power.binom.test: Power Analysis for the Generic Binomial Test

Description

Calculates power or find Probability (Non-Centrality) for the generic binomial test with (optional) Type 1 and Type 2 error plots.

Usage

power.binom.test(
  power = NULL,
  size = NULL,
  prob = NULL,
  null.prob = 0.5,
  req.sign = "+",
  alpha = 0.05,
  alternative = c("two.sided", "one.sided", "two.one.sided"),
  plot = TRUE,
  verbose = 1,
  utf = FALSE
)

Value

power: statistical power \((1 - \beta)\).
size: number of trials (zero or more).
prob: probability of success on each trial under alternative.
null.prob: probability of success on each trial under null.
alpha: type 1 error rate.
alternative: direction or type of the hypothesis test.
binom.alpha: critical value(s).

Arguments

power: statistical power \((1 - \beta)\); either power, size, or prob needs to be NULL (and is then estimated).
size: number of trials (zero or more); either power, size, or prob needs to be NULL (and is then estimated).
prob: probability of success on each trial under alternative; either power, size or prob needs to be NULL (and is then estimated).
null.prob: probability of success on each trial under null.
req.sign: whether 'prob' is expected to be greater '+1', less than '-1', or within '0' the null.prob' bounds.
alpha: type 1 error rate, defined as the probability of incorrectly rejecting a true null hypothesis, denoted as \(\alpha\).
alternative: character; the direction or type of the hypothesis test: "two.sided", "one.sided", or "two.one.sided". For non-inferiority or superiority tests, add or subtract the margin from the null hypothesis value and use alternative = "one.sided".
plot: logical; FALSE switches off Type 1 and Type 2 error plot. TRUE by default.
verbose: 1 by default (returns test, hypotheses, and results), if 2 a more detailed output is given (plus key parameters and definitions), if 0 no output is printed on the console.
utf: logical; whether the output should show Unicode characters (if encoding allows for it). FALSE by default.

Examples

Run this code

# one-sided
power.binom.test(size = 200, prob = 0.6, null.prob = 0.5, alpha = 0.05,
                 alternative = "one.sided")
power.binom.test(power = 0.80, size = 200, req.sign = "+", null.prob = 0.5,
                 alpha = 0.05, alternative = "one.sided")

# two-sided
power.binom.test(size = 200, prob = 0.4, null.prob = 0.5, alpha = 0.05,
                 alternative = "two.sided")
power.binom.test(power = 0.80, size = 200, req.sign = "+", null.prob = 0.5,
                 alpha = 0.05, alternative = "two.sided")

# equivalence
power.binom.test(size = 200, prob = 0.5, null.prob = c(0.4, 0.6),
                 alpha = 0.05, alternative = "two.one.sided")
power.binom.test(power = 0.80, size = 200, req.sign = "0",
                 null.prob = c(0.4, 0.6), alpha = 0.05,
                 alternative = "two.one.sided")

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