test2r.steigerz2: 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 z2 method

Description

Differences in Pearson correlations are tested with the Steiger's Z2 method. The test is appropriate when the correlations are dependent. More specifically r(jk) is tested versus r(hm)in one sample of cases. Thus there are four different variables involved in the analysis. The function requires the input of the six possible bivariate Pearson product-moment correlations among the four variables. One, and two-tailed tests are available.

Usage

test2r.steigerz2(rjk, rhm, rjh, rkh, rkm, rjm, n, twotailed = TRUE)

Arguments

rjk	The pearson product moment correlation that is to be tested against rhm .
rhm	The pearson product moment correlation that is to be tested against rjk.
rjh	One of the remaining four zero-order correlations among variables j,k,h, and m.
rkh	One of the remaining four zero-order correlations among variables j,k,h, and m.
rkm	One of the remaining four zero-order correlations among variables j,k,h, and m.
rjm	One of the remaining four zero-order correlations among variables j,k,h, and m.
n	Sample Size
twotailed	The test can be two-tailed (twotailed=TRUE) or one-tailed (twotailed=FALSE). The default is two-tailed.

Value

z	The test statistic value, a standard normal deviate (z'.)
pvalue	the one- or two-tailed probability of the 't'.

Related Functions

test2r.steigerz2 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, the present function

• 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.steigerz2(.6,.25,.4,.4,.4,.4,n=125)
test2r.steigerz2(.6,.25,.4,.4,.4,.4,n=125,twotailed=TRUE)
test2r.steigerz2(.6,.25,.4,.4,.4,.4,n=125,twotailed=FALSE)
test2r.steigerz2(.75,.50,.5,.4,.3,.76,n=100,twotailed=TRUE)
test2r.steigerz2(.75,.50,.5,.4,.3,.76,n=40,twotailed=TRUE)

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