simulate_t_tests: simulate one-sample t-tests

In StoreyLab/fFDR: Functional FDR for multiple hypothesis testing

Description

simulateTTests simulates a number of one-sample t-tests on Normally distributed samples with varying mean mu0 and sample size.

Usage

simulate_t_tests(
  m = 4000,
  pi0 = 0.5,
  mu.sd = 0.3,
  mu.min = 0,
  n.lmean = 2,
  n.lsd = 2.5,
  sample.sd = 1,
  seed = NULL,
  ...
)

Arguments

m	Number of hypotheses to simulate
pi0	Either a value for the fraction of true null hypotheses for which mu=0, or a vector each of whose entries is the likelihood of a true null hypothesis
mu.sd	Standard deviation used to generate the means of the Normal distributions under the alternative hypothesis
mu.min	The minumum value of abs(mu) for the means of the Normal distributions under the alternative hypothesis
n.lmean	Mean of the sample sizes on a log scale
n.lsd	Standard deviation of the sample sizes on a log scale
sample.sd	Standard deviation for the Normal distributions
seed	Optionally, random seed to set before simulating
...	Extra arguments, such as replication (may not be used)

Details

Each sample and test is constructed according to the following generative process.

The mean of a Normal distribution, mu, is either 0 under the null hypothesis, or generated as (mu.min + abs(Norm(0, mu.sd)) under the alternative hypothesis. So, the means are always either positive or 0. mu.min can be used to ensure a minimal effect size between the null hypothesis and the weakest alternative hypothesis (since by default an alternative hypothesis can be arbitrarily close to being a true null hypothesis).

The sample size of each sample, n, is generated from a log-normal distribution, independent of the means of the Normal distributions. Specifically, it is generated as 2 + round(LNorm(n.lmean, n.lsd)), such that the sample size is never less than 2 (which would make a t-test impossible).

At this point, a random sample of size n is generated from the Norm(mu, sample.sd) distribution. A one-sample two-sided t-test is performed and the p-value obtained.

Value

A data frame, one row per hypothesis, with the columns

p.value	Two-sided t-test p-value
n	Sample size of each sample
mu	Mean of each sample
oracle	TRUE if the alternative hypothesis holds, and FALSE for a true null hypothesis

StoreyLab/fFDR documentation built on March 8, 2021, 10:14 p.m.