Power Analysis for Independent Correlations

Calculates power or sample size (only one can be NULL at a time) to test difference between two independent (Pearson) correlations using Fisher's z transformation.

Formulas are validated using PASS and G*Power.

Usage

power.z.twocors(
  rho1,
  rho2,
  n2 = NULL,
  n.ratio = 1,
  power = NULL,
  alpha = 0.05,
  alternative = c("two.sided", "one.sided"),
  ceiling = TRUE,
  verbose = 1,
  utf = FALSE
)

Arguments

rho1: correlation in the first group.
rho2: correlation in the second group.
n2: sample size in the second group. Sample size in the first group can be calculated as n2*kappa. By default, n1 = n2 because n.ratio = 1.
n.ratio: n1 / n2 ratio.
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".
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 (Z-Test)
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 for the first and second groups, in the form of c(n1, n2).

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

Chow, S. C., Shao, J., Wang, H., & Lokhnygina, Y. (2018). Sample size calculations in clinical research (3rd ed.). Taylor & Francis / CRC.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.

Examples

# difference between r1 and r2 is different from zero
# it could be -0.10 as well as 0.10
power.z.twocors(rho1 = 0.20, rho2 = 0.30,
               power = 0.80, alpha = 0.05,
               alternative = "two.sided")
#> +--------------------------------------------------+
#> |             SAMPLE SIZE CALCULATION              |
#> +--------------------------------------------------+
#> 
#> Independent Correlations
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : rho1 - rho2  = 0
#>   H1 (Alternative) : rho1 - rho2 != 0
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Sample Size          = 1380 and 1380  <<
#>   Type 1 Error (alpha) = 0.050
#>   Type 2 Error (beta)  = 0.200
#>   Statistical Power    = 0.800
#> 

# difference between r1 and r2 is greater than zero
power.z.twocors(rho1 = 0.30, rho2 = 0.20,
               power = 0.80, alpha = 0.05,
               alternative = "one.sided")
#> +--------------------------------------------------+
#> |             SAMPLE SIZE CALCULATION              |
#> +--------------------------------------------------+
#> 
#> Independent Correlations
#> 
#> ----------------------------------------------------
#> Hypotheses
#> ----------------------------------------------------
#>   H0 (Null)        : rho1 - rho2 <= 0
#>   H1 (Alternative) : rho1 - rho2  > 0
#> 
#> ----------------------------------------------------
#> Results
#> ----------------------------------------------------
#>   Sample Size          = 1088 and 1088  <<
#>   Type 1 Error (alpha) = 0.050
#>   Type 2 Error (beta)  = 0.200
#>   Statistical Power    = 0.800
#>