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The two-sample test can be additionally performed by providing the
two sample to be compared as x
and y
. We
generate the sample \(y = (y_1,
\ldots,y_n)\) from a skew-normal distribution \(SN_d(0,I_d, \lambda)\), where \(d=4\), \(n=200\) and \(\lambda= (0.5,\ldots,0.5)\).
## Warning: il pacchetto 'sn' รจ stato creato con R versione 4.3.3
library(mvtnorm)
library(QuadratiK)
n <- 200
d <- 4
skewness_y <- 0.5
set.seed(2468)
x_2 <- rmvnorm(n, mean = rep(0,d))
y_2 <- rmsn(n=n, xi=0, Omega = diag(d), alpha=rep(skewness_y,d))
For the two-sample case, the summary
function provides
the results from the test and the descriptive statistics per variable
and per group, as similarly described for the \(k\)-sample test. Additionally, it generates
the qq-plots comparing the quantiles of the two groups for each
variable.
## Registered S3 methods overwritten by 'ggpp':
## method from
## heightDetails.titleGrob ggplot2
## widthDetails.titleGrob ggplot2
##
## Kernel-based quadratic distance two-sample test
## Test_Statistic Critical_Value Reject_H0
## 1 4.276823 0.7745576 TRUE
## 2 9.843008 1.7831227 TRUE
## [[1]]
## Group 1 Group 2 Overall
## mean 0.021762263 0.3799990 0.2008806
## sd 1.014655344 0.9498167 0.9977884
## median -0.005110155 0.3833061 0.2125618
## IQR 1.471877262 1.1310211 1.3666010
## min -2.675477796 -2.2219439 -2.6754778
## max 2.300153117 3.1690406 3.1690406
##
## [[2]]
## Group 1 Group 2 Overall
## mean -0.03347117 0.2216529 0.09409085
## sd 1.06408749 1.0304067 1.05383755
## median 0.02476594 0.1717768 0.09272994
## IQR 1.52458343 1.3739349 1.45668193
## min -3.22222061 -2.6162342 -3.22222061
## max 2.96751758 2.3300745 2.96751758
##
## [[3]]
## Group 1 Group 2 Overall
## mean -0.06473408 0.3312699 0.1332679
## sd 0.93818786 0.9868499 0.9818422
## median -0.07044427 0.4006745 0.1382735
## IQR 1.37135831 1.2185714 1.3854150
## min -2.86000669 -3.0246026 -3.0246026
## max 2.56476485 2.7590501 2.7590501
##
## [[4]]
## Group 1 Group 2 Overall
## mean -0.1658894 0.2065222 0.02031639
## sd 1.0175325 0.9718613 1.01104987
## median -0.2371959 0.1427746 0.04889195
## IQR 1.3802070 1.2320445 1.32957715
## min -2.5899601 -2.0159679 -2.58996007
## max 2.7066430 2.6637589 2.70664302
The figure automatically generated by the summary
function on the result of the two-sample test displays the qq-plots
between the two samples with a table of the standard descriptive
statistics for each variable, computed per group and overall.
If a value of \(h\) is not provided,
the function automatically perform the function
select_h
.
For a more accurate search of the tuning parameter, the function
select_h
can be used. This function needs the input
x
and y
as the function kb.test
for the two-sample problem.
The figure generated by the select_h
function on the
result of the selection of \(h\)
algorithm on the two-sample data set displays the obtained power versus
the considered \(h\), for the
alternatives \(\delta\).
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.