Skip to contents

Power Analysis for the Test of One Proportion (Exact Method)

Source: R/proportions.onetwo.R
power.exact.oneprop.Rd

Calculates power or sample size (only one can be NULL at a time) for test of a proportion against a constant using the exact method.

Formulas are validated using PASS documentation.

Usage

power.exact.oneprop(
  prob,
  null.prob = 0.5,
  n = NULL,
  power = NULL,
  alpha = 0.05,
  alternative = c("two.sided", "one.sided", "two.one.sided"),
  verbose = 1,
  utf = FALSE
)

Arguments

prob

probability of success under alternative.

null.prob

probability of success under null.

n

integer; sample size.

power

statistical power, defined as the probability of correctly rejecting a false null hypothesis, denoted as \(1 - \beta\).

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 margin to the null hypothesis value and use alternative = "one.sided".

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

parms

list of parameters used in calculation.

test

type of the statistical test ("exact").

delta

difference between prob and null.prob

odds.ratio

Odds-ratio \((prob / (1 - prob)) / (null.prob / (1 - null.prob))\)

prob

probability of success under alternative.

null.prob

probability of success under null.

binom.alpha

critical value(s).

power

statistical power \((1 - \beta)\).

n

sample size.

References

Bulus, M., & Polat, C. (2023). pwrss R paketi ile istatistiksel guc analizi [Statistical power analysis with pwrss R package]. Ahi Evran Universitesi Kirsehir Egitim Fakultesi Dergisi, 24(3), 2207-2328. https://doi.org/10.29299/kefad.1209913

Examples

# power'
power.exact.oneprop(prob = 0.45, null.prob = 0.50,
                    alpha = 0.05, n = 500,
                    alternative = "one.sided")
#> +--------------------------------------------------+
#> |                POWER CALCULATION                 |
#> +--------------------------------------------------+
#> 
#> One Proportion
#> 
#>   Method                 : Exact
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : prob - null.prob >= 0
#>   H1 (Alternative) : prob - null.prob  < 0
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Sample Size          = 500
#>   Type 1 Error (alpha) = 0.049
#>   Type 2 Error (beta)  = 0.279
#>   Statistical Power    = 0.721  <<
#> 

# sample size
power.exact.oneprop(prob = 0.45, null.prob = 0.50,
                    alpha = 0.05, power = 0.80,
                    alternative = "one.sided")
#> +--------------------------------------------------+
#> |             SAMPLE SIZE CALCULATION              |
#> +--------------------------------------------------+
#> 
#> One Proportion
#> 
#>   Method                 : Exact
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : prob - null.prob >= 0
#>   H1 (Alternative) : prob - null.prob  < 0
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Sample Size          = 633  <<
#>   Type 1 Error (alpha) = 0.047
#>   Type 2 Error (beta)  = 0.197
#>   Statistical Power    = 0.803
#>