test2r.steigerz1: Test the difference between two dependent correlations with...

In bcdudek/bcdstats: A collection of functions to support B. Dudek's APSY510/511 classes

Test the difference between two dependent correlations with the the Steiger's z1 method

Description

Differences in Pearson correlations are tested with the Steiger's Z1 method. The test is appropriate when the correlations are dependent. More specifically r(yx1) is tested versus r(yx2)in one sample of cases. The function requires the three Pearson product moment correlations between three variables called y, x1 and x2 in the notation here. Both one- and two-tailed p-values are returned.

Usage

test2r.steigerz1(ry.x1, ry.x2, rx1.x2, n)

Arguments

ry.x1	y is the variable common to the two correlations. It is labeled y since the most common usage of this test is when a dependent variable (y) is correlated with two different independent variables (x1, and x2). This argument ry.x1 is the first of the two correlations of y with the IV's.
ry.x2	This argument ry.x2 is the second of the two correlations of y with the IV's.
rx1.x2	The function and test require the Pearson correlation between the two X's as well.
n	Sample Size

Details

The Steiger1980 method uses the Fisher's Z transformation of the Pearson correlation coefficients and produces a standard normal deviate.

Value

z	The test statistic value, a 'z'.
pvalue	one- and two-tailed probabilities of the 'z' test statistic.

Related Functions

test2r.steigerz1 is a member of a set of functions that provide tests of differences between independent and dependent correlations. The functions were inspired by the paired.r function in the psych package and some of the code is modeled on code from that function. See:

• test2r.t2, Test two dependent correlations with the the T2 method: r(yx1) vs r(yx2)

• test2r.mengz1, Test the difference between two dependent correlations with the the Meng z1 method: r(yx1) vs r(yx2)in one sample of cases.

• test2r.steigerz1, the present function

• test2r.steigerz2, Test the difference between two dependent correlations with the the Steiger z2 method: r(jk) vs r(hm) in one sample of cases.

• test2r.ind, Test two r(xy) from Independent Groups

Author(s)

Bruce Dudek [e-mail]

References

Cheung, M. W. L., & Chan, W. (2004). Testing dependent correlation coefficients via structural equation modeling. Organizational Research Methods, 7(2), 206-223.
Dunn, O. J., & Clark, V. (1971). Comparison of tests of the equality of dependent correlation coefficients. Journal of the American Statistical Association, 66(336), 904-908.
Hays, W. L. (1994). Statistics (5th ed.). Fort Worth: Harcourt College Publishers.
Hendrickson, G. F., Stanley, J. C., & Hills, J. R. (1970). Olkin's new formula for significance of r13 vs. r23 compared with Hotelling's method. American Educational Research Journal, 7(2), 189-195.
Hittner, J. B., May, K., & Silver, N. C. (2003). A Monte Carlo evaluation of tests for comparing dependent correlations. The Journal of general psychology, 130(2), 149-168.
Howell, D. C. (2013). Statistical methods for psychology (8th ed.). Belmont, CA: Wadsworth Cengage Learning.
Meng, X. L., Rosenthal, R., & Rubin, D. B. (1992). Comparing correlated correlation coefficients. Psychological Bulletin, 111(1), 172-175.
Neill, J. J., & Dunn, O. J. (1975). Equality of dependent correlation coefficients. Biometrics, 31(2), 531-543.
Olkin, I., & Finn, J. D. (1990). Testing correlated correlations. Psychological Bulletin, 108(2), 330-333.
Silver, N. C., Hittner, J. B., & May, K. (2004). Testing dependent correlations with nonoverlapping variables: A Monte Carlo simulation. The Journal of experimental education, 73(1), 53-69.
Steiger, J. H. (1980). Tests for comparing elements of a correlation matrix. Psychological Bulletin, 87(2), 245-251.
Wilcox, R. R. (2012). Introduction to robust estimation and hypothesis testing

See Also

Analysts are also encouraged to explore robust methods for evaluation of correlation comparison hypotheses. For example, see work of R. Wilcox (texts above and also http://dornsife.usc.edu/labs/rwilcox/software/

Examples

test2r.steigerz1(.6,.31,.73,75)
test2r.steigerz1(.45,.03,.65,100)
test2r.steigerz1(.45,.03,.15,35)

bcdudek/bcdstats documentation built on Jan. 3, 2024, 10:09 p.m.