correlations.steiger: Power Analysis for Dependent Correlations (Steiger's Z-Test)

In pwrss: Statistical Power and Sample Size Calculation Tools

Power Analysis for Dependent Correlations (Steiger's Z-Test)

Description

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

Validated via PASS and G*Power.

Usage

power.z.twocors.steiger(rho12, rho13, rho23,
                        rho14 = NULL, rho24 = NULL, rho34 = NULL,
                        n = NULL, power = NULL, alpha = 0.05,
                        alternative = c("two.sided", "one.sided"),
                        pooled = TRUE, common.index = FALSE,
                        ceiling = TRUE, verbose = TRUE, pretty = FALSE)

Arguments

rho12	correlation between variable V1 and V2 (one common index and no common index). Check examples below.
rho13	correlation between variable V1 and V3 (one common index and no common index). Check examples below.
rho23	correlation between variable V2 and V3 (one common index and no common index). Check examples below.
rho14	correlation between variable V1 and V4 (no common index only). Check examples below.
rho24	correlation between variable V2 and V4 (no common index only). Check examples below.
rho34	correlation between variable V3 and V4 (no common index only). Check examples below.
n	integer; sample size.
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".
pooled	logical; whether standard error should be pooled. TRUE by default.
common.index	logical; whether calculations pertain to one common index. TRUE means calculations involve correlations with a common index (where both correlations share one variable). FALSE (default) means calculations pertain to correlations with no common index (where all relevant correlations must be explicitly specified). Check examples below.
ceiling	logical; if TRUE rounds up sample size.
verbose	logical; if FALSE no output is printed on the console.
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

Steiger, J. H. (1980). Tests for comparing elements of a correlation matrix. Psychological Bulletin, 87(2), 245-251. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1037/0033-2909.87.2.245")}

Examples

# example data for one common index
# compare cor(V1, V2) to cor(V1, V3)

# subject    V1       V2      V3
# <int>    <dbl>    <dbl>    <dbl>
#   1       1.2      2.3      0.8
#   2      -0.0      1.1      0.7
#   3       1.9     -0.4     -2.3
#   4       0.7      1.3      0.4
#   5       2.1     -0.1      0.8
#   ...     ...      ...      ...
#   1000   -0.5      2.7     -1.7

# V1: socio-economic status (common)
# V2: pretest
# V3: post-test

power.z.twocors.steiger(rho12 = 0.35, rho13 = 0.45, rho23 = 0.05,
                        n = 1000, power = NULL, alpha = 0.05,
                        alternative = "two.sided",
                        common.index = TRUE)


# example data for no common index
# compare cor(V1, V2) to cor(V3, V4)

# subject    V1       V2       V3       V4
# <int>    <dbl>    <dbl>    <dbl>    <dbl>
#   1       1.2      2.3      0.8      1.2
#   2      -0.0      1.1      0.7      0.9
#   3       1.9     -0.4     -2.3     -0.1
#   4       0.7      1.3      0.4     -0.3
#   5       2.1     -0.1      0.8      2.7
#   ...     ...      ...      ...      ...
#   1000   -0.5      2.7     -1.7      0.8

# V1: pretest reading
# V2: pretest math
# V3: post-test reading
# V4: post-test math

power.z.twocors.steiger(rho12 = 0.45, rho13 = 0.45, rho23 = 0.50,
                        rho14 = 0.50, rho24 = 0.80, rho34 = 0.55,
                        n = 1000, power = NULL, alpha = 0.05,
                        alternative = "two.sided",
                        common.index = FALSE)

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