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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“45) were higher than those between the other gradients and T1w/T2w, as assessed by Steiger’s test (29) (G1 left, r = 0.”
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“The fit of the two-factor model to the data can be compared to the fit of the statistical model using Williams' t statistic for comparing dependent correlations between non-nested models regressed on the same dependent variable (Steiger, 1980).”
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“Although the difference between the Universalism-social and Universalism-nature correlations with ethnocentrism was directionally as predicted, it was not significant ( Steiger's, 1980 , Z (198) = –.”
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“We followed the Steigers Z test [45] used by Philipp et al.”
Method
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“…of beauty and excellence. t = significance test for difference between correlation coefficients for the comparison of dependent correlations Steiger (1980) * p \ .05; ** p \ .01 Character strengths Private life Working life t Creativity 0.53 0.45 2.94** Curiosity 0.33 0.27 1.91 Judgment…”
BackgroundInfluential
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“As shown, the global score was a significantly better zero order predictor of life satisfaction than the specific score, t = 11.06, p < 0.001 (Cohen and Cohen, 1983; Steiger, 1980).”
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Method
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Method
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“were performed using Hotelling’s statistic [60], a test for the difference between two non-independent correlations [61].”
Method
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Method
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“Vallerand et al. (2003) proposed a conceptualization of passion that can shed light on the psychological mechanisms underlying activity involvement in general, and gambling involvement in particular.”
BackgroundMethod
Effects of increased processing demands on age differences in working memory.
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Age, anger regulation and well-being
Phillips, L. H., Henry, J. D., Hosie, J. A., & Milne, A. B. (2006) · Aging & Mental Health · doi:10.1080/13607860500310385 · Cited by 223
“A method developed by Steiger (1980) was adapted to test whether the partial correlations between age and the well being measures were significantly lower than the raw correlations between these variables; see Crawford, Deary, Starr and Whalley (2001) for details of this method.”
Method
Rostral locus coeruleus integrity is associated with better memory performance in older adults
Dahl, M. J., Mather, M., Düzel, S., Bodammer, N., Lindenberger, U., Kühn, S., & Werkle‐Bergner, M. (2019) · Nature Human Behaviour · doi:10.1038/s41562-019-0715-2 · Cited by 228
Performance of the ARX-derived Auditory Evoked Potential Index as an Indicator of Anesthetic Depth
Struys, M. M. R. F., Jensen, E. W., Smith, W., Smith, N. T., Rampil, I. J., Dumortier, F. J. E., Mestach, C., & Mortier, E. P. (2002) · Anesthesiology · doi:10.1097/00000542-200204000-00006 · Cited by 223
Age and sex differences in the cerebellum and the ventral pons: a prospective MR study of healthy adults.
Raz, N., Gunning‐Dixon, F. M., Head, D. M., Williamson, A. L., & Acker, J. D. (2001) · PubMed Central · Cited by 221
Empowering behaviour and leader fairness and integrity: Studying perceptions of ethical leader behaviour from a levels-of-analysis perspective
Hartog, D. N. D., & Hoogh, A. H. B. D. (2008) · European Journal of Work and Organizational Psychology · doi:10.1080/13594320802362688 · Cited by 221
“To examine the significance of these differences between correlations we performed t-tests (see Steiger, 1980).”
Method
The effects of usability and web design attributes on user preference for e-commerce web sites
Lee, S., & Koubek, R. J. (2010) · Computers in Industry · doi:10.1016/j.compind.2009.12.004 · Cited by 220
“(Note: Hostelling’s t test [65] is still used as the traditional and standard test for comparing two correlated correlation coefficients, but Steiger [66] argued that it potentially had some problems in psychological research.”
MethodInfluential
Use of concurrent pupil dilation assessment to inform interpretation and analysis of fMRI data
Siegle, G. J., Steinhauer, S. R., Stenger, V. A., Konecky, R. O., & Carter, C. S. (2003) · NeuroImage · doi:10.1016/s1053-8119(03)00298-2 · Cited by 228
Fixing the Problem With Empathy
Vachon, D. D., & Lynam, D. R. (2015) · Assessment · doi:10.1177/1073191114567941 · Cited by 253
Validation of the ostracism experience scale for adolescents
Gilman, R., Carter-Sowell, A., DeWall, C. N., Adams, R. E., & Carboni, I. (2013) · Psychological Assessment · doi:10.1037/a0030913 · Cited by 221
Effects of negative mood states on risk in everyday decision making
Hockey, G. R. J., Maule, A. J., Clough, P., & Bdzola, L. (2000) · Cognition & Emotion · doi:10.1080/02699930050156654 · Cited by 219
“However, the effect is present (and significant) for both types of scenario, and a test for differences between non-independent correlations (Steiger, 1980) shows that the r-values do not differ significantly, t(34) = 0.”
BackgroundInfluential
Predicting Long-term Adherence to Aerobic Exercise: A Comparison of Two Models
Garcia, A., & King, A. C. (1991) · Journal of Sport and Exercise Psychology · doi:10.1123/jsep.13.4.394 · Cited by 219
Assimilation of GRACE terrestrial water storage into a land surface model: Evaluation and potential value for drought monitoring in western and central Europe
Li, B., Rodell, M., Zaitchik, B. F., Reichle, R. H., Koster, R. D., & van Dam, T. M. (2012) · Journal of Hydrology · doi:10.1016/j.jhydrol.2012.04.035 · Cited by 218
“5 by DA all exceeded the 0.05 significance level based on the William–Hotelling t-test (Steiger, 1980; Van Sickle, 2005).”
MethodInfluential
Age-related differences in regional brain volumes: A comparison of optimized voxel-based morphometry to manual volumetry
Kennedy, K. M., Erickson, K. I., Rodrigue, K. M., Voss, M. W., Colcombe, S. J., Kramer, A. F., Acker, J. D., & Raz, N. (2008) · Neurobiology of Aging · doi:10.1016/j.neurobiolaging.2007.12.020 · Cited by 214
“We used Steiger's Z* statistic, which takes into account the dependence between the members of bivariate correlations (Steiger, 1980), to quantitatively compare the correlations of age and regional volumes obtained by the two methods for significant departure.”
The role of transformational leadership in enhancing team reflexivity
Schippers, M. C., Den Hartog, D. N., Koopman, P. L., & van Knippenberg, D. (2008) · Human Relations · doi:10.1177/0018726708096639 · Cited by 215
“Using Steiger’s test for comparing elements of a correlation matrix (Steiger, 1980), these differences in magnitude between the correlations proved not significant (z = .”
Method
Psychometric Properties of a Spanish Version of the UPPS–P Impulsive Behavior Scale: Reliability, Validity and Association With Trait and Cognitive Impulsivity
Verdejo‐García, A., Lozano, O. M., Moya, M., Alcázar‐Córcoles, M. Á., & Pérez-Garcı́a, M. (2009) · Journal of Personality Assessment · doi:10.1080/00223890903382369 · Cited by 236
What do you learn about someone over time? The relationship between length of acquaintance and consensus and self-other agreement in judgments of personality.
Biesanz, J. C., West, S. G., & Millevoi, A. (2007) · Journal of Personality and Social Psychology · doi:10.1037/0022-3514.92.1.119 · Cited by 217
The painful duality of envy: Evidence for an integrative theory and a meta-analysis on the relation of envy and schadenfreude.
Lange, J., Weidman, A. C., & Crusius, J. (2018) · Journal of Personality and Social Psychology · doi:10.1037/pspi0000118 · Cited by 219
“We calculated the covariances with a formula taken from Steiger (1980).”
Method
Messung des subjektiven sozialen Status in der Gesundheitsforschung mit einer deutschen Version der MacArthur Scale
Hoebel, J., Müters, S., Kuntz, B., Lange, C., & Lampert, T. (2015) · Bundesgesundheitsblatt - Gesundheitsforschung - Gesundheitsschutz · doi:10.1007/s00103-015-2166-x · Cited by 224
“3 Korrelationskoeffizienten mit 95 %-Konfidenzintervallen für den Zusammenhang zwischen subjektivem sozialen Status und konstruktverwandten/konstruktfremden Indikatoren Männer Frauen Gesamt SSS SSS SSS Konstruktverwandte Indikatoren Objektiver SES-Index 0,60*** (0,55–0,65) 0,52*** (0,47–0,57) 0,56*** (0,52–0,60) Bildu…”
BackgroundInfluential
Does attention-deficit/hyperactivity disorder have a dimensional latent structure? A taxometric analysis.
Marcus, D. K., & Barry, T. D. (2011) · Journal of Abnormal Psychology · doi:10.1037/a0021405 · Cited by 214
“Steiger's (1980) method for comparing two dependent correlations (i.”
Method
Choice history biases subsequent evidence accumulation
Urai, A. E., de Gee, J. W., Tsetsos, K., & Donner, T. H. (2019) · eLife · doi:10.7554/elife.46331 · Cited by 237
“41 coefficients that shared a common variable, and its associated p-value, was computed using Steiger’s test (Steiger, 1980).”
Method
SEX-RELATED DIFFERENCES IN JOB ATTITUDES AND DISPOSITIONAL VARIABLES: NOW YOU SEE THEM...
Lefkowitz, J. M. (1994) · Academy of Management Journal · doi:10.2307/256832 · Cited by 214
Parents' emotional availability and infant emotional competence: Predictors of parent-infant attachment and emerging self-regulation.
Volling, B. L., McElwain, N. L., Notaro, P. C., & Herrera, C. (2002) · Journal of Family Psychology · doi:10.1037//0893-3200.16.4.447 · Cited by 214
Achieving high efficiency and well-kept ductility in ternary all-polymer organic photovoltaic blends thanks to two well miscible donors
Ma, R., Zhou, K., Sun, Y., Liu, T., Kan, Y., Xiao, Y., Peña, T. A. D., Li, Y., Zou, X., Xing, Z., et al. (2022) · Matter · doi:10.1016/j.matt.2021.12.002 · Cited by 214
Reliability and validity of a short form of the Marijuana Craving Questionnaire
Heishman, S. J., Evans, R. J., Singleton, E. G., Levin, K. H., Copersino, M. L., & Gorelick, D. A. (2009) · Drug and Alcohol Dependence · doi:10.1016/j.drugalcdep.2008.12.010 · Cited by 212
“Goodness-of-fit for the unrotated factors was examined using the Steiger-Lind root mean square error of approximation statistic (RMSEA; Steiger, 1980) produced in CEFA.”
Method
Development of inhibition during childhood: Evidence for situational specificity and a two-factor model.
Asendorpf, J. B. (1990) · Developmental Psychology · doi:10.1037/0012-1649.26.5.721 · Cited by 274
“Following the suggestions of Steiger (1980), the Z* statistic was applied.”
Method
Exploring the Relation Between Bullying and Homophobic Verbal Content: The Homophobic Content Agent Target (HCAT) Scale
Poteat, V. P., & Espelage, D. L. (2005) · Violence and Victims · doi:10.1891/vivi.2005.20.5.513 · Cited by 212
Individual differences in anterior EEG asymmetry: methodological problems and solutions
Hagemann, D. (2004) · Biological Psychology · doi:10.1016/j.biopsycho.2004.03.006 · Cited by 217
The struggle with employee engagement: Measures and construct clarification using five samples.
Byrne, Z. S., Peters, J. M., & Weston, J. W. (2016) · Journal of Applied Psychology · doi:10.1037/apl0000124 · Cited by 258
Comparison of single-trait and multiple-trait genomic prediction models
Guo, G., Zhao, F., Wang, Y., Zhang, Y., Du, L., & Su, G. (2014) · BMC Genetics · doi:10.1186/1471-2156-15-30 · Cited by 211
“A Hotelling-Williams t test [32,33] was used to determine the difference between the validation correlations obtained from the single-trait and multi-trait models.”
Method
Central serotonin activity and aggression: inverse relationship with prolactin response to d-fenfluramine, but not CSF 5-HIAA concentration, in human subjects
Coccaro, E. F., Kavoussi, R. J., Cooper, T. B., & Hauger, R. L. (1997) · American Journal of Psychiatry · doi:10.1176/ajp.154.10.1430 · Cited by 208
“Differences between correlations were evaluated with the t statistic, where two correlations are not independent, as devised by Williams (36) and endorsed later by Steiger (37).”
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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