Power Analysis for the Generic Binomial Test

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

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  <<
#>