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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“Williams test 3 (Williams, 1959) evaluates the signiﬁcance of a difference in dependent correlations (Steiger, 1980).”
Background
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Littman‐Ovadia, H., Lavy, S., & Boiman-Meshita, M. (2016) · Journal of Happiness Studies · doi:10.1007/s10902-016-9739-8 · Cited by 157
Aroused with heart: Modulation of heartbeat evoked potential by arousal induction and its oscillatory correlates
Luft, C. D. B., & Bhattacharya, J. (2015) · Scientific Reports · doi:10.1038/srep15717 · Cited by 143
“…alpha power in HA and LA conditions, we used the Williams’ version of the Hotelling’s T test for comparing dependant correlations in small samples 28 and observed a significant difference between the two correlations ( William’s t (13) = − 2.19, p .05), indicating a higher correlation between…”
Influential
Narcissism and self-presentation: Profiling grandiose and vulnerable Narcissists' self-presentation tactic use
Hart, W., Adams, J., Burton, K. A., & Tortoriello, G. K. (2017) · Personality and Individual Differences · doi:10.1016/j.paid.2016.06.062 · Cited by 143
Emotion Regulation and the Quality of Social Interaction: Does the Ability to Evaluate Emotional Situations and Identify Effective Responses Matter?
Lopes, P. N., Nezlek, J. B., Extremera, N., Hertel, J., Fernández‐Berrocal, P., Schütz, A., & Salovey, P. (2010) · Journal of Personality · doi:10.1111/j.1467-6494.2010.00689.x · Cited by 151
Gender Differences in Connectome-based Predictions of Individualized Intelligence Quotient and Sub-domain Scores
Jiang, R., Calhoun, V. D., Fan, L., Zuo, N., Jung, R., Qi, S., Lin, D., Li, J., Zhuo, C., Song, M., et al. (2020) · Cerebral Cortex · doi:10.1093/cercor/bhz134 · Cited by 126
Assessment of implicit personality self‐concept using the implicit association test (IAT): Concurrent assessment of anxiousness and angriness
Schnabel, K., Banse, R., & Asendorpf, J. B. (2006) · British Journal of Social Psychology · doi:10.1348/014466605x49159 · Cited by 142
The relation of peer social support and psychological symptomatology during the transition to junior high school: A two‐year longitudinal analysis
Hirsch, B. J., & DuBois, D. L. (1992) · American Journal of Community Psychology · doi:10.1007/bf00937913 · Cited by 142
“3Using a procedure described by Steiger (1980) for statistical comparison of correlations obtained from the same sample, it was determined that the pattern of across-time symptom-support correlations was significantly different (p < .05) from the pattern of across-time support-symptoms correlations.”
Method
Suppressor Variables in Multiple Regression/Correlation
Smith, R. L., Ager, J. W., & Williams, D. L. (1992) · Educational and Psychological Measurement · doi:10.1177/001316449205200102 · Cited by 142
Evaluating convergent and discriminant validity of temperament questionnaires for preschoolers, toddlers, and infants.
Goldsmith, H. H., Rieser-Danner, L. A., & Briggs, S. R. (1991) · Developmental Psychology · doi:10.1037/0012-1649.27.4.566 · Cited by 142
Applicability of traditional and revised models of psychopathy to the Psychopathy Checklist: Screening Version.
Skeem, J. L., Mulvey, E. P., & Grisso, T. (2003) · Psychological Assessment · doi:10.1037/1040-3590.15.1.41 · Cited by 142
“The former association ( .34) was significantly stronger than the latter ( .24), T1(807) 2.34, p .05 (see Steiger, 1980, for tests of differences between nonindependent correlation coefficients).”
BackgroundResultInfluential
Psychometric properties of the Strength and Difficulties Questionnaire from five European countries
Essau, C. A., Olaya, B., Anastassiou‐Hadjicharalambous, X., Pauli, G., Gilvarry, C. M., Bray, D. E., O’Callaghan, J., & Ollendick, T. H. (2012) · International Journal of Methods in Psychiatric Research · doi:10.1002/mpr.1364 · Cited by 157
“…(i.e. convergent validity) than correlations between SDQ conduct and hyperactivity-inattention subscales (i.e. divergent validity), the Steiger’s Z (Steiger, 1980) ree-factor model in the five countries with and without T ab le 2 C or re la tio ns be tw ee n S D Q an d S C A S in th e fi ve co…”
Background
Individual differences in reward prediction error: contrasting relations between feedback-related negativity and trait measures of reward sensitivity, impulsivity and extraversion
Cooper, A. J., Duke, Ã., Pickering, A. D., & Smillie, L. D. (2014) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2014.00248 · Cited by 149
Combining Reaction Time and Accuracy
Draheim, C., Hicks, K. L., & Engle, R. W. (2016) · Perspectives on Psychological Science · doi:10.1177/1745691615596990 · Cited by 155
“In the test for differences between dependent correlations (Steiger, 1980), use of the binning procedure resulted in four out of the six correlations being significantly different from correlations found via use of latency switch costs.”
Method
The effect of acquaintanceship on the validity of personality impressions: A longitudinal study.
Paulhus, D. L., & Bruce, M. N. (1992) · Journal of Personality and Social Psychology · doi:10.1037/0022-3514.63.5.816 · Cited by 141
Verbal and visual-spatial working memory and mathematical ability in different domains throughout primary school
van de Weijer‐Bergsma, E., Kroesbergen, E. H., & Luit, J. E. H. V. (2014) · Memory & Cognition · doi:10.3758/s13421-014-0480-4 · Cited by 141
“To test whether differences in independent standardized estimates and covariances between the lowest and highest grades are statistically significant, we used the Fisher r -to- z transformation (Lowry, 2013; Steiger, 1980).”
Flat meridional temperature gradient in the early Eocene in the subsurface rather than surface ocean
Ho, S. L., & Laepple, T. (2016) · Nature Geoscience · doi:10.1038/ngeo2763 · Cited by 140
The role of attention control in complex real-world tasks
Draheim, C., Pak, R., Draheim, A. A., & Engle, R. W. (2022) · Psychonomic Bulletin & Review · doi:10.3758/s13423-021-02052-2 · Cited by 172
Do Mexican-American Mothers’ Food-Related Parenting Practices Influence Their Children’s Weight and Dietary Intake?
Matheson, D., Robinson, T. N., Varady, A. N., & Killen, J. D. (2006) · Journal of the American Dietetic Association · doi:10.1016/j.jada.2006.08.004 · Cited by 140
What Does the Implicit Association Test Measure? A Test of the Convergent and Discriminant Validity of Prejudice-Related IATs
Gawronski, B. (2002) · Experimental Psychology (formerly Zeitschrift für Experimentelle Psychologie) · doi:10.1026//1618-3169.49.3.171 · Cited by 140
Validation of the WHI Brief Physical Activity Questionnaire among Women Diagnosed with Breast Cancer
Johnson-Kozlow, M. F., Rock, C. L., Gilpin, E. A., HOLLENBACH, K. A., & Pierce, J. P. (2007) · American Journal of Health Behavior · doi:10.5993/ajhb.31.2.8 · Cited by 138
The Role of Simple Emotion Recognition Skills among School Aged Boys at Risk of ADHD
Kats-Gold, I., Besser, A., & Priel, B. (2007) · Journal of Abnormal Child Psychology · doi:10.1007/s10802-006-9096-x · Cited by 139
“Model fit was assessed using the following indices: χ2 divided by degrees of freedom (χ2/df), the NonNormed Fit Index (NNFI, Bentler & Bonett, 1980), the Comparative Fit Index (CFI, Bentler, 1990), and the Root Mean Square of Approximation (RMSEA, Steiger, 1980).”
Charismatic leadership, environmental dynamism, and performance
Hoogh, A. H. B. D., Hartog, D. N. D., Koopman, P. L., Thierry, H., van den Berg, P., der Weide, J. G. V., & Wilderom, C. P. M. (2004) · European Journal of Work and Organizational Psychology · doi:10.1080/13594320444000164 · Cited by 139
“To examine the significance of this difference between correlations, we performed a t-test (see Steiger, 1980).”
Method
Substance Use, Health, and Mental Health: Problems and Service Utilization Among Incarcerated Women
Staton, M., Leukefeld, C. G., & Webster, J. M. (2003) · International Journal of Offender Therapy and Comparative Criminology · doi:10.1177/0306624x03251120 · Cited by 139
“…for spurious relations between variables given the large number of correlations coupled with the relatively small sample size, a procedure recommended by Steiger (1980) was used to verify that the sample correlation matrices significantly differed from an identity (zero) correlation matrix.”
Method
Comparison of the Associations of Apolipoprotein B and Non-High-Density Lipoprotein Cholesterol With Other Cardiovascular Risk Factors in Patients With the Metabolic Syndrome in the Insulin Resistance Atherosclerosis Study
Sattar, N. A., Williams, K., Sniderman, A. D., D’Agostino, R., & Haffner, S. M. (2004) · Circulation · doi:10.1161/01.cir.0000145660.60487.94 · Cited by 139
Children's Reports of Their Life Satisfaction
Gilman, R., & Huebner, E. S. (1997) · School Psychology International · doi:10.1177/0143034397183004 · Cited by 139
Patterns of parent-reported homework problems among ADHD-referred and non-referred children.
Power, T. J., Werba, B. E., Watkins, M. W., Angelucci, J. G., & Eiraldi, R. B. (2006) · School Psychology Quarterly · doi:10.1521/scpq.2006.21.1.13 · Cited by 135
“To examine whether a differential relationship existed between each BASC subscale and the two HPC factors, a Z statistic was used to evaluate the difference between two correlations derived from a single set of participants (Steiger, 1980).”
Promoting Us or Preventing Them: Regulatory Focus and Manifestations of Intergroup Bias
Shah, J. Y., Brazy, P. C., & Higgins, E. T. (2004) · Personality and Social Psychology Bulletin · doi:10.1177/0146167203261888 · Cited by 138
“Two additional analyses on these partial correlations (see Steiger, 1980) found that the partial correlations of participants’ motivation for interpersonal stimulation and security to their ingroup approach score were significantly different from each other, t(42) = 2.82, p .01, as were the same…”
BackgroundInfluential
A longitudinal study of awareness of deficit after moderate to severe traumatic brain injury
Hart, T., Seignourel, P. J., & Sherer, M. (2008) · Neuropsychological Rehabilitation · doi:10.1080/09602010802188393 · Cited by 138
“The procedure developed by Steiger (1980) for correlations drawn from non-independent samples was used to assess the significance of differences between correlations.”
Method
Cerebrovascular Regulation During Transient Hypotension and Hypertension in Humans
Tzeng, Y., Willie, C. K., Atkinson, G., Lucas, S. J. E., Wong, A., & Ainslie, P. N. (2010) · Hypertension · doi:10.1161/hypertensionaha.110.152066 · Cited by 138

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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