correlations.two: Power Analysis for Independent Correlations

In pwrss: Statistical Power and Sample Size Calculation Tools

Power Analysis for Independent Correlations

Description

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 = TRUE, pretty = 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 kappa = 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; 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	logical; whether the output should be printed on the console. TRUE by default.
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 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. \Sexpr[results=rd]{tools:::Rd_expr_doi("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 = .20, rho2 = 0.30,
               alpha = 0.05, power = .80,
               alternative = "two.sided")

# difference between r1 and r2 is greater than zero
power.z.twocors(rho1 = .30, rho2 = 0.20,
               alpha = 0.05, power = .80,
               alternative = "one.sided")

pwrss documentation built on Sept. 16, 2025, 9:11 a.m.