Calculating T2 statistics in R
I have a matrix x:
> x
x1 x2
[1,] 6 9
[2,] 10 6
[3,] 8 3
I am trying to T^2 statistics:
> library(DescTools)
> HotellingsT2Test(x)
Hotelling's one sample T2-test for mu' = [9, 5]
data: x
T.2 = 28, df1 = 2, df2 = 1, p-value = 0.1325
alternative hypothesis: true location is not equal to c(0,0)
The statistics seems to be off (the correct answer is 7/9). What am I doing wrong?
Other variables:
> mu
[1] 9 5
> means
x1 x2
8 6
> S # variance-covariance matrix
[,1] [,2]
[1,] 4 -3
[2,] -3 9
> S_inv # inverse matrix
[,1] [,2]
[1,] 0.3333333 0.1111111
[2,] 0.1111111 0.1481481
r matrix mean covariance variance
asked Nov 23 '18 at 19:59
Feyzi BagirovFeyzi Bagirov
3901722
add a comment |
I have a matrix x:
> x
x1 x2
[1,] 6 9
[2,] 10 6
[3,] 8 3
I am trying to T^2 statistics:
> library(DescTools)
> HotellingsT2Test(x)
Hotelling's one sample T2-test for mu' = [9, 5]
data: x
T.2 = 28, df1 = 2, df2 = 1, p-value = 0.1325
alternative hypothesis: true location is not equal to c(0,0)
The statistics seems to be off (the correct answer is 7/9). What am I doing wrong?
Other variables:
> mu
[1] 9 5
> means
x1 x2
8 6
> S # variance-covariance matrix
[,1] [,2]
[1,] 4 -3
[2,] -3 9
> S_inv # inverse matrix
[,1] [,2]
[1,] 0.3333333 0.1111111
[2,] 0.1111111 0.1481481
r matrix mean covariance variance
asked Nov 23 '18 at 19:59
Feyzi BagirovFeyzi Bagirov
3901722
add a comment |
I have a matrix x:
> x
x1 x2
[1,] 6 9
[2,] 10 6
[3,] 8 3
I am trying to T^2 statistics:
> library(DescTools)
> HotellingsT2Test(x)
Hotelling's one sample T2-test for mu' = [9, 5]
data: x
T.2 = 28, df1 = 2, df2 = 1, p-value = 0.1325
alternative hypothesis: true location is not equal to c(0,0)
The statistics seems to be off (the correct answer is 7/9). What am I doing wrong?
Other variables:
> mu
[1] 9 5
> means
x1 x2
8 6
> S # variance-covariance matrix
[,1] [,2]
[1,] 4 -3
[2,] -3 9
> S_inv # inverse matrix
[,1] [,2]
[1,] 0.3333333 0.1111111
[2,] 0.1111111 0.1481481
r matrix mean covariance variance
asked Nov 23 '18 at 19:59
Feyzi BagirovFeyzi Bagirov
3901722
I have a matrix x:
> x
x1 x2
[1,] 6 9
[2,] 10 6
[3,] 8 3
I am trying to T^2 statistics:
> library(DescTools)
> HotellingsT2Test(x)
Hotelling's one sample T2-test for mu' = [9, 5]
data: x
T.2 = 28, df1 = 2, df2 = 1, p-value = 0.1325
alternative hypothesis: true location is not equal to c(0,0)
The statistics seems to be off (the correct answer is 7/9). What am I doing wrong?
Other variables:
> mu
[1] 9 5
> means
x1 x2
8 6
> S # variance-covariance matrix
[,1] [,2]
[1,] 4 -3
[2,] -3 9
> S_inv # inverse matrix
[,1] [,2]
[1,] 0.3333333 0.1111111
[2,] 0.1111111 0.1481481
r matrix mean covariance variance
r matrix mean covariance variance
asked Nov 23 '18 at 19:59
Feyzi BagirovFeyzi Bagirov
3901722
asked Nov 23 '18 at 19:59
Feyzi BagirovFeyzi Bagirov
3901722
asked Nov 23 '18 at 19:59
Feyzi BagirovFeyzi Bagirov
3901722
asked Nov 23 '18 at 19:59
Feyzi BagirovFeyzi Bagirov
3901722
asked Nov 23 '18 at 19:59
Feyzi BagirovFeyzi Bagirov
3901722
3901722
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
First, you are not providing the mu parameter to the function. But then
HotellingsT2Test(x, mu = mu)
#
# Hotelling's one sample T2-test
#
# data: x
# T.2 = 0.19444, df1 = 2, df2 = 1, p-value = 0.8485
# alternative hypothesis: true location is not equal to c(9,5)
still isn't what you expect, and that is because by default the decision is based on the F-distribution, in which case the statistic is multiplied by another factor (which is (n - p)/(p * (n - 1)), with n = 3 and p = 2 in your case). Using chi-squared approximation we get, as needed,
HotellingsT2Test(x, mu = mu, test = "chi")
#
# Hotelling's one sample T2-test
#
# data: x
# T.2 = 0.77778, df = 2, p-value = 0.6778
# alternative hypothesis: true location is not equal to c(9,5)
answered Nov 23 '18 at 20:13
Julius VainoraJulius Vainora
33.3k75979
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
First, you are not providing the mu parameter to the function. But then
HotellingsT2Test(x, mu = mu)
#
# Hotelling's one sample T2-test
#
# data: x
# T.2 = 0.19444, df1 = 2, df2 = 1, p-value = 0.8485
# alternative hypothesis: true location is not equal to c(9,5)
still isn't what you expect, and that is because by default the decision is based on the F-distribution, in which case the statistic is multiplied by another factor (which is (n - p)/(p * (n - 1)), with n = 3 and p = 2 in your case). Using chi-squared approximation we get, as needed,
HotellingsT2Test(x, mu = mu, test = "chi")
#
# Hotelling's one sample T2-test
#
# data: x
# T.2 = 0.77778, df = 2, p-value = 0.6778
# alternative hypothesis: true location is not equal to c(9,5)
answered Nov 23 '18 at 20:13
Julius VainoraJulius Vainora
33.3k75979
add a comment |
First, you are not providing the mu parameter to the function. But then
HotellingsT2Test(x, mu = mu)
#
# Hotelling's one sample T2-test
#
# data: x
# T.2 = 0.19444, df1 = 2, df2 = 1, p-value = 0.8485
# alternative hypothesis: true location is not equal to c(9,5)
still isn't what you expect, and that is because by default the decision is based on the F-distribution, in which case the statistic is multiplied by another factor (which is (n - p)/(p * (n - 1)), with n = 3 and p = 2 in your case). Using chi-squared approximation we get, as needed,
HotellingsT2Test(x, mu = mu, test = "chi")
#
# Hotelling's one sample T2-test
#
# data: x
# T.2 = 0.77778, df = 2, p-value = 0.6778
# alternative hypothesis: true location is not equal to c(9,5)
answered Nov 23 '18 at 20:13
Julius VainoraJulius Vainora
33.3k75979
add a comment |
First, you are not providing the mu parameter to the function. But then
HotellingsT2Test(x, mu = mu)
#
# Hotelling's one sample T2-test
#
# data: x
# T.2 = 0.19444, df1 = 2, df2 = 1, p-value = 0.8485
# alternative hypothesis: true location is not equal to c(9,5)
still isn't what you expect, and that is because by default the decision is based on the F-distribution, in which case the statistic is multiplied by another factor (which is (n - p)/(p * (n - 1)), with n = 3 and p = 2 in your case). Using chi-squared approximation we get, as needed,
HotellingsT2Test(x, mu = mu, test = "chi")
#
# Hotelling's one sample T2-test
#
# data: x
# T.2 = 0.77778, df = 2, p-value = 0.6778
# alternative hypothesis: true location is not equal to c(9,5)
answered Nov 23 '18 at 20:13
Julius VainoraJulius Vainora
33.3k75979
First, you are not providing the mu parameter to the function. But then
HotellingsT2Test(x, mu = mu)
#
# Hotelling's one sample T2-test
#
# data: x
# T.2 = 0.19444, df1 = 2, df2 = 1, p-value = 0.8485
# alternative hypothesis: true location is not equal to c(9,5)
still isn't what you expect, and that is because by default the decision is based on the F-distribution, in which case the statistic is multiplied by another factor (which is (n - p)/(p * (n - 1)), with n = 3 and p = 2 in your case). Using chi-squared approximation we get, as needed,
HotellingsT2Test(x, mu = mu, test = "chi")
#
# Hotelling's one sample T2-test
#
# data: x
# T.2 = 0.77778, df = 2, p-value = 0.6778
# alternative hypothesis: true location is not equal to c(9,5)
answered Nov 23 '18 at 20:13
Julius VainoraJulius Vainora
33.3k75979
answered Nov 23 '18 at 20:13
Julius VainoraJulius Vainora
33.3k75979
answered Nov 23 '18 at 20:13
Julius VainoraJulius Vainora
33.3k75979
answered Nov 23 '18 at 20:13
Julius VainoraJulius Vainora
33.3k75979
33.3k75979
add a comment |
add a comment |
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