Power Analysis for the Generic Binomial Test

Calculates power for the generic binomial test with (optional) Type 1 and Type 2 error plots.

Usage

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

Arguments

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, 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.

Value

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.
binom.alpha: critical value(s).
power: statistical power \((1-\beta)\).

Examples

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

#> +--------------------------------------------------+
#> |                POWER CALCULATION                 |
#> +--------------------------------------------------+
#> 
#> Generic Binomial Test
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : prob <= null.prob
#>   H1 (Alternative) : prob  > null.prob
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Type 1 Error (alpha) = 0.038
#>   Type 2 Error (beta)  = 0.140
#>   Statistical Power    = 0.860  <<
#> 

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

#> +--------------------------------------------------+
#> |                POWER CALCULATION                 |
#> +--------------------------------------------------+
#> 
#> Generic Binomial Test
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : prob  = null.prob
#>   H1 (Alternative) : prob != null.prob
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Type 1 Error (alpha) = 0.040
#>   Type 2 Error (beta)  = 0.213
#>   Statistical Power    = 0.787  <<
#> 

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

#> +--------------------------------------------------+
#> |                POWER CALCULATION                 |
#> +--------------------------------------------------+
#> 
#> Generic Binomial Test
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : prob <= min(null.prob) or
#>                      prob >= max(null.prob)
#>   H1 (Alternative) : prob  > min(null.prob) and
#>                      prob  < max(null.prob)
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Type 1 Error (alpha) = 0.049
#>   Type 2 Error (beta)  = 0.229
#>   Statistical Power    = 0.771  <<
#>