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 = TRUE, pretty = 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: 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: logical; whether the output should be printed on the console. TRUE by default.
pretty: 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 Claim) : prob <= null.prob 
#>   H1 (Alt. Claim) : prob > null.prob 
#> 
#> ---------------------------------------------------
#> Results
#> ---------------------------------------------------
#>   Type 1 Error (alpha)   = 0.038
#>   Type 2 Error (beta)    = 0.140
#>   Statistical Power      = 0.86  <<
#> 

# 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 Claim) : prob = null.prob 
#>   H1 (Alt. Claim) : 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 Claim) : prob <= min(null.prob) or 
#>                     prob >= max(null.prob) 
#>   H1 (Alt. Claim) : 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  <<
#>