Cited by 4,621Psychometric Methodologies and TestingMultidisciplinary Science and Engineering ResearchStatistical Methods and Applications

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Tests for comparing elements of a correlation matrix

Steiger, James H.·1980·Psychological Bulletin

DOI 10.1037/0033-2909.87.2.245

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Abstract

In a variety of situations in psychological research, it is desirable to be able to make statistical comparisons between correlation coefficients measured on the same individuals. For example, an experimenter may wish to assess whether two predictors correlate equally with a criterion variable. In another situation, the experimenter may wish to test the hypothesis that an entire matrix of correlations has remained stable over time. The present article reviews the literature on such tests, points out some statistics that should be avoided, and presents a variety of techniques that can be used safely with medium to large samples. Several illustrative numerical examples are provided.

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“Because only 14 were recruited successfully, these data are not reported separately in the text*see supplementary materials for a report.”
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“We tested whether cognitive JI and affective JI correlate equally with other variables (Steiger, 1980) and found that they correlated differently with the two organizational factors (involvement z= 2.03, p< .05; communication z = 1.69, p< .10), but their correlations with the two outcomes…”
BackgroundResultInfluential
Development and validation of an instrument to measure factors related to colorectal cancer screening adherence.
Vernon, S. W., Myers, R. E., & Tilley, B. C. (1997) · PubMed · Cited by 174
A longitudinal analysis of English language learners’ word decoding and reading comprehension
Nakamoto, J., Lindsey, K. A., & Manis, F. R. (2006) · Reading and Writing · doi:10.1007/s11145-006-9045-7 · Cited by 191
“Not surprisingly, the decoding cluster and the reading comprehension scores were more highly correlated (Z2* = 3.23, P Steiger, 1980, for the Z2* test of dependent correlations) in first grade (r = 0.75, P < 0.001, n = 218) compared to their correlation in sixth grade (r = 0.61, P < 0.001, n = 218) for children for wh…”
Influential
Challenges in measuring individual differences in functional connectivity using fMRI: The case of healthy aging
Geerligs, L., Tsvetanov, K. A., Cam‐CAN, & Henson, R. N. (2017) · Human Brain Mapping · doi:10.1002/hbm.23653 · Cited by 176
“However, when we used a parametric test to compare the strength of these correlations [Steiger, 1980], we found that the difference between these two correlation coefficients was not significant (z 5 1.”
MethodInfluential
Satellite-based reflectances capture large fraction of variability in global gross primary production (GPP) at weekly time scales
Joiner, J., & Yoshida, Y. (2020) · Agricultural and Forest Meteorology · doi:10.1016/j.agrformet.2020.108092 · Cited by 174
Validation of the Dyadic Coping Inventory with Chinese couples: Factorial structure, measurement invariance, and construct validity.
Xu, F., Hilpert, P., Randall, A. K., Li, Q., & Bodenmann, G. (2016) · Psychological Assessment · doi:10.1037/pas0000329 · Cited by 177
The Hearing-Aid Speech Perception Index (HASPI)
Kates, J. M., & Arehart, K. H. (2014) · Speech Communication · doi:10.1016/j.specom.2014.06.002 · Cited by 172
Comparison of four scoring methods for the reading span test
Friedman, N. P., & Miyake, A. (2005) · Behavior Research Methods · doi:10.3758/bf03192728 · Cited by 172
“To examine whether the correlations using the different scoring methods were significantly different from each other, we computed t values for each comparison, using the formula for comparing nonindependent correlations (Cohen & Cohen, 1983; Steiger, 1980).”
Method
Response inhibition and response re-engagement in attention-deficit/hyperactivity disorder, disruptive, anxious and normal children
Oosterlaan, J., & Sergeant, J. A. (1998) · Behavioural Brain Research · doi:10.1016/s0166-4328(97)00167-8 · Cited by 176
Protestant Ethic, conservatism, and values.
Feather, N. T. (1984) · Journal of Personality and Social Psychology · doi:10.1037//0022-3514.46.5.1132 · Cited by 171
Global patterns of macroinvertebrate production in marine benthic habitats
Cusson, M., & Bourget, E. (2005) · Marine Ecology Progress Series · doi:10.3354/meps297001 · Cited by 170
Effects of a low dose of alcohol on cognitive biases and craving in heavy drinkers
Schoenmakers, T. M., Wiers, R. W. H. J., & Field, M. (2007) · Psychopharmacology · doi:10.1007/s00213-007-1023-5 · Cited by 170
“Using Steiger’s test for calculating the differences between correlations (Steiger 1980), we found that the Pearson correlation was significantly higher in the alcohol session than in the placebo session, z=1.70, p= 0.04, indicating a significant increase in the correlation between these cognitive…”
MethodInfluential
Types of Aggression, Responsiveness to Provocation, and Callous-unemotional Traits in Detained Adolescents
Centifanti, L. C. M., Frick, P. J., Kimonis, E. R., & Aucoin, K. J. (2007) · Research on Child and Adolescent Psychopathology · doi:10.1007/s10802-007-9137-0 · Cited by 184
Passionate and Companionate Love in Courting and Young Married Couples
Sprecher, S., & Regan, P. C. (1998) · Sociological Inquiry · doi:10.1111/j.1475-682x.1998.tb00459.x · Cited by 170
Computer anxiety: relationship with computer experience and prevalence
Bozionelos, N. (2001) · Computers in Human Behavior · doi:10.1016/s0747-5632(00)00039-x · Cited by 170
Response burden, reliability, and validity of the CAGE, Short MAST, and AUDIT alcohol screening measures
Hays, R. D., Merz, J. F., & Nicholas, R. (1995) · Behavior Research Methods, Instruments, & Computers · doi:10.3758/bf03204745 · Cited by 169
Negative Urgency, Distress Tolerance, and substance abuse among college students
Kaiser, A. J., Milich, R. S., Lynam, D. R., & Charnigo, R. J. (2012) · Addictive Behaviors · doi:10.1016/j.addbeh.2012.04.017 · Cited by 190
“Differences in correlations were tested for statistical significance using a Z-test (Steiger, 1980).”
Adaptive History Biases Result from Confidence-Weighted Accumulation of past Choices
Braun, A., Urai, A. E., & Donner, T. H. (2018) · Journal of Neuroscience · doi:10.1523/jneurosci.2189-17.2017 · Cited by 166
“We used the parametric 2-tailed Steiger’s test (Steiger, 1980) for comparing across-subjects correlations between individual adaptivitiy indices (correlation coefficients) and their proportion of correct choices with the corresponding correlations between individual perceptual sensitivity and the…”
Method
Motivation and studying in high school science
Nolen, S. B., & Haladyna, T. M. (1990) · Journal of Research in Science Teaching · doi:10.1002/tea.3660270204 · Cited by 169
Anxiety sensitivity: An examination of theoretical and methodological issues
Lilienfeld, S. O., Turner, S. M., & Jacob, R. G. (1993) · Advances in Behaviour Research and Therapy · doi:10.1016/0146-6402(93)90019-x · Cited by 174
“…determine whether the AS1 predicted posttest anxiety significantly better than did the STAI, because tests for the significance of the difference between dependent correlations (Cohen & Cohen, 1983, pp. 54-57; Steiger, 1980) were not performed, and several relevant correlations were not reported.”
Background
Combining information from multiple sources for the diagnosis of autism spectrum disorders for toddlers and young preschoolers from 12 to 47 months of age
Kim, S. H., & Lord, C. (2011) · Journal of Child Psychology and Psychiatry · doi:10.1111/j.1469-7610.2011.02458.x · Cited by 167
“Correlation coefficients were compared usingFisher’s Z transformations (Steiger, 1980).”
Method
Perceived Health Contributes to the Attractiveness of Facial Symmetry, Averageness, and Sexual Dimorphism
Rhodes, G., Yoshikawa, S., Palermo, R., Simmons, L. W., Peters, M., Lee, K., Halberstadt, J. B., & Crawford, J. R. (2007) · Perception · doi:10.1068/p5712 · Cited by 167
Volume of white matter hyperintensities in healthy adults: Contribution of age, vascular risk factors, and inflammation-related genetic variants
Raz, N., Yang, Y., Dahle, C. L., & Land, S. J. (2011) · Biochimica et Biophysica Acta (BBA) - Molecular Basis of Disease · doi:10.1016/j.bbadis.2011.08.007 · Cited by 169
“The GLM analyses were followed by univariate analyses of simple effects, and testing the differences among the levels of the categorical variables with Fisher’s Least Significant Difference (LSD) test, or correlation coefficients with Steiger’s Z* statistic that takes into account dependence between the compared corre…”
Method
Human mobility networks reveal increased segregation in large cities
Nilforoshan, H., Looi, W., Pierson, E., Villanueva, B., Fishman, N., Chen, Y., Sholar, J., Redbird, B., Grusky, D. B., & Leskovec, J. (2023) · Nature · doi:10.1038/s41586-023-06757-3 · Cited by 190
“66).”
It Ain’t What You Do, It’s the Way that You Do It! Teaching Style Affects Children’s Motivation in Track and Field Lessons
Γούδας, Μ., Biddle, S., Fox, K. R., & Underwood, M. (1995) · The Sport Psychologist · doi:10.1123/tsp.9.3.254 · Cited by 166
“The Williams F test (Steiger, 1980) for comparing correlations with a common index showed that the lesson-specific measures of task involvement and work avoidance correlated significantly higher with intrinsic motivation and intention than the general task and work avoidance orientation scores, both for direct and dif…”
Method
Convergent and Discriminant Validity of Psychopathy Factors Assessed Via Self-Report
Benning, S. D., Patrick, C. J., Salekin, R. T., & Leistico, A.-M. R. (2005) · Assessment · doi:10.1177/1073191105277110 · Cited by 165
Where is the Support in Perceived Support? The Role of Generic Relationship Satisfaction and Enacted Support in Perceived Support's Relation to Low Distress
Kaul, M., & Lakey, B. (2003) · Journal of Social and Clinical Psychology · doi:10.1521/jscp.22.1.59.22761 · Cited by 165
The Facial Expression Coding System (FACES): Development, validation, and utility.
Kring, A. M., & Sloan, D. M. (2007) · Psychological Assessment · doi:10.1037/1040-3590.19.2.210 · Cited by 173
“On the basis of the Dunn-Clark z test for the equality of two dependent correlations (Dunn & Clark, 1969; for a review, see Steiger, 1980), correlations between EMFACS enjoyment smile ratings and FACES positive ratings were significantly higher than the correlations between EMFACS social smile…”
Method
Social and Cognitive Factors Affecting the Own-Race Bias in Whites
Slone, A. E., Brigham, J. C., & Meissner, C. A. (2000) · Basic and Applied Social Psychology · doi:10.1207/15324830051036162 · Cited by 165
Understanding extraverts' enjoyment of social situations: The importance of pleasantness.
Lucas, R. E., & Diener, E. (2001) · Journal of Personality and Social Psychology · doi:10.1037/0022-3514.81.2.343 · Cited by 273
Variations in patterns of attraction of same- and other-sex peers during early adolescence.
Bukowski, W. M., Sippola, L. K., & Newcomb, A. F. (2000) · Developmental Psychology · doi:10.1037/0012-1649.36.2.147 · Cited by 266
Self-Efficacy and Political Skill as Comparative Predictors of Task and Contextual Performance: A Two-Study Constructive Replication
Jawahar, I. M. “., Meurs, J. A., Ferris, G. R., & Hochwarter, W. A. (2008) · Human Performance · doi:10.1080/08959280801917685 · Cited by 175
“57; Meng, Rosenthal, & Rubin, 1992 ; Steiger, 1980 , p.”
The role of peer and adult models for drug taking at different stages in adolescence
Huba, G. J., & Bentler, P. M. (1980) · Journal of Youth and Adolescence · doi:10.1007/bf02087681 · Cited by 164
“Hypothesis 5--that there would not be a greater relationship between self-use and the number of peer models than between self-use and the number of adult models at middle adolescence than in early adolescencewas tested using the Dunn-Clark z statistic for assessing the difference between correlated correlations ( Stei…”
Method

Authors: Steiger, J. H.
Affiliations: University of British Columbia (CA)
Corresponding author: Steiger, James H.
Venue: Psychological Bulletin
Publisher: American Psychological Association (APA)
Published: 1980-03
Volume: 87
Issue: 2
Pages: 245-251
ISSN: 0033-2909 (ISSN-L)
1939-1455
DOI: 10.1037/0033-2909.87.2.245
OpenAlex: W2097137621
Cited by: 4,621
References: 17
Citations by year: 2026: 227 · 2025: 157 · 2024: 152 · 2023: 168 · 2022: 212 · 2021: 214 · 2020: 242 · 2019: 259 · 2018: 302 · 2017: 265 · 2016: 261 · 2015: 260 · 2014: 189 · 2013: 197 · 2012: 148
FWCI: 16.67
Type: journal article
Language: en
Open access: closed
Locations: Psychological Bulletin (publishedVersion)
Topics: Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Multidisciplinary Science and Engineering Research
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
Keywords: correlation coefficient, hypothesis testing

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Tests for comparing elements of a correlation matrix

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