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Compute Bootstrap p-values

Source: R/boot.pval.R
boot.pval.Rd

Compute bootstrap p-values through confidence interval inversion, as described in Hall (1992) and Thulin (2024).

Usage

boot.pval(
  boot_res,
  type = "perc",
  theta_null = 0,
  pval_precision = NULL,
  alternative = "two.sided",
  ...
)

Arguments

boot_res

An object of class "boot" containing the output of a bootstrap calculation.

type

A vector of character strings representing the type of interval to base the test on. The value should be one of "norm", "basic", "stud", "perc" (the default), and "bca".

theta_null

The value of the parameter under the null hypothesis.

pval_precision

The desired precision for the p-value. The default is 1/R, where R is the number of bootstrap samples in boot_res.

alternative

A character string specifying the alternative hypothesis. Must be one of "two.sided" (default), "greater", or "less".

...

Additional arguments passed to boot.ci.

Value

A bootstrap p-value.

Details

p-values can be computed by inverting the corresponding confidence intervals, as described in Section 14.2 of Thulin (2024) and Section 3.12 in Hall (1992). This function computes p-values in this way from "boot" objects. The approach relies on the fact that:

  • the p-value of the two-sided test for the parameter theta is the smallest alpha such that theta is not contained in the corresponding 1-alpha confidence interval,

  • for a test of the parameter theta with significance level alpha, the set of values of theta that aren't rejected by the two-sided test (when used as the null hypothesis) is a 1-alpha confidence interval for theta.

References

hall92boot.pval thulin21boot.pval

See also

boot_t_test() for bootstrap t-tests, boot_median_test() for bootstrap tests for medians, boot_summary() for bootstrap tests for coefficients of regression models.

Examples

# Hypothesis test for the city data
# H0: ratio = 1.4
library(boot)
ratio <- function(d, w) sum(d$x * w)/sum(d$u * w)
city.boot <- boot(city, ratio, R = 99, stype = "w", sim = "ordinary")
boot.pval(city.boot, theta_null = 1.4)
#> [1] 0.3838384

# Studentized test for the two sample difference of means problem
# using the final two series of the gravity data.
diff.means <- function(d, f)
{
  n <- nrow(d)
  gp1 <- 1:table(as.numeric(d$series))[1]
  m1 <- sum(d[gp1,1] * f[gp1])/sum(f[gp1])
  m2 <- sum(d[-gp1,1] * f[-gp1])/sum(f[-gp1])
  ss1 <- sum(d[gp1,1]^2 * f[gp1]) - (m1 *  m1 * sum(f[gp1]))
  ss2 <- sum(d[-gp1,1]^2 * f[-gp1]) - (m2 *  m2 * sum(f[-gp1]))
  c(m1 - m2, (ss1 + ss2)/(sum(f) - 2))
}
grav1 <- gravity[as.numeric(gravity[,2]) >= 7, ]
grav1.boot <- boot(grav1, diff.means, R = 99, stype = "f",
                   strata = grav1[ ,2])
boot.pval(grav1.boot, type = "stud", theta_null = 0)
#> [1] 0.01010101