Power Analysis for Testing Difference Between Two Proportions (Exact Method)

Calculates power or sample size (only one can be NULL at a time) for two proportions using the exact method. The function is a wrapper for power.exact.mcnemar (if paired == TRUE), or power.exact.fisher (if paired == FALSE)

Validated via G*Power and PASS documentation.

Usage

power.exact.twoprops(
  prob1,
  prob2,
  n.ratio = 1,
  n2 = NULL,
  power = NULL,
  alpha = 0.05,
  alternative = c("two.sided", "one.sided"),
  paired = FALSE,
  rho.paired = 0.5,
  method = c("exact", "approximate"),
  ceiling = TRUE,
  verbose = 1,
  utf = FALSE
)

Arguments

prob1: probability of success in the first group.
prob2: probability of success in the second group.
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" or "one.sided".
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).
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".
delta: difference between prob1 and prob2
odds.ratio: Odds-ratio \((prob1 / (1 - prob1)) / (prob2 / (1 - prob2))\)
size: ... (applies to paired proportions).
prob: ... (applies to paired proportions).
null.prob: ... (applies to paired proportions).
binom.alpha: critical value(s) (applies to paired proportions).
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.
alternative: standard deviation of the null distribution.
z.alpha: critical value(s).
power: statistical power \((1 - \beta)\).
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. https://doi.org/10.29299/kefad.1209913

Examples

  # power
  power.exact.twoprops(prob1 = 0.70, prob2 = 0.60,
                       alpha = 0.05, n2 = 500,
                       alternative = "one.sided")
#> +--------------------------------------------------+
#> |                POWER CALCULATION                 |
#> +--------------------------------------------------+
#> 
#> Independent Proportions
#> 
#>   Method : Fisher's Exact
#> 
#> ----------------------------------------------------
#> 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)  = 0.053
#>   Statistical Power    = 0.947  <<
#> 

  power.exact.twoprops(prob1 = 0.70, prob2 = 0.60,
                       alpha = 0.05, n2 = 500,
                       alternative = "one.sided",
                       paired = TRUE)
#> +--------------------------------------------------+
#> |                POWER CALCULATION                 |
#> +--------------------------------------------------+
#> 
#> Paired Proportions
#> 
#>   Method : McNemar's Exact
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : prob10 - prob01 <= 0
#>   H1 (Alternative) : prob10 - prob01  > 0
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Paired Sample Size   = 500
#>   Type 1 Error (alpha) = 0.040
#>   Type 2 Error (beta)  = 0.001
#>   Statistical Power    = 0.999  <<
#> 

  # sample size
  power.exact.twoprops(prob1 = 0.70, prob2 = 0.60,
                       alpha = 0.05, power = 0.80,
                       alternative = "one.sided")
#> +--------------------------------------------------+
#> |             SAMPLE SIZE CALCULATION              |
#> +--------------------------------------------------+
#> 
#> Independent Proportions
#> 
#>   Method : Fisher's Exact
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : prob1 - prob2 <= 0
#>   H1 (Alternative) : prob1 - prob2  > 0
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Sample Size          = 302 and 302  <<
#>   Type 1 Error (alpha) = 0.050
#>   Type 2 Error (beta)  = 0.199
#>   Statistical Power    = 0.801
#> 

  power.exact.twoprops(prob1 = 0.70, prob2 = 0.60,
                       alpha = 0.05, power = 0.80,
                       alternative = "one.sided",
                       paired = TRUE)
#> +--------------------------------------------------+
#> |             SAMPLE SIZE CALCULATION              |
#> +--------------------------------------------------+
#> 
#> Paired Proportions
#> 
#>   Method : McNemar's Exact
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : prob10 - prob01 <= 0
#>   H1 (Alternative) : prob10 - prob01  > 0
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Paired Sample Size   = 158  <<
#>   Type 1 Error (alpha) = 0.036
#>   Type 2 Error (beta)  = 0.195
#>   Statistical Power    = 0.805
#>