A Two Factor ANOVA-like Test for Correlated Correlations: CORANOVA

Autor/inn/en	Bilker, Warren B.; Brensinger, Colleen; Gur, Ruben C.
Titel	A Two Factor ANOVA-like Test for Correlated Correlations: CORANOVA
Quelle	In: Multivariate Behavioral Research, 39 (2004) 4, S.565-594 (30 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0027-3171
Schlagwörter	Statistical Analysis; Interaction; Testing; Factor Analysis; Correlation; Gender Differences; Memory; Verbal Learning; Cognitive Processes; Brain + Suchen Sie Ihr Suchwort? Statistische Analyse; Interaktion; Testdurchführung; Testen; Faktorenanalyse; Korrelation; Geschlechterkonflikt; Gedächtnis; Verbales Lernen; Cognitive process; Kognitiver Prozess; Gehirn
Abstract	Testing homogeneity of correlations with Fisher's Z is inappropriate when correlations are themselves correlated. Suppose measurements of brain activation and performance are taken before and during a verbal memory task. Of interest are changes in activity gradients in specific regions, R1, R2, R3, and performance, V. The "correlated correlations" of interest ?V,R1, ?V,R2, and ?V,R3, have a single variable, V, in common. We wish to compare these correlations between males and females, across regions, and to assess an interaction of the correlation. Fisher's Z can compare pairs of correlations, and Olkin and Finn's (1990) method can test homogeneity of correlated correlations across a single within factor (based on asymptotic normality), but no current procedure can test a region by gender (within by between) interaction of correlations. We propose a nonparametric method for testing this interaction and both main effects. The procedure is analogous to two-way ANOVA, but hypotheses test homogeneity of correlations, not means. The null distributions are estimated with permutations, avoiding asymptotic distributional assumptions and enhancing applicability to smaller samples and non-normal data. Simulations demonstrated maintenance of correct level (power = alpha level under the null) for normal and non-normal data and small samples. The Olkin-Finn test had inflated level for non-normal data or small samples. The Fisher's Z had inflated level for non-normal data, but not for small samples. Our method had better efficiency across contrasts and data types and sizes. Applied to correlations between regional laterality of blood flow and verbal memory performance, the method showed sensitivity to a biologically meaningful sex by region interaction in these correlations. A SAS macro for CORANOVA is available. (Author).
Anmerkungen	Lawrence Erlbaum Associates, Inc., Journal Subscription Department, 10 Industrial Avenue, Mahwah, NJ 07430-2262. Tel: 800-926-6579 (Toll Free); e-mail: journals@erlbaum.com.
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10