Power Analysis for the Test of One Proportion (Normal Approximation Method)

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

Formulas are validated using the PASS documentation and G*Power.

Usage

power.z.oneprop(
  prob,
  null.prob = 0.5,
  n = NULL,
  power = NULL,
  alpha = 0.05,
  alternative = c("two.sided", "one.sided", "two.one.sided"),
  std.error = c("null", "alternative"),
  arcsine = FALSE,
  correct = FALSE,
  ceiling = TRUE,
  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".

std.error

character; whether to calculate standard error using "null" or "alternative" value. "null" by default.

arcsine

logical; whether arcsine transformation should be applied. FALSE by default. Note that when arcsine = TRUE, any specification to correct and std.error will be ignored.

correct

logical; whether Yate's continuity correction should be applied.

ceiling

logical; whether sample size should be rounded up. 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

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

mean

mean of the alternative distribution.

sd

standard deviation of the alternative distribution.

null.mean

mean of the null distribution.

null.sd

standard deviation of the null distribution.

z.alpha

critical value(s).

power

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

n

sample size.

Details

• NB: The pwrss.z.prop() function is deprecated, but it will remain available as a wrapper for the power.z.oneprop() function during a transition period.

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.z.oneprop(prob = 0.45, null.prob = 0.50,
                alpha = 0.05, n = 500,
                alternative = "one.sided")
#> +--------------------------------------------------+
#> |                POWER CALCULATION                 |
#> +--------------------------------------------------+
#> 
#> One Proportion
#> 
#>   Method                 : Normal Approximation
#>   Continuity Correction  : FALSE
#>   Arcsine Transformation : FALSE
#>   Standard Error         : Calculated From Null
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : prob - null.prob >= 0
#>   H1 (Alternative) : prob - null.prob  < 0
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Sample Size          = 500
#>   Type 1 Error (alpha) = 0.050
#>   Type 2 Error (beta)  = 0.276
#>   Statistical Power    = 0.724  <<
#> 

# sample size
power.z.oneprop(prob = 0.45, null.prob = 0.50,
                alpha = 0.05, power = 0.80,
                alternative = "one.sided")
#> +--------------------------------------------------+
#> |             SAMPLE SIZE CALCULATION              |
#> +--------------------------------------------------+
#> 
#> One Proportion
#> 
#>   Method                 : Normal Approximation
#>   Continuity Correction  : FALSE
#>   Arcsine Transformation : FALSE
#>   Standard Error         : Calculated From Null
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : prob - null.prob >= 0
#>   H1 (Alternative) : prob - null.prob  < 0
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Sample Size          = 617  <<
#>   Type 1 Error (alpha) = 0.050
#>   Type 2 Error (beta)  = 0.200
#>   Statistical Power    = 0.800
#>