Power of the GRIM binomial test

grim_binomial_power() computes the statistical power of grim_binomial() for given parameters, to judge whether the test is informative for a data set before interpreting its p-value. Like the test itself, it has not been tested extensively.

Usage

grim_binomial_power(
  p0,
  p1,
  k = NULL,
  alternative = c("greater", "less", "two.sided"),
  alpha = 0.05
)

Arguments

p0

Numeric. Null probability of GRIM consistency per value set, i.e., 1 - grim_exp_incon(...). Either one value per value set, or a single value shared by all, in which case k is required.

p1

Numeric (length 1). Probability of consistency under the alternative, shared by all value sets.

k

Numeric (length 1). Number of value sets. Required if p0 has length 1; otherwise ignored in favor of length(p0).

alternative

String (length 1). One of "greater" (the default), "less", and "two.sided".

alpha

Numeric (length 1). Significance level. Default is 0.05.

Value

Numeric (length 1). The probability of rejecting the null hypothesis when the alternative is true.

Examples

# 10 means with a null probability of 0.5 each, 90% truly consistent:
grim_binomial_power(p0 = 0.50, p1 = 0.9, k = 10)
#> [1] 0.7360989

# The same with 30 means:
grim_binomial_power(p0 = 0.50, p1 = 0.9, k = 30)
#> [1] 0.9999109

# One null probability per value set:
grim_binomial_power(p0 = c(0.5, 0.7, 0.8, 0.9, 0.6, 0.5, 0.4), p1 = 0.9)
#> [1] 0.4782969