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Power Analysis for Testing Difference Between Two Proportions (Normal Approximation Method)

Source: R/proportions.onetwo.R
power.z.twoprops.Rd

Calculates power or sample size (only one can be NULL at a time) for two proportions using the normal approximation method.

Validated via G*Power and PASS documentation.

Usage

power.z.twoprops(
  prob1,
  prob2,
  margin = 0,
  n.ratio = 1,
  n2 = NULL,
  power = NULL,
  alpha = 0.05,
  alternative = c("two.sided", "one.sided", "two.one.sided"),
  arcsine = FALSE,
  correct = FALSE,
  paired = FALSE,
  rho.paired = 0.5,
  std.error = c("pooled", "unpooled"),
  ceiling = TRUE,
  verbose = 1,
  utf = FALSE
)

Arguments

prob1

probability of success in the first group.

prob2

probability of success in the second group.

margin

ignorable prob1 - prob2 difference. For two one-sided tests provide lower and upper margins in the form of c(lower, upper).

n.ratio

sample size ratio (n1 / n2).

n2

integer; sample size for the second group.

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".

arcsine

logical; whether arcsine transformation should be applied. Note that this only applies to independent proportions without continuity correction.

correct

logical; whether Yates' continuity correction should be applied to the test statistic. Ignored for the paired test.

paired

logical; if TRUE samples are paired. FALSE by default.

rho.paired

correlation between paired observations.

std.error

character; whether to calculate standard error using "pooled" or "unpooled" standard deviation. Ignored for the paired test.

ceiling

logical; TRUE rounds up sample size in each group.

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 test, which is "z" or "exact".

power

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

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).

n

sample size in the form of c(n1, n2) (applies to independent proportions).

n.total

total sample size (applies to independent proportions).

n.paired

paired sample size (applies to paired proportions).

Details

  • NB: The pwrss.z.2props() function is deprecated, but it will remain available as a wrapper for the power.z.twoprops() 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.twoprops(prob1 = 0.65, prob2 = 0.60,
                   alpha = 0.05, n2 = 500,
                   alternative = "one.sided")
#> +--------------------------------------------------+
#> |                POWER CALCULATION                 |
#> +--------------------------------------------------+
#> 
#> Independent Proportions
#> 
#>   Method : Normal Approximation
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : prob1 - prob2 <= 0
#>   H1 (Alternative) : prob1 - prob2  > 0
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Sample Size          = 500 and 500
#>   Type 1 Error (alpha) = 0.050
#>   Type 2 Error (beta)  = 0.505
#>   Statistical Power    = 0.495  <<
#> 

  # sample size
  power.z.twoprops(prob1 = 0.65, prob2 = 0.60,
                   alpha = 0.05, power = 0.80,
                   alternative = "one.sided")
#> +--------------------------------------------------+
#> |             SAMPLE SIZE CALCULATION              |
#> +--------------------------------------------------+
#> 
#> Independent Proportions
#> 
#>   Method : Normal Approximation
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : prob1 - prob2 <= 0
#>   H1 (Alternative) : prob1 - prob2  > 0
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Sample Size          = 1159 and 1159  <<
#>   Type 1 Error (alpha) = 0.050
#>   Type 2 Error (beta)  = 0.200
#>   Statistical Power    = 0.800
#>