test2r.ind: Test Two Correlations from Independent Groups

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

Test Two Correlations from Independent Groups

Description

Differences in Pearson correlations of two variables are tested when they are measured in independent samples, for example r(xy) in group 1 vs r(xy) in group 2. The method employed is one that utilizes Fisher's Z transformation of the Pearson correlation coefficients. The test statistic is a standard normal deviate. The method can be found in standard textbook sources (e.g., Hays, 1993, Howell, 2013.) If the user wishes to perform tests of two r's from independent groups with standard methods that do no utilize Fisher's Z transform, they are encouraged to use linear regression models that employ an interaction term.

Usage

test2r.ind(r1, r2, n1, n2, twotailed = TRUE)

Arguments

r1	The Pearson correlation coefficient (rxy) in group 1.
r2	The Pearson correlation coefficient (rxy) in group 2.
n1	Sample size in group 1
n2	Sample size in group 1
twotailed	The test can be either two- or one-tailed by specifying twotailed=T or twotailed=F, respectively.

Related Functions

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

• 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, the present function

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.ind(.30,.35,n1=50,n2=60)
test2r.ind(.10,.45,n1=60,n2=80)
test2r.ind(.41,.59,n1=100,n2=105)
test2r.ind(.41,.59,n1=100,n2=105,twotailed=FALSE)

bcdudek/bcdstats documentation built on Aug. 15, 2024, 7:24 p.m.