Bootstrap one-sample t-test — bootstrap

Perform a simple non-parametric bootstrap procedure for the one-sample t-test on a population mean with unknown variance.

Usage

bootstrap_ttest(
  x,
  mu0 = 0,
  nboot = 1000,
  conf.level = 0.95,
  alternative = c("two.sided", "less", "greater"),
  seed = NULL
)

Arguments

x: Numeric vector of observations.
mu0: Hypothesized population mean under the null hypothesis.
nboot: Number of bootstrap resamples (integer, usually at least 100).
conf.level: Confidence level for the bootstrap confidence interval.
alternative: Character string specifying the alternative hypothesis, one of "two.sided", "less", or "greater".
seed: Optional integer seed for reproducibility.

Value

A list of class "oneMeanTest_bootstrap" with components:

t.obs: Observed t-statistic.
t.boot: Numeric vector of bootstrap t-statistics.
mean.obs: Observed sample mean.
mean.boot: Numeric vector of bootstrap means.
conf.int: Bootstrap percentile confidence interval for the mean (numeric vector of length 2 with attribute conf.level).
p.value: Bootstrap p-value.
nboot: Number of bootstrap resamples.
mu0: Hypothesized mean.
alternative: Alternative hypothesis used.
call: The matched function call.

Details

The function resamples the observed data with replacement, computes the t-statistic for each bootstrap sample, and uses the empirical distribution of these statistics to obtain a bootstrap p-value and a percentile confidence interval for the mean.

This is useful for illustrating resampling-based inference and for comparing classical t-test results with bootstrap results.

Examples

set.seed(123)
x <- rnorm(30, mean = 5, sd = 2)

boot_res <- bootstrap_ttest(
  x,
  mu0 = 5,
  nboot = 500,
  conf.level = 0.95,
  alternative = "two.sided",
  seed = 123
)
boot_res
#> Bootstrap one-sample t-test
#> 
#> Call:
#> bootstrap_ttest(x = x, mu0 = 5, nboot = 500, conf.level = 0.95, 
#>     alternative = "two.sided", seed = 123)
#> 
#> Observed t-statistic: -0.2630
#> Bootstrap p-value  : 0.826
#> 95.0000% bootstrap CI for the mean:
#>   [4.1933, 5.5355]
#> Number of resamples: 500