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

Description Usage Arguments Details Value Author(s) See Also Examples

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

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

`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.

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.

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.

Anna Vesely.

True discovery guarantee: sumStats, sumPvals

# 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)