# power_exp: Simulation-based experiment for power analysis In funStatTest: Statistical Testing for Functional Data

 power_exp R Documentation

## Simulation-based experiment for power analysis

### Description

Computation of the statistical power (i.e. risk to reject the null hypothesis when it is false) associated to any statistics described in the package based on simulation permutation-based p-values computations. See Smida et al (2022) for more details.

### Usage

``````power_exp(
n_simu = 100,
alpha = 0.05,
n_perm = 100,
stat = c("mo", "med"),
n_point = 100,
n_obs1 = 50,
n_obs2 = 50,
c_val = 1,
delta_shape = "constant",
distrib = "normal",
max_iter = 10000,
verbose = FALSE
)
``````

### Arguments

 `n_simu` integer value, number of simulations to compute the statistical power. `alpha` numerical value, between 0 and 1, type I risk level to reject the null hypothesis in the simulation. Default value is `⁠5%⁠`. `n_perm` integer, number of permutation to compute the p-values. `stat` character string or vector of character string, name of the statistics for which the p-values will be computed, among `"mo"`, `"med"`, `"wmw"`, `"hkr"`, `"cff"`. `n_point` integer value, number of points in the trajectory. `n_obs1` integer value, number of trajectories in the first sample. `n_obs2` integer value, number of trajectories in the second sample. `c_val` numeric value, level of divergence between the two samples. `delta_shape` character string, shape of the divergence between the two samples, among `"constant"`, `"linear"`, `"quadratic"`. `distrib` character string, type of probability distribution used to simulate the data among `"normal"`, `"cauchy"`, `"dexp"`, `"student"`. `max_iter` integer, maximum number of iteration for the iterative simulation process. `verbose` boolean, if TRUE, enable verbosity.

### Details

The `c_val` input argument should be strictly positive so that the null hypothesis is not verified when simulating the data (i.e. so that the two sample are not generated from the same probability distribution).

### Value

a list with the following elements:

• `power_res`: a list of named numeric value corresponding to the power values for each statistic listed in `stat` input.

• `pval_res`: a list of named numeric values corresponding to the p-values for each simulation and each statistic listed in the `stat` input.

• `simu_config`: information about input parameters used for simulation, including `n_simu`, ` c_val`, ` distrib`, ` delta_shape`, ` n_point`, ` n_obs1`, ` n_obs2`.

### Author(s)

Zaineb Smida, Ghislain DURIF, Lionel Cucala

### References

Zaineb Smida, Lionel Cucala, Ali Gannoun & Ghislain Durif (2022) A median test for functional data, Journal of Nonparametric Statistics, 34:2, 520-553, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/10485252.2022.2064997")}, hal-03658578

`stat_mo()`, `stat_med()`, `stat_wmw()`, `stat_hkr()`, `stat_cff()`, `comp_stat()`

### Examples

``````# simulate a few small data for the example
res <- power_exp(
n_simu = 20, alpha = 0.05, n_perm = 100,
stat = c("mo", "med", "wmw", "hkr", "cff"),
n_point = 25, n_obs1 = 4, n_obs2 = 5, c_val = 10, delta_shape = "constant",
distrib = "normal", max_iter = 10000, verbose = FALSE
)
res\$power_res
``````

funStatTest documentation built on May 29, 2024, 10:26 a.m.