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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“3 Model fit was assessed with the following indices: v2 divided by degrees of freedom (v2/df), the Non-Normed Fit Index (NNFI; Bentler & Bonett, 1980), the Comparative Fit Index (CFI; Bentler, 1990), and the Root Mean Square Error of Approximation (RMSEA; Steiger, 1980).”
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Method
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Method
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Background
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Method
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Method
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BackgroundMethod
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“This is because they did not report results from analyses that directly compared these magnitudes (e.g., differences between dependent correlations; see Steiger, 1980).”
Background
Cerebral Autoregulation of Blood Velocity and Volumetric Flow During Steady-State Changes in Arterial Pressure
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“In the ICA, we compared the linear regression slopes of ΔCVRi% and ΔCVR% (ie, velocity versus volumetric flow for assessment of changes in CVR) to ΔMAP% according to the Steiger method.(19) Slopes are expressed as mean±SE.”
Method
Distinct contributions of the fornix and inferior longitudinal fasciculus to episodic and semantic autobiographical memory
Hodgetts, C. J., Postans, M., Warne, N., Varnava, A., Lawrence, A. D., & Graham, K. S. (2017) · Cortex · doi:10.1016/j.cortex.2017.05.010 · Cited by 90
“To determine whether these correlations were significantly different, we conducted a directional Steiger Z-test for comparing dependent correlations (Steiger, 1980).”
Method
Visual form perception is fundamental for both reading comprehension and arithmetic computation
Cui, J., Zhang, Y., Wan, S., Chen, C., Zeng, J., & Zhou, X. (2019) · Cognition · doi:10.1016/j.cognition.2019.03.014 · Cited by 83
Does phonological recoding occur during silent reading, and is it necessary for orthographic learning?
de Jong, P. F., Bitter, D. J. L., van Setten, M., & Marinus, E. (2009) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2009.06.002 · Cited by 81
“A z score test for the difference between dependent correlations (see Steiger, 1980) revealed that the correlation of target decoding with novel pseudoword naming was lower than its correlation with target and homophone naming, z = 2.66, p < .01, and z = 2.77, p < .01, respectively.”
BackgroundInfluential
Neurobehavioral Traits as Transdiagnostic Predictors of Clinical Problems
Nelson, L. D., Strickland, C. M., Krueger, R. F., Arbisi, P. A., & Patrick, C. J. (2015) · Assessment · doi:10.1177/1073191115570110 · Cited by 83
“…divergence was especially evident in the symptom composites, where THT+ and INH− showed rs of .47 and .23, respectively, with fear symptoms as a whole (t[468] for comparison of rs = 4.36, p < .001; Steiger, 1980), and rs of .27 and .40 with distress symptoms as a whole (t[468] = −2.31, p = .021).”
BackgroundInfluential
A prospective analysis of life events, problem behaviours and depression in adults with intellectual disability
Esbensen, A. J., & Benson, B. A. (2006) · Journal of Intellectual Disability Research · doi:10.1111/j.1365-2788.2005.00816.x · Cited by 81
Does Weighting Capture What’s Important? Revisiting Subjective Importance Weighting with a Quality of Life Measure
Russell, L. B., Hubley, A. M., Palepu, A., & Zumbo, B. D. (2005) · Social Indicators Research · doi:10.1007/s11205-004-2528-5 · Cited by 81
“Steiger's (1980) Z tests of the difference between the weighted and unweighted IDUQOL correlations with each of the convergent and discriminant measures are also shown in Table II.”
Method
Advanced brand concept maps: A new approach for evaluating the favorability of brand association networks
Schnittka, O., Sattler, H., & Zenker, S. (2012) · International Journal of Research in Marketing · doi:10.1016/j.ijresmar.2012.04.002 · Cited by 81
Linking Peer Victimization to the Development of Depressive Self-Schemas in Children and Adolescents
Cole, D. A., Dukewich, T. L., Roeder, K., Sinclair-McBride, K., McMillan, J., Will, E., Bilsky, S. A., Martin, N. C., & Felton, J. W. (2013) · Research on Child and Adolescent Psychopathology · doi:10.1007/s10802-013-9769-1 · Cited by 83
“We tested these differences using Steiger’s Z (1980) for dependent correlations.”
Friendship, Marriage and Self-Esteem
Voss, K., Markiewicz, D., & Doyle, A. B. (1999) · Journal of Social and Personal Relationships · doi:10.1177/0265407599161006 · Cited by 81
Job knowledge, ratee familiarity, conceptual similarity and halo error: An exploration.
Kozlowski, S. W. J., Kirsch, M. P., & Chao, G. T. (1986) · Journal of Applied Psychology · doi:10.1037//0021-9010.71.1.45 · Cited by 81
Interpreting correlations between children's perceived control and cognitive performance: Control, agency, or means€nds beliefs?
Chapman, M., Skinner, E. A., & Baltes, P. B. (1990) · Developmental Psychology · doi:10.1037/0012-1649.26.2.246 · Cited by 81
“ing Steiger's X2 statistic. As described by Steiger (1980), X2 is a”
BackgroundMethod
Where the wind blows: Assessing the effect of fixed and premium based feed-in tariffs on the spatial diversification of wind turbines
Schmidt, J., Lehecka, G. V., Gass, V., & Schmid, E. (2013) · Energy Economics · doi:10.1016/j.eneco.2013.07.004 · Cited by 80
The true self online: Personality correlates of preference for self-expression online, and observer ratings of personality online and offline
Marriott, T. C., & Buchanan, T. (2014) · Computers in Human Behavior · doi:10.1016/j.chb.2013.11.014 · Cited by 80
A happier and less sinister past, a more hedonistic and less fatalistic present and a more structured future: time perspective and well-being
Sailer, U., Rosenberg, P., Nima, A. A., Gamble, A., Gärling, T., Archer, T., & Garcia, D. (2014) · PeerJ · doi:10.7717/peerj.303 · Cited by 80
“…good at managing the responsibilities of my daily life”), autonomy (e.g., “I have confidence in my own opinions, even if they are contrary to the general consensus”), and positive relations with others (e.g., “People would describe me as a giving person, willing to share my time with others”).”
Background
Factors Predicting the Rate of Functional Progression in Early and Suspected Glaucoma
Gardiner, S. K., Johnson, C. A., & Demirel, S. (2012) · Investigative Ophthalmology & Visual Science · doi:10.1167/iovs.11-9065 · Cited by 80
Individual differences in interpersonal touch: On the development, validation, and use of the “comfort with interpersonal touch” (CIT) scale
Webb, A., & Peck, J. (2014) · Journal of Consumer Psychology · doi:10.1016/j.jcps.2014.07.002 · Cited by 80
“To test for significant difference between the strength of the association across our two subdimensions, Steiger's z was calculated (Steiger, 1980).”
Method
LUMP‐SUM BONUS SATISFACTION: TESTING THE CONSTRUCT VALIDITY OF A NEW PAY SATISFACTION DIMENSION
Sturman, M. C., & Short, J. C. (2000) · Personnel Psychology · doi:10.1111/j.1744-6570.2000.tb00218.x · Cited by 79
Refinement of anxiety sensitivity measurement: the short scale anxiety sensitivity index (SSASI)
Zvolensky, M. J., Garey, L., Fergus, T. A., Gallagher, M. W., Viana, A. G., Shepherd, J. M., Mayorga, N. A., Kelley, L. P., Griggs, J. O., & Schmidt, N. B. (2018) · Psychiatry Research · doi:10.1016/j.psychres.2018.08.115 · Cited by 74
“Subsequently, the strength of the associations were compared using the Steiger method (Steiger, 1980; Zou, 2007); this approach appropriately considers the non-independent nature of the compared correlations.”
Method
Chronic pain acceptance and affective well-being: a coping perspective
Kranz, D., Bollinger, A., & Nilges, P. (2010) · European Journal of Pain · doi:10.1016/j.ejpain.2010.03.010 · Cited by 79
“This asymmetry proved significant when comparing the respective correlation coefficients (rs), that is, |.44| and |.27| for pain willingness, z = 1.97, p .05, and |.51| and |.35| for activity engagement, z = 1.86, p .05 (for procedural details, see Steiger, 1980).”
BackgroundInfluential
Early starting, aggressive, and/or callous–unemotional? Examining the overlap and predictive utility of antisocial behavior subtypes.
Hyde, L. W., Burt, S. A., Shaw, D. S., Donnellan, M. B., & Forbes, E. E. (2015) · Journal of Abnormal Psychology · doi:10.1037/abn0000029 · Cited by 84
Proenkephalin Compared to Conventional Methods to Assess Kidney Function in Critically Ill Sepsis Patients
Beunders, R., van Groenendael, R., Leijte, G. P., Kox, M., & Pickkers, P. (2020) · Shock · doi:10.1097/shk.0000000000001510 · Cited by 81
“Correlation coefficients were reciprocally tested using the method described by Steiger (26, 27).”
Method
Physical topography is associated with human personality
Götz, F. M., Stieger, S., Gosling, S. D., Potter, J., & Rentfrow, P. J. (2020) · Nature Human Behaviour · doi:10.1038/s41562-020-0930-x · Cited by 90
Testing Dependent Correlations With Nonoverlapping Variables: A Monte Carlo Simulation
Silver, N. C., Hittner, J. B., & May, K. O. (2004) · The Journal of Experimental Education · doi:10.3200/jexe.71.1.53-70 · Cited by 79
Forecasting Tornado Pathlengths Using a Three-Dimensional Object Identification Algorithm Applied to Convection-Allowing Forecasts
Clark, A., Kain, J., Marsh, P. T., Correia, J., Xue, M., & Kong, F. (2012) · Weather and Forecasting · doi:10.1175/waf-d-11-00147.1 · Cited by 79
“This function follows procedures recommended by Steiger (1980) for comparing elements of a correlation matrix.”
Method
Self-Assessment of Linguistic Skills by Bilingual Hispanics
Delgado, P., Guerrero, G., Goggin, J. P., & Ellis, B. B. (1999) · Hispanic Journal of Behavioral Sciences · doi:10.1177/0739986399211003 · Cited by 82
“…accuracy of selfassessments, correlations based on the initial self-ratings (Table 2) were compared with those based on posttest self-ratings (Table 3) using at test that is appropriate for testing the difference between two nonindependent correlation coefficients (cf. Howell, 1997; Steiger, 1980).”
Method
Differential effects of age and history of hypertension on regional brain volumes and iron
Rodrigue, K. M., Haacke, E. M., & Raz, N. (2010) · NeuroImage · doi:10.1016/j.neuroimage.2010.09.068 · Cited by 80
The General Functioning Scale of the Family Assessment Device: Does it work with Chinese adolescents?
Shek, D. T. L. (2001) · Journal of Clinical Psychology · doi:10.1002/jclp.1113 · Cited by 79
Does high quality leader–member exchange accentuate the effects of organizational justice?
Piccolo, R. F., Bardes, M., Mayer, D. M., & Judge, T. A. (2008) · European Journal of Work and Organizational Psychology · doi:10.1080/13594320701743517 · Cited by 85
“The authors also noted, ‘‘trust in authority acts as an important moderator of procedural fairness, [a] finding [that] corroborates the argument of Van den Bos (2001)’’ (p.”
MethodResult
Using an Approximate Chi‐Square Statistic to Test the Number of Dimensions Underlying the Responses to a Set of Items
Gessaroli, M. E., & Champlain, A. F. D. (1996) · Journal of Educational Measurement · doi:10.1111/j.1745-3984.1996.tb00487.x · Cited by 79
Community viral load, antiretroviral therapy coverage, and HIV incidence in India: a cross-sectional, comparative study
Solomon, S. S., Mehta, S. H., McFall, A. M., Srikrishnan, A. K., Saravanan, S., Laeyendecker, O. B., Balakrishnan, P., Celentano, D. D., Solomon, S., & Lucas, G. M. (2016) · The Lancet HIV · doi:10.1016/s2352-3018(16)00019-9 · Cited by 79
Assessing daily management of childhood diabetes using 24-hour recall interviews: Reliability and stability.
Freund, A., Johnson, S. B., Silverstein, J. H., & Thomas, J. A. (1991) · Health Psychology · doi:10.1037//0278-6133.10.3.200 · Cited by 79

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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