PCT2 | R Documentation |
The function implements the Partition Closed Testing procedure for testing mean differences between two functional populations. Functional data are tested locally and unadjusted and adjusted p-value functions are provided. The unadjusted p-value function controls the point-wise error rate. The adjusted p-value function controls the family-wise error rate asymptotically.
PCT2(
data1,
data2,
mu = 0,
B = 1000,
paired = FALSE,
dx = NULL,
partition,
alternative = "two.sided"
)
data1 |
First population's data. Either pointwise evaluations of the functional data set on a uniform grid, or a |
data2 |
Second population's data. Either pointwise evaluations of the functional data set on a uniform grid, or a |
mu |
Functional mean difference under the null hypothesis. Three possibilities are available for |
B |
The number of iterations of the MC algorithm to evaluate the p-values of the permutation tests. The defualt is |
paired |
Flag indicating whether a paired test has to be performed. Default is |
dx |
Used only if a |
partition |
Vector of length |
alternative |
A character string specifying the alternative hypothesis, must be one of " |
PCT2
returns an object of class
"fdatest2
" containing the following components:
test |
String vector indicating the type of test performed. In this case equal to |
mu |
Evaluation on a grid of the functional mean difference under the null hypothesis (as entered by the user). |
unadjusted_pval |
Evaluation on a grid of the unadjusted p-value function. |
adjusted_pval |
Evaluation on a grid of the adjusted p-value function. |
data.eval |
Evaluation on a grid of the functional data. |
ord_labels |
Vector of labels indicating the group membership of data.eval |
Abramowicz, K., Pini, A., Schelin, L., Stamm, A., & Vantini, S. (2022). “Domain selection and familywise error rate for functional data: A unified framework. Biometrics 79(2), 1119-1132.
Pini, A., & Vantini, S. (2017). Interval-wise testing for functional data. Journal of Nonparametric Statistics, 29(2), 407-424
See also plot.fdatest2
for plotting the results.
# Importing the NASA temperatures data set
data(NASAtemp)
# Performing the PCT for two populations
# Choosing as partition the 4 seasons of the year
partition = c(rep(1,31+28+21),rep(2,10+30+31+21),rep(3,9+31+31+23),rep(4,7+31+30+21),rep(1,10))
partition = factor(partition)
PCT.result <- PCT2(NASAtemp$paris,NASAtemp$milan,partition=partition)
# Plotting the results of the PCT
plot(PCT.result,xrange=c(0,12),main='PCT results for testing mean differences')
# Selecting the significant components at 5% level
which(PCT.result$adjusted_pval < 0.05)
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