pwrss (version 1.3.1)

power.z.twocors: 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 = NULL,
  rho2 = NULL,
  req.sign = "+",
  n2 = NULL,
  n.ratio = 1,
  power = NULL,
  alpha = 0.05,
  alternative = c("two.sided", "one.sided"),
  ceil.n = TRUE,
  verbose = 1,
  utf = FALSE
)
power.z.twocor(
  rho1 = NULL,
  rho2 = NULL,
  req.sign = "+",
  n2 = NULL,
  n.ratio = 1,
  power = NULL,
  alpha = 0.05,
  alternative = c("two.sided", "one.sided"),
  ceil.n = TRUE,
  verbose = 1,
  utf = FALSE
)

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).

Arguments

rho1

correlation in the first group.

rho2

correlation in the second group.

req.sign

whether estimated rho is smaller or larger than the other (when minimum detectable rho is of interest).

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".

ceil.n

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.

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")

# 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")