pwrss.z.2corrs {pwrss}

Difference between Two Correlations (Independent Samples z Test)

Description

Calculates statistical power or minimum required 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 Monte Carlo simulation, G*Power, and tables in PASS documentation.

Usage

pwrss.z.2corrs(r1 = 0.50, r2 = 0.30,
               alpha = 0.05, kappa = 1,
               alternative = c("not equal","greater","less"),
               n2 = NULL, power = NULL, verbose = TRUE)

Arguments

r1

expected correlation in the first group

r2

expected 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

kappa

n1/n2 ratio

power

statistical power (1-\beta)

alpha

probability of type I error

alternative

direction or type of the hypothesis test: "not equal", "greater", or "less"

verbose

if FALSE no output is printed on the console

Value

parms

list of parameters used in calculation

test

type of the statistical test (z test)

ncp

non-centrality parameter

power

statistical power (1-\beta)

n

sample size for the first and second groups

References

Bulus, M., & Polat, C. (in press). pwrss R paketi ile istatistiksel guc analizi [Statistical power analysis with pwrss R package]. Ahi Evran Universitesi Kirsehir Egitim Fakultesi Dergisi. https://osf.io/ua5fc/download/

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
pwrss.z.2corrs(r1 = .20, r2 = 0.30,
               alpha = 0.05, power = .80,
               alternative = "not equal")

# difference between r1 and r2 is greater than zero
pwrss.z.2corrs(r1 = .30, r2 = 0.20,
               alpha = 0.05, power = .80,
               alternative = "greater")