# simData: Simulating Matrix of Statistics In sumSome: Permutation True Discovery Guarantee by Sum-Based Tests

## Description

This function simulates a matrix of permutation statistics, by performing a t test on normal data.

## Usage

 `1` ```simData(prop, m, B = 200, rho = 0, n = 50, alpha = 0.05, pw = 0.8, p = TRUE, seed = NULL) ```

## Arguments

 `prop` proportion of non-null hypotheses. `m` total number of variables. `B` number of permutations, including the identity. `rho` level of equicorrelation between pairs of variables. `n` number of observations. `alpha` significance level. `pw` power of the t test. `p` logical, `TRUE` to compute p-values, `FALSE` to compute t-scores. `seed` seed.

## Details

The function applies the one-sample two-sided t test to a matrix of simulated data, for `B` data permutations. Data is obtained by simulating `n` independent observations from a multivariate normal distribution, where a proportion `prop` of the variables has non-null mean. This mean is such that the one-sample t test with significance level `alpha` has power equal to `pw`. Each pair of distinct variables has equicorrelation `rho`.

## Value

`simData` returns a matrix where the `B` rows correspond to permutations (the first is the identity), and the `m` columns correspond to variables. The matrix contains p-values if `p` is `TRUE`, and t-scores otherwise. The first columns (a proportion `prop`) correspond to non-null hypotheses.

## Author(s)

Anna Vesely.

True discovery guarantee: `sumStats`, `sumPvals`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```# generate matrix of p-values for 5 variables and 10 permutations G <- simData(prop = 0.6, m = 5, B = 10, alpha = 0.4, seed = 42) # subset of interest (variables 1 and 2) S <- c(1,2) # create object of class sumObj # combination: harmonic mean (Vovk and Wang with r = -1) res <- sumPvals(G, S, alpha = 0.4, r = -1) res summary(res) # lower confidence bound for the number of true discoveries in S discoveries(res) # lower confidence bound for the true discovery proportion in S tdp(res) # upper confidence bound for the false discovery proportion in S fdp(res) ```