Power Analysis for Testing Difference Between Two Proportions (Normal Approximation and Exact Methods)

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

Validated via G*Power and PASS documentation.

NOTE: The pwrss.z.2props() function is deprecated, but it will remain available as a wrapper for the power.z.twoprops() function during the transition period.

power.z.twoprops(prob1, prob2, margin = 0,
                 n2 = NULL, n.ratio = 1,
                 power = NULL, alpha = 0.05,
                 alternative = c("two.sided", "one.sided", "two.one.sided"),
                 arcsine = FALSE, correct = FALSE,
                 paired = FALSE, rho.paired = 0.50,
                 std.error = c("pooled", "unpooled"),
                 ceiling = TRUE, verbose = TRUE, pretty = FALSE)

power.exact.twoprops(prob1, prob2, n2 = NULL, n.ratio = 1,
                     power = NULL, alpha = 0.05,
                     alternative = c("two.sided", "one.sided"),
                     paired = FALSE, rho.paired = 0.50,
                     method = c("exact", "approximate"),
                     ceiling = TRUE, verbose = TRUE, pretty = 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).
n2: integer; sample size for the second group.
n.ratio: sample size ratio (n1 / n2).
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 \(\alpha\).
paired: logical; if TRUE samples are paired. FALSE by default.
rho.paired: correlation between paired observations.
method: character; whether to use "approximate" or "exact" method. Default is "exact" (only in the power.exact.twoprops() function).
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.
std.error: character; whether to calculate standard error using "pooled" or "unpooled" standard deviation. Ignored for the paired test.
alternative: character; direction or type of the hypothesis test: "two.sided", "one.sided", or "two.one.sided".
ceiling: logical; TRUE rounds up sample size in each group.
verbose: logical; TRUE prints the output on the console.
pretty: 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).

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. doi: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 Claim) : prob1 - prob2 <= 0 
#>   H1 (Alt. Claim) : 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 Claim) : prob1 - prob2 <= 0 
#>   H1 (Alt. Claim) : prob1 - prob2 > 0 
#> 
#> ---------------------------------------------------
#> Results
#> ---------------------------------------------------
#>   Sample Size          = 1159 and 1159  <<
#>   Type 1 Error (alpha) = 0.050
#>   Type 2 Error (beta)  = 0.200
#>   Statistical Power    = 0.8
#>