
#> 13 -1.2 0.8 -2.6 -0.9
#> 14 -1.8 0.1 -3.6 -1.3
#> 15 0.2 1.1 -2.4 -1.1
#> 16 -1.0 1.3 -2.9 -1.0
#> 17 -0.2 0.9 -3.2 -1.1
#> 18 -0.7 0.8 -2.7 -0.7
#> 19 -0.5 1.6 -2.8 -1.2
#> 20 -0.5 1.3 -2.4 -0.8
#> 21 -0.5 0.2 -3.1 -1.6
#> 22 -1.0 0.9 -2.5 -0.9
#> 23 -1.7 1.1 -3.9 -1.3
#> 24 -1.0 0.5 -3.0 -0.7
#> 25 -1.6 0.5 -2.4 -1.1
#> 26 -1.6 0.0 -2.8 -1.2
#> 27 -1.8 0.6 -3.2 -1.0
#> 28 -1.5 0.5 -3.5 -1.5
#> 29 -0.8 0.5 -3.1 -1.3
#> 30 -1.0 0.6 -1.9 -0.8
#> 31 -0.7 0.7 -2.2 -0.9
#> 32 -0.1 1.0 -2.2 -0.6
#> 33 -0.6 1.4 -2.4 -1.1
#> 34 -0.5 1.5 -3.7 -1.4
#> 35 -0.5 0.1 -3.0 -1.3
#> 36 -1.0 -0.2 -3.3 -1.4
#> 37 -1.2 0.4 -3.4 -1.3
#> 38 -1.4 1.3 -3.0 -1.2
#> 39 -1.2 0.0 -2.8 -1.1
#> 40 -0.4 0.9 -2.5 -1.1
#> 41 -0.5 0.9 -3.1 -0.9
#> 42 -1.6 -0.7 -3.3 -1.1
#> 43 -1.4 0.6 -2.7 -1.0
#> 44 0.0 1.2 -1.7 -0.4
#> 45 -0.5 1.1 -2.3 -0.9
#> 46 -0.9 0.0 -2.8 -0.9
#> 47 -0.6 0.9 -2.6 -1.1
#> 48 -1.6 0.3 -2.9 -1.1
#> 49 0.2 1.2 -1.5 -0.9
#> 50 -0.7 0.5 -2.7 -1.1