# Simulation-based experiment for power analysis

`power_exp.Rd`

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.

## 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`

.

## 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).

## References

Zaineb Smida, Lionel Cucala, Ali Gannoun & Ghislain Durif (2022) A median test for functional data, Journal of Nonparametric Statistics, 34:2, 520-553, doi:10.1080/10485252.2022.2064997 , hal-03658578

## 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
#> $mo
#> [1] 1
#>
#> $med
#> [1] 1
#>
#> $wmw
#> [1] 1
#>
#> $hkr
#> T1 T2
#> 1 1
#>
#> $cff
#> [1] 1
#>
```