The DOI matches its Crossref record; 17 of the 17 references it cites were found in a registry or an index.
Tests for comparing elements of a correlation matrix
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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“As seen in Table 4, all between-subscale differences in correlation coefficients were statistically significant (all ps < 0.001).”
From Spanish adaptation of the experiential approach scale (Eas) (2021) · cites this paper as [33]
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Items 1,001–1,061 of 1,061
Moruzzi, S., Rijsdijk, F., & Battaglia, M. (2014) · Journal of Abnormal Child Psychology · doi:10.1007/s10802-013-9725-0 · Cited by 67
“The within-subject correlation between SCT and INP is almost twice the correlation between SCT and HIP, a significant (p 0.001) difference according to Williams’ formula to test the difference between two dependent correlations (Steiger 1980).”
BackgroundInfluentialMachine learning‐based multimodal prediction of language outcomes in chronic aphasia
Kristinsson, S., Zhang, W., Rorden, C., Newman‐Norlund, R., Basilakos, A., Bonilha, L., Yourganov, G., Xiao, F., Hillis, A., & Fridriksson, J. (2021) · Human Brain Mapping · doi:10.1002/hbm.25321 · Cited by 64
“A one-sided Hotelling – Williams test was used to test whether the multimodal prediction model was significantly more accurate than any of the single-modality prediction models for each language measure (Steiger, 1980; Williams, 1959).”
MethodAdolescent cognitive control, theta oscillations, and social observation
Buzzell, G. A., Barker, T. V., Troller-Renfree, S. V., Bernat, E. M., Bowers, M. E., Morales, S., Bowman, L. C., Henderson, H. A., Pine, D. S., & Fox, N. A. (2019) · NeuroImage · doi:10.1016/j.neuroimage.2019.04.077 · Cited by 65
“A modified Fisher’s r-to-z transformation (Steiger 1980) demonstrated that the correlation coefficient associating rostral-LFC and PERI was significantly different from the coefficient for caudal-LFC and PERI, (Z = 2.04, p = .041), suggesting PERI was exclusively predicted by rostral-LFC…”
MethodInfluentialTaft, C. T., Murphy, C. M., King, L. A., Dedeyn, J. M., & Musser, P. H. (2005) · Journal of Abnormal Psychology · doi:10.1037/0021-843x.114.2.259 · Cited by 65
“05 (Steiger, 1980).”
ResultInfluentialCusack, S. E., Cash, T. V., & Vrana, S. R. (2018) · Journal of Obsessive-Compulsive and Related Disorders · doi:10.1016/j.jocrd.2018.06.004 · Cited by 63
Replicability Analysis for Natural Language Processing: Testing Significance with Multiple Datasets
Dror, R., Baumer, G., Bogomolov, M., & Reichart, R. (2017) · Transactions of the Association for Computational Linguistics · doi:10.1162/tacl_a_00074 · Cited by 63
Bragdon, L. B., Gibb, B. E., & Coles, M. E. (2018) · Depression and Anxiety · doi:10.1002/da.22785 · Cited by 57
“Correlations between neuropsychological outcomes and symptom groups in each study were compared using Steiger's Z-test of dependent correlations (Steiger, 1980) and these Z-scores were then included in the between-groups meta-analysis.”
MethodNarrative Fiction and Expository Nonfiction Differentially Predict Verbal Ability
Mar, R. A., & Rain, M. (2015) · Scientific Studies of Reading · doi:10.1080/10888438.2015.1069296 · Cited by 72
“A post hoc test based on the reported data (Steiger, 1980) finds that fiction is a stronger predictor of vocabulary than nonfiction, t(109) = 2.53, p = .01.”
MethodInfluentialThe effects of the Transcendental Meditation program on mindfulness
Tanner, M. A., Travis, F., Gaylord‐King, C., Haaga, D. A. F., Grosswald, S., & Schneider, R. H. (2009) · Journal of Clinical Psychology · doi:10.1002/jclp.20544 · Cited by 59
“, nonindependent correlations) were conducted using methods described by Steiger (1980). 583 Transcendental Meditation and Mindfulness”
Changes in functional connectivity following treatment with emotion regulation therapy
Scult, M. A., Fresco, D. M., Gunning, F. M., Liston, C., Seeley, S. H., García, E., & Mennin, D. S. (2019) · Frontiers in Behavioral Neuroscience · doi:10.3389/fnbeh.2019.00010 · Cited by 57
“For instance, we conducted some post hoc, unplanned tests of dependent correlations (Steiger, 1980) comparing the strength of correlation with self-report measures of attention and metacognition to the extract clusters associated with ERT-linked neural change.”
MethodAffektiv-motivational adaptive und handlungsadaptive Reaktionen auf Fehler im Lernprozess
Dresel, M., Schober, B., Ziegler, A., Grassinger, R., & Steuer, G. (2013) · Zeitschrift für Pädagogische Psychologie · doi:10.1024/1010-0652/a000111 · Cited by 55
Gros, D. F., Simms, L. J., & Antony, M. M. (2010) · Behavior Therapy · doi:10.1016/j.beth.2009.07.001 · Cited by 55
Murphy, C. M., Stojek, M. K., Few, L. R., Rothbaum, A. O., & MacKillop, J. (2014) · Experimental and Clinical Psychopharmacology · doi:10.1037/a0034535 · Cited by 54
“…associations were examined with PACS as both a continuous variable and a trichotomized variable, to evaluate potential loss of information resulting from categorizing dimensional data, by generating the correlation confidence intervals and testing for differences between the two (Steiger, 1980).”
Vandenkerckhove, B., Soenens, B., Van der Kaap-Deeder, J., Brenning, K., Luyten, P., & Vansteenkiste, M. (2019) · Learning and Individual Differences · doi:10.1016/j.lindif.2018.11.009 · Cited by 56
Hauschildt, M., Dar, R., Schröder, J., & Moritz, S. (2019) · Psychiatry Research · doi:10.1016/j.psychres.2019.01.092 · Cited by 53
A simple test of the Law of Initial Values
GEENEN, R., & VAN DE VIJVER, F. J. R. (1993) · Psychophysiology · doi:10.1111/j.1469-8986.1993.tb02076.x · Cited by 52
Aderka, I. M., McLean, C. P., Huppert, J. D., Davidson, J. R. T., & Foa, E. B. (2013) · Behaviour Research and Therapy · doi:10.1016/j.brat.2013.03.007 · Cited by 49
“…using the following fit indices: the StorraeBentler scaled c2 index, the Non-Normed Fit Index (NNFI; Bentler & Bonett, 1980, labeled the TuckereLewis Index (TLI) in AMOS), the Comparative Fit Index (CFI; Bentler, 1990), and the Root Mean Square Error of Approximation (RMSEA; Steiger, 1980).”
MethodThreat sensitivity, incentive sensitivity, and the experience of relief.
Carver, C. S. (2009) · Journal of Personality · doi:10.1111/j.1467-6494.2008.00540.x · Cited by 50
“Comparison of the significant correlations using the procedures described by Steiger (1980) indicate that they did not differ significantly from one another.”
MethodInfluentialMiller, J. D., Gentile, B., Carter, N. T., Crowe, M., Hoffman, B. J., & Campbell, W. K. (2018) · Journal of Personality Assessment · doi:10.1080/00223891.2017.1310731 · Cited by 49
ZAHN, T., & PICKAR, D. (2005) · Schizophrenia Research · doi:10.1016/j.schres.2005.05.025 · Cited by 43
“Because of the large number of correlations computed a test of the hypothesis that all correlations are zero (Steiger, 1980) was made for each matrix.”
BackgroundOlofsdotter, S., Sonnby, K., Vadlin, S., Furmark, T., & Nilsson, K. W. (2016) · Assessment · doi:10.1177/1073191115583858 · Cited by 41
“Significance tests for dependent correlations were conducted to determine if the strength of the relation with the K-SADS screening interview differed between the SCAS and the SCAS-P (Steiger, 1980).”
MethodSzkodny, L. E., & Newman, M. G. (2019) · Assessment · doi:10.1177/1073191117698753 · Cited by 38
Increased Attention Regulation from Emotion Regulation Therapy for Generalized Anxiety Disorder
Renna, M. E., Seeley, S. H., Heimberg, R. G., Etkin, A., Fresco, D. M., & Mennin, D. S. (2018) · Cognitive Therapy and Research · doi:10.1007/s10608-017-9872-7 · Cited by 36
“Results revealed no significant difference between the relationship of FFMQ Observing and FFMQ Non-Reactivity to conflict adaptation (Z = 1.43, p = .15, Hedge’s g = .73; Steiger 1980) but a large effect size, potentially due to the small sample size.”
BackgroundInfluentialWong, Q. J. J., Gregory, B., Gaston, J. E., Rapee, R. M., Wilson, J. K., & Abbott, M. J. (2017) · Journal of Affective Disorders · doi:10.1016/j.jad.2016.09.020 · Cited by 36
“Tests of the difference between the correlations (Steiger, 1980) showed that the Trait CBQ was more strongly related to DASS depression than the social anxiety composite (Z=2.”
BackgroundInfluentialHershenberg, R., McDonald, W. M., Crowell, A., Riva-Posse, P., Craighead, W. E., Mayberg, H. S., & Dunlop, B. W. (2020) · Journal of Affective Disorders · doi:10.1016/j.jad.2020.01.108 · Cited by 40
“To examine if the magnitude of associations between CR and PRO measures were significantly greater in the TRD compared to the treatment naïve patients, we computed r to z transformations (Steiger, 1980).”
MethodIs working memory capacity a causal factor in fluid intelligence?
Burgoyne, A. P., Hambrick, D. Z., & Altmann, E. M. (2019) · Psychonomic Bulletin & Review · doi:10.3758/s13423-019-01606-9 · Cited by 30
Moritz, S., Lüdtke, T., Westermann, S., Hermeneit, J., Watroba, J., & Lincoln, T. M. (2016) · Schizophrenia Research · doi:10.1016/j.schres.2016.04.025 · Cited by 36
“A test for correlational differences (Steiger, 1980) indicated that these correlations were significantly stronger than those seen for the CAPE positive dimension (traditional algorithm, p b 0.”
InfluentialDynamics of Positive Emotion Regulation: Associations with Youth Depressive Symptoms
Fussner, L. M., Luebbe, A. M., & Bell, D. J. (2015) · Journal of Abnormal Child Psychology · doi:10.1007/s10802-014-9916-3 · Cited by 34
Assessment of Head Tremor with Accelerometers Versus Gyroscopic Transducers
Elble, R. J., Hellriegel, H., Raethjen, J., & Deuschl, G. (2017) · Movement Disorders Clinical Practice · doi:10.1002/mdc3.12379 · Cited by 35
“Statistical comparison of correlation coefficients for TRS versus displacement (accelerometry) and TRS versus rotation (gyroscopy) was performed with a web-based calculator,17 using the method of Steiger.18 MDC was estimated as follows.”
MethodFrielink, N., Schuengel, C., & Embregts, P. J. C. M. (2019) · European Journal of Psychological Assessment · doi:10.1027/1015-5759/a000366 · Cited by 36
“A Steiger’s Z-test was conducted to compare the dependent correlations derived from the cross-construct and the withinconstruct.”
MethodSharp, C., Vanwoerden, S., Jouriles, E. N., Godfrey, D. A., Babcock, J., McLaren, V., McFarlane, J., Brashear, B., Walton, Q., & Temple, J. R. (2020) · Child Abuse & Neglect · doi:10.1016/j.chiabu.2020.104448 · Cited by 34
García-Campayo, J., Barceló-Soler, A., Martínez-Rubio, D., Navarrete, J., Pérez-Aranda, A., Feliu-Soler, A., Luciano, J. V., Baer, R., Kuyken, W., & Montero-Marin, J. (2024) · Assessment · doi:10.1177/10731911231203966 · Cited by 35
“Then, a z -value was calculated using the Fisher r -to- z transformation (Fisher, 1925), and the significance of the difference between correlation coefficients was computed (Steiger, 1980).”
MethodGoodrich, J. M., & Namkung, J. M. (2019) · Early Childhood Research Quarterly · doi:10.1016/j.ecresq.2019.04.006 · Cited by 33
Yankouskaya, A., Babiker, A., Rizvi, S., Alshakhsi, S., Liebherr, M., & Ali, R. (2025) · ACM Transactions on the Web · doi:10.1145/3765895 · Cited by 32
Fisher, P., Robie, C., Christiansen, N., Speer, A., & Schneider, L. (2019) · Personnel Assessment and Decisions · doi:10.25035/pad.2019.01.003 · Cited by 31
“Criterion-related validity coefficients for the 11 different samples for CTT and TIRT scoring methods are presented in Table 1.2 Tests of dependent correlations (|Z|; Steiger, 1980) were used to compare the correlations across scoring methods.”
MethodInfluentialLatent dimensions of social anxiety disorder: A re-evaluation of the Social Phobia Inventory (SPIN)
Campbell-Sills, L., Espejo, E., Ayers, C. R., Roy-Byrne, P., & Stein, M. B. (2015) · Journal of Anxiety Disorders · doi:10.1016/j.janxdis.2015.09.007 · Cited by 29
“…was indeed significantly larger than its correlation with Fear of Negative Evaluation (r = .42; z = 6.49, one-tailed p < .001 for test of difference between two dependent correlation coefficients; Steiger, 1980) and Fear of Uncertainty in Social Situations (r = .33; z = 4.95, one-tailed p < .001).”
BackgroundInfluentialMeyer, T., Krans, J., van Ast, V., & Smeets, T. (2017) · Journal of Behavior Therapy and Experimental Psychiatry · doi:10.1016/j.jbtep.2016.07.010 · Cited by 28
Guo, Q.-H., Cheng, Y.-B., Zhang, D.-Y., Wang, Y., Huang, Q.-F., Sheng, C.-S., Xu, T.-Y., Li, Y., & Wang, J.-G. (2019) · Hypertension · doi:10.1161/hypertensionaha.119.12955 · Cited by 27
“We performed Pearson correlation analysis and determined the partial correlation coefficients of vascular indices associated with various morning BP and compared the coefficients using the Hotelling-William test.(17) Vascular indices among groups were compared using the ANCOVA.”
MethodElucidating the relationship between borderline personality disorder and intimate partner violence
Munro, O. E., & Sellbom, M. (2020) · Personality and Mental Health · doi:10.1002/pmh.1480 · Cited by 26
Louis, J. P., Wood, A. M., & Lockwood, G. (2018) · PLOS ONE · doi:10.1371/journal.pone.0205605 · Cited by 24
“The z-test proposed by Steiger [76] was used to PLOS ONE | https://doi.org/10.1371/journal.pone.0205605 November 7, 2018 9 / 26 show, as evidence for divergent validity, that differences in correlations between most concordant subscales in the YPI-R2 and s-EMBU were statistically and significantly higher than differen…”
MethodResultInfluentialSchmits, E., Heeren, A., & Quertemont, E. (2014) · Psychologica Belgica · doi:10.5334/pb.al · Cited by 25
Potential sources of criterion bias in supervisor ratings used for test validation
Lefkowitz, J., & Battista, M. (1995) · Journal of Business and Psychology · doi:10.1007/bf02230978 · Cited by 25
Is Narcissism Inversely Related to Satisfaction? An Examination of Data From Two U.S. Samples
Kopelman, R. E., & Mullins, L. S. (1992) · The Journal of Psychology · doi:10.1080/00223980.1992.10543346 · Cited by 24
Ritzmann, R., Freyler, K., Krause, A., & Gollhofer, A. (2016) · Journal of Applied Physiology · doi:10.1152/japplphysiol.00692.2016 · Cited by 21
“Furthermore, to compare correlations from dependent samples obtained in LG, MG, and EG, correlation coefficients (rLG, rMG, rEG) were converted into a z-score using Fisher’s r-to-z transformation (53).”
MethodWilliams, C., Daley, D., Burnside, E., & Hammond-Rowley, S. (2010) · Personality and Individual Differences · doi:10.1016/j.paid.2010.02.006 · Cited by 19
Schneider, M. N., Zavos, H. M. S., McAdams, T. A., Kovas, Y., Sadeghi, S., & Gregory, A. M. (2019) · Behaviour Research and Therapy · doi:10.1016/j.brat.2018.11.002 · Cited by 17
Wammen Rathenborg, F. L., Zdaniuk, B., & Brotto, L. A. (2019) · The Journal of Sexual Medicine · doi:10.1016/j.jsxm.2018.12.001 · Cited by 17
Understanding colourism in the UK: development and assessment of the everyday colourism scale
Craddock, N., Phoenix, A., White, P., Gentili, C., Diedrichs, P. C., & Barlow, F. (2023) · Ethnic and Racial Studies · doi:10.1080/01419870.2022.2149275 · Cited by 17
“Model fit for the CFA was evaluated using the comparative fit index (CFI; Bentler 1990), Tucker-Lewis index (TLI; Tucker and Lewis 1973), root mean square error of approximation (RMSEA; Steiger 1980a), and minimum discrepancy per degree of freedom (CMIN/df).”
MethodJohnson, E. G., Mooney, L., Graf Estes, K., Nordahl, C. W., & Ghetti, S. (2021) · Current Biology · doi:10.1016/j.cub.2021.09.058 · Cited by 13
Brüggemeier, B., Breiter, M., Kurz, M., & Schiwy, J. (2020) · Proceedings of the 2nd Conference on Conversational User Interfaces · doi:10.1145/3405755.3406122 · Cited by 12
“In this case [51]’s procedure [51] was used.”
MethodOccipital sleep spindles predict sequence learning in a visuo-motor task
Lutz, N. D., Admard, M., Genzoni, E., Born, J., & Rauss, K. (2021) · SLEEP · doi:10.1093/sleep/zsab056 · Cited by 12
“To test for differences between correlations of Training and Test, we used Steiger’s Z test [85, 86].”
MethodThe Experiential Approach Scale: Development and preliminary psychometric properties
Swails, J. A., Zettle, R. D., Burdsal, C. A., & Snyder, J. J. (2016) · The Psychological Record · doi:10.1007/s40732-016-0188-x · Cited by 12
“We used a Z test (created by Steiger, 1980, and updated by Hoerger, 2013) to determine the statistical significance of differences in correlation coefficients between the two subscales and AAQ-II.”
MethodCrewther, B., Witek, K., Draga, P., Zmijewski, P., & Obmiński, Z. (2019) · International Journal of Sport Nutrition and Exercise Metabolism · doi:10.1123/ijsnem.2018-0076 · Cited by 10
Cervellati, C., Bonaccorsi, G., Cremonini, E., Romani, A., Castaldini, C., Ferrazzini, S., Giganti, M., Fila, E., Massari, L., & Bergamini, C. M. (2014) · Scandinavian Journal of Clinical and Laboratory Investigation · doi:10.3109/00365513.2013.860618 · Cited by 10
Gibson, B. S., Gondoli, D. M., Ralph, K. J., & Sztybel, P. (2018) · Child Neuropsychology · doi:10.1080/09297049.2016.1225706 · Cited by 10
“dependent correlations were conducted (Steiger, 1980).”
MethodSmees, R., Simner, J., Hoare, D. J., & Ward, J. (2025) · International Journal of Audiology · doi:10.1080/14992027.2024.2419558 · Cited by 7
“The method of Steiger (1980) was used to compare two correlations within the same sample of participants (r 12 and r 13 ) and considering the degree of relationship between the two measures (r 23 ).”
Renna, M. E., Spaeth, P. E., Quintero, J. M., O'Toole, M. S., Sandman, C. F., Fresco, D. M., & Mennin, D. S. (2023) · Behaviour Research and Therapy · doi:10.1016/j.brat.2023.104420 · Cited by 7
Spanish adaptation of the experiential approach scale (Eas)
Reyes-Martín, S., Hernández-López, M., & Rodríguez-Valverde, M. (2021) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph182412873 · Cited by 2
“In order to determine whether correlation coefficients across EAS subscales differed significantly, we used an updated version of Steiger’s Z [33,34] that tests for the statistical significance of differences in dependent correlations.”
Shek, D. T. L. (1993) · Journal of Clinical Psychology · doi:10.1002/1097-4679(199305)49:3
Friedman (2000) · doi:10.1002/1097-0029(20001001)51:1
de Beurs, E., Wilson, K. A., Chambless, D. L., Goldstein, A. J., & Feske, U. (1997) · Depression and Anxiety · doi:10.1002/(sici)1520-6394(1997)6:4
Metadata
- Authors
- Steiger, J. H.
- Affiliations
- University of British Columbia (CA)
- Corresponding author
- Steiger, James H.
- Venue
- Psychological Bulletin
- Published
- 1980-03
- Volume
- 87
- Issue
- 2
- Pages
- 245-251
- ISSN
- 0033-2909 (ISSN-L)
- 1939-1455
- 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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