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On choosing a test statistic in multivariate analysis of variance
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“Accordingly, Pillai's Trace was used as a multivariate test statistic to control for inflation in Type I error rate (45).”
From Improving Acceptability and Uptake Behavior for Internet-Based Cognitive-Behavioral Therapy (2021) · cites this paper as [45]
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A comparative analysis of cultural value orientations for understanding sport fan motivations
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MANOVA Simultaneous Test Procedures: The Power and Robustness of Restricted Multivariate Contrasts
Sheehan, J. K. (1998) · Educational and Psychological Measurement · doi:10.1177/0013164498058006001 · Cited by 33
Inquiry-based training improves teaching effectiveness of biology teaching assistants
Hughes, P. W., & Ellefson, M. R. (2013) · PLoS ONE · doi:10.1371/journal.pone.0078540 · Cited by 36
“assessed significance of training group as a multivariate effect using the Pillai’s Trace statistic, since Pillai’s Trace is the multivariate measure which is both: (1) most robust to multivariate non-normality; and (2) conservative when the sample size is small (<100) [40].”
Post-traumatic stress symptoms in relatives in the first weeks after severe traumatic brain injury
Pielmaier, L., Walder, B., Rebetez, M. M. L., & Maercker, A. R. A. (2011) · Brain Injury · doi:10.3109/02699052.2010.542429 · Cited by 33
“measure for differences [20], this apparent gender effect should be interpreted with caution because more than two thirds of the participants were women.”
BackgroundMethodSteyermark, A. C., & Spotila, J. R. (2001) · Copeia · doi:10.1643/0045-8511(2001)001[0129:eomiai]2.0.co;2 · Cited by 33
Steyerberg, E. W., Eijkemans, M. J. C., Harrell, F. E., & Habbema, J. D. F. (2000) · Statistics in Medicine · doi:10.1002/(sici)1097-0258(20000430)19:8 · Cited by 789
Univariate Repeated Measures Techniques Applied to Multivariate Data
Thomas, D. R. (1983) · Psychometrika · doi:10.1007/bf02293686 · Cited by 32
Improving Acceptability and Uptake Behavior for Internet-Based Cognitive-Behavioral Therapy
Molloy, A., Ellis, D. M., Su, L., & Anderson, P. L. (2021) · Frontiers in Digital Health · doi:10.3389/fdgth.2021.653686 · Cited by 29
“Accordingly, Pillai’s Trace was used as a multivariate test statistic to control for inflation in Type I error rate (45).”
MethodUntied, A. S., Orchowski, L. M., Mastroleo, N. R., & Gidycz, C. A. (2012) · Violence and Victims · doi:10.1891/0886-6708.27.6.957 · Cited by 31
“Olsen (1976) suggests that the Pillai-Bartlett V is a robust indicator of group differences.”
MethodRevisiting the Assumptions for Inferential Statistical Analyses: A Conceptual Guide
Chen, A., & Zhu, W. (2001) · Quest · doi:10.1080/00336297.2001.10491756 · Cited by 31
Use of Repeated-Measures Designs in Family Research
Ball, D., McKenry, P. C., & Price‐Bonham, S. (1983) · Journal of Marriage and the Family · doi:10.2307/351801 · Cited by 31
Whang, H., Ko, E., Zhang, T., & Mattila, P. (2015) · International Journal of Advertising · doi:10.1080/02650487.2015.1057381 · Cited by 30
“However, instead of Wilk’s lambda, Phillai’s trace was used, because it is considered to be more robust than the other significance test (Olson 1976).”
MethodEisa, E. A., Honfi, P., Tilly-Mándy, A., & Gururani, M. A. (2023) · Horticulturae · doi:10.3390/horticulturae9020262 · Cited by 30
Dream Content, Dream Recurrence and Well-Being: A Replication with a Younger Sample
Zadra, A. L., O’Brien, S., & Donderi, D. C. (1998) · Imagination Cognition and Personality · doi:10.2190/llxl-d4db-9cp5-brgt · Cited by 30
“The Pillais-Bartlett statistic was used because it is robust with respect to possible violations of normality and homogeneity of variance [50].”
MethodTransitions, Wellness, and Life Satisfaction: Implications for Counseling Midlife Women
Degges‐White, S., & Myers, J. E. (2006) · Journal of Mental Health Counseling · doi:10.17744/mehc.28.2.eaumlpbm0rxdrldk · Cited by 30
Perceived Roles and Preparation Experiences of Elementary Counselors: Suggestions for Change.
Carroll, B. W. (1993) · Elementary school guidance and counseling · Cited by 30
Unknown Words in Self-Reported Personality: Lethargic and Provincial in Texas
Graziano, W. G., Jensen‐Campbell, L. A., Steele, R. G., & Hair, E. C. (1998) · Personality and Social Psychology Bulletin · doi:10.1177/0146167298248008 · Cited by 30
Parental expectations and childhood deviance in clinic‐referred and non‐clinic children
Rickard, K. M., Graziano, W., & Forehand, R. (1984) · Journal of Clinical Child Psychology · doi:10.1080/15374418409533187 · Cited by 29
Maurissen, J. P. J., & Vidmar, T. J. (2016) · Neurotoxicology and Teratology · doi:10.1016/j.ntt.2016.10.003 · Cited by 30
Todorov, H., Searle-White, E., & Gerber, S. (2020) · PLoS ONE · doi:10.1371/journal.pone.0230798 · Cited by 28
“In agreement with previous reports, Pillai’s criterion was the most conservative, which would make it more appropriate when assumptions of MANOVA are violated [40, 41].”
ResultNeufeld, R. W. J., & Gardner, R. C. (1990) · Journal of Mathematical Psychology · doi:10.1016/0022-2496(90)90033-6 · Cited by 28
Presumption of Innocence: Congruence Bias Induced and Overcome
Helgeson, V. S., & Shaver, K. G. (1990) · Journal of Applied Social Psychology · doi:10.1111/j.1559-1816.1990.tb00412.x · Cited by 28
Population and Geographic Variation of Peromyscus leucopus in Relation to Climatic Factors
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Performance of Four Multivariate Tests Under Variance-Covariance Heteroscedasticity
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Does 3D Phenotyping Yield Substantial Insights in the Genetics of the Mouse Mandible Shape?
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“Here, pLOD scores are derived from the Pillai ’ s trace, a classic multi-variate statistic, which makes use of covariances and is proven to be fairly robust in a variety of situations (Olson 1974, 1976; Tabachnick and Fidell 2013).”
A Typological Approach to Testing the Evolutionary Functions of Human Female Orgasm
King, R., & Belsky, J. (2012) · Archives of Sexual Behavior · doi:10.1007/s10508-012-0001-0 · Cited by 26
“, second orgasm), a number judged insufficient to perform planned multivariate analysis on this set while providing sufficient power (Ito, 1962; Läuter, 1978; Olson, 1976; Pillai & Jayachandran, 1967; Tabachnick & Fidell, 2001).”
BackgroundEvent-related potentials and comorbidity in alcohol-dependent adult males
Malone, S. M., Iacono, W. G., & McGue, M. K. (2001) · Psychophysiology · doi:10.1111/1469-8986.3830367 · Cited by 27
Six NSCL/P Loci Show Associations With Normal-Range Craniofacial Variation
Indencleef, K., Roosenboom, J., Hoskens, H., White, J. D., Shriver, M. D., Richmond, S., Peeters, H., Feingold, E., Marazita, M. L., Shaffer, J. R., et al. (2018) · Frontiers in Genetics · doi:10.3389/fgene.2018.00502 · Cited by 30
“The correlation is tested for significance based on Rao’s F-test approximation (right tail, one-sided test; Olson, 1976).”
Young, J. W. (1978) · Academy of Management Journal · doi:10.2307/255667 · Cited by 26
Andiliou, A., Ramsay, C. M., Murphy, P. K., & Fast, J. (2011) · Contemporary Educational Psychology · doi:10.1016/j.cedpsych.2011.10.001 · Cited by 25
Effect of Intrinsic and Extrinsic Factors on Global and Regional Cortical Thickness
Govindarajan, K. A., Freeman, L. A., Cai, C. C., Rahbar, M. H., & Narayana, P. A. (2014) · PLoS ONE · doi:10.1371/journal.pone.0096429 · Cited by 25
“cortical thickness was evaluated using Pillai’s trace test [23,24].”
MethodFlaten, M. A., & Blumenthal, T. D. (1998) · Biological Psychology · doi:10.1016/s0301-0511(98)00018-0 · Cited by 25
The statistical analysis of dyadic social behavior: A multivariate approach.
Mendoza, J. L., & Graziano, W. G. (1982) · Psychological Bulletin · doi:10.1037//0033-2909.92.2.532 · Cited by 25
On the analysis of repeated measures over time in medical, pharmacological, and behavioral research
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Holland's theory: Stability of avocational interests
Varca, P. E., & Shaffer, G. S. (1982) · Journal of Vocational Behavior · doi:10.1016/0001-8791(82)90037-9 · Cited by 25
Crane, A. L., & Ferrari, M. C. O. (2016) · Animal Behaviour · doi:10.1016/j.anbehav.2016.06.005 · Cited by 24
“Because MANOVA assumptions were not fully met, we used Pillai's trace for its robustness to covariance heterogeneity and non-normality (Olson, 1976), which occurred for some treatment groups for some response variables.”
MethodHay, J. B., Drager, K., & Warren, P. (2009) · Australian Journal of Linguistics · doi:10.1080/07268600902823128 · Cited by 24
“rather than points (Olson, 1976)) or differences in F1 and F2 (which are directional, and so would reveal if the distinction is being produced in the wrong direction).”
Craig, M., & Roberts, J. D. (2005) · Biological Conservation · doi:10.1016/j.biocon.2004.12.014 · Cited by 24
Christabel, H. M.-F., & Vincent, N. C.-W. (2003) · Construction Management and Economics · doi:10.1080/0144619032000065117 · Cited by 24
“But for some practical situations, Pillai’s Trace may be more robust and powerful than Wilks’ Lambda (Olsen, 1976).”
BackgroundInfluentialTesting larval fish dispersal hypotheses using maximum likelihood analysis of otolith chemistry data
Sandin, S. A., Regetz, J., & Hamilton, S. L. (2005) · Marine and Freshwater Research · doi:10.1071/mf04144 · Cited by 24
“InTable 1 we only report results of Pillai’s trace test, which appears to be the most robust to violations of assumptions concerning homogeneity of the covariance matrix (Olson 1976); however, Wilk’s lambda, Hotelling-Lawley trace, and Roy’s maximum root all yielded identical outcomes.”
MethodBlashfield, R. K., Aldenderfer, M. S., & Morey, L. C. (1982) · Handbook of statistics · doi:10.1016/s0169-7161(82)02014-8 · Cited by 24
Utilization of psychophysiological indices in behavioral assessment: Some methodological issues
Ray, R. L., & Kimmel, H. D. (1979) · Journal of Psychopathology and Behavioral Assessment · doi:10.1007/bf01322018 · Cited by 24
Berumen, M. L., Trip, E. D. L., Pratchett, M. S., & Choat, J. H. (2011) · Coral Reefs · doi:10.1007/s00338-011-0838-z · Cited by 23
Zinko, R., Burgh-Woodman, H. C. D., Furner, Z. Z., & Kim, S. J. (2020) · Journal of Organizational and End User Computing · doi:10.4018/joeuc.20210301.oa5 · Cited by 24
“Therefore, the Pillai’s Trace test - which is the most robust of the multivariate tests in face of the assumption violation (Olson, 1976) - was used, resulting in a value of .959, F = 4101.043, p .000.”
MethodInfluentialSample size matters in calculating Pillai scores.
Stanley, J. A., & Sneller, B. (2023) · Journal of the Acoustical Society of America · doi:10.1121/10.0016757 · Cited by 28
Deng, X., Ali‐Adeeb, R., Andrews, J. L., Shreeves, P., Lum, J. J., Brolo, A. G., & Jirasek, A. I. (2020) · Applied Spectroscopy · doi:10.1177/0003702820906221 · Cited by 23
“Hence, the Pillai’s criterion was selected since it is robust against the nonnormality and heterogeneity of covariance matrices.(39) Results in Table III showed statistically significant multivariate effects in the independent variables (cell line, dose, and day).”
MethodUtilitarian Value in the Internet
Beldona, S., Kline, S. F., & Morrison, A. M. (2004) · Journal of Travel & Tourism Marketing · doi:10.1300/j073v17n02_06 · Cited by 23
“Pillai’s trace is more robust than the other significance tests namely Wilks’ Lambda and Hotelling’s trace (Olson, 1976).”
MethodAn Investigation of Big Five Personality and Propensity to Commit White-Collar Crime
Turner, M. J. (2014) · Emerald Group Publishing Limited eBooks · doi:10.1108/s1475-148820140000017002 · Cited by 23
A Comparison of Learning and Study Strategies of Gifted and Average-Ability Junior High Students
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Oculomotor and skeletal motor systems share one map of visual space
Nemire, K. E., & Bridgeman, B. (1987) · Vision Research · doi:10.1016/0042-6989(87)90088-5 · Cited by 23
Controlling the maximum familywise Type I error rate in analyses of multivariate experiments.
Bird, K. D., & Hadži-Pavlović, D. (2013) · Psychological Methods · doi:10.1037/a0033806 · Cited by 22
Brand, D. (2002) · Journal of Outdoor and Environmental Education · doi:10.1007/bf03400743 · Cited by 22
Analyzing RM ANOVA Related Data Using SPSS10
Liu, Y. (2002) · Measurement in Physical Education and Exercise Science · doi:10.1207/s15327841mpee0601_3 · Cited by 22
“In general, Wilks’s lambda, Hotelling’s trace, and Roy’s largest root are more powerful than Pillai’s trace when there is more than one degree of freedom for the particular effect (Tabachnick & Fidell, 1996), but Pillai’s trace is said to be more robust than the other three (Olson, 1976).”
BackgroundFox, A. D., Bergersen, E. A., Tombre, I., & Madsen, J. J. (2006) · Polar Biology · doi:10.1007/s00300-006-0235-1 · Cited by 22
“We calculated Pillai’s trace statistic (V) as a multivariate tool to test whether there were signiWcant diVerences between these categories (considered the most powerful, robust but conservative of the possible tests available in SAS; Olson 1976).”
MethodIsotopic trends in the diets of hunter-gatherers of the lower Paraná wetland, South America
Loponte, D., Acosta, A. A., & Corriale, M. J. (2016) · Journal of Archaeological Science Reports · doi:10.1016/j.jasrep.2016.07.023 · Cited by 22
Ramsey, P. H. (1980) · Journal of Applied Psychology · doi:10.1037//0021-9010.65.3.317 · Cited by 22
Academic Achievement, Motivation and Future Selves
Leondari, A., Syngollitou, E., & Kiosseoglou, G. (1998) · International Journal of Adolescence and Youth · doi:10.1080/02673843.1998.9747820 · Cited by 22
“The multivariate test used was the Pillais test which is considered the most robust and powerful test of multivariate effects (Olson, 1976).”
BackgroundMethodAttributions of Blame and Coping Following Spinal Cord Injury: Is Self-Blame Adaptive?
Nielson, W. R., & MacDonald, M. R. (1988) · Journal of Social and Clinical Psychology · doi:10.1521/jscp.1988.7.2-3.163 · Cited by 22
On the Interrelationships among Exposure to Death and Dying, Fear of Death, and Anxiety
Hoelter, J. W., & Hoelter, J. A. (1981) · OMEGA - Journal of Death and Dying · doi:10.2190/ty4e-kv6q-we9d-7dat · Cited by 22
Neacsiu, A. D., & Tkachuck, M. A. (2016) · Borderline Personality Disorder and Emotion Dysregulation · doi:10.1186/s40479-016-0041-5 · Cited by 21
“001) indicated that the covariance matrices of the dependent variables were significantly different across levels of the independent variable; therefore, Pillai’s Trace was reported given the more robust nature of the statistic [62].”
Li, J., & McLellan, R. (2021) · Contemporary Educational Psychology · doi:10.1016/j.cedpsych.2021.101991 · Cited by 23
Effects of Applying the PETTLEP Model on Vividness and Ease of Imaging Movement
Anuar, N. A., Cumming, J., & Williams, S. E. (2015) · Journal of Applied Sport Psychology · doi:10.1080/10413200.2015.1099122 · Cited by 21
“For these analyses, Pillai’s trace was reported because it is the most robust to violations of the homogeneity of the covariance matrix assumption (Olson, 1976).”
MethodChildren's Attractiveness, Gender, and Race Biases: A Comparison of Their Strength and Generality
Rennels, J. L., & Langlois, J. H. (2014) · Child Development · doi:10.1111/cdev.12226 · Cited by 21
“To be conservative, however, the reported MANOVA statistics reflect Pillai’s trace test, which is considered the most robust of the four analyses SPSS reports (Olson, 1976).”
MethodQuinton, M. L., Zanten, J. V., Trotman, G. P., Cumming, J., & Williams, S. E. (2019) · Frontiers in Psychology · doi:10.3389/fpsyg.2019.01657 · Cited by 21
An Intergroup Theories Approach to Direct Political Action among African Americans
Berman, S. L., & Wittig, M. A. (2004) · Group Processes & Intergroup Relations · doi:10.1177/1368430204039971 · Cited by 21
“Otherwise, Pillai’s criterion was reported (Olson, 1976, cited in Tabachnick & Fidell, 1989).”
Seelman, K. L., & Walls, N. E. (2010) · Journal of Social Work Education · doi:10.5175/jswe.2010.200800082 · Cited by 21
“…significant differences existed among the groups of students on the combination of the dependent variables using the Pillai- Bartlett trace criteria, because it has been shown to be the most robust statistical test against any violations of assumptions (Olson, 1974, 1976; Stevens, 1979).”
Cognitive Trauma Therapy for Battered Women: Replication and extension.
Beck, J. G., Tran, H. N., Dodson, T. S., Henschel, A. V., Woodward, M. J., & Eddinger, J. R. (2015) · Psychology of Violence · doi:10.1037/vio0000024 · Cited by 21
“Olson, C. L. (1976). On choosing a test statistic in multivariate analysis of variance. Psychological Bulletin, 83, 579 –586. http://dx.doi.org/10 .1037/0033-2909.83.4.579 Perez, S., & Johnson, D. M. (2008). PTSD compromises battered women’s future safety. Journal of Interpersonal Violence, 23, 635–651. http://dx .doi…”
BackgroundMethodInfluentialAdolescent representations of socio‐economic status
Dickinson, J. (1990) · British Journal of Developmental Psychology · doi:10.1111/j.2044-835x.1990.tb00850.x · Cited by 21
Repeated-measures analysis: Issues and options
Bramwell, A. T., Bittner, A. C., & Morrissey, S. J. (1992) · International Journal of Industrial Ergonomics · doi:10.1016/0169-8141(92)90032-u · Cited by 21
Grosemans, I., Coertjens, L., & Kyndt, E. (2018) · British Journal of Educational Psychology · doi:10.1111/bjep.12258 · Cited by 20
Zidenberg, A. M., Sparks, B., Harkins, L., & Lidstone, S. K. (2019) · Journal of Interpersonal Violence · doi:10.1177/0886260519872978 · Cited by 20
“001), the more robust Pillai’s trace (Olsen, 1976) was used to interpret the results of the MANOVA (Tabachnick & Fidell, 2014).”
MethodPrabhu, R., Miller, S. R., Simpson, T. W., & Meisel, N. A. (2020) · Journal of Engineering Design · doi:10.1080/09544828.2020.1851661 · Cited by 21
Episodic and semantic memory in early versus late onset Alzheimer's disease*1
Grosse, D. A. (1991) · Brain and Language · doi:10.1016/0093-934x(91)90172-w · Cited by 20
Craig, M. (2002) · Conservation Biology · doi:10.1046/j.1523-1739.2002.00567.x · Cited by 20
“The Pillai trace value was used, as recommended by Olson (1974, 1976), and I used a univariate ANOVA to determine differences in individual tree variables.”
MethodNew Test Statistics for MANOVA/Descriptive Discriminant Analysis
Coombs, W. T., & Algina, J. J. (1996) · Educational and Psychological Measurement · doi:10.1177/0013164496056003002 · Cited by 20
The evaluational consequences of topic reciprocity and self‐disclosure reciprocity
Hosman, L. A. (1987) · Communication Monographs · doi:10.1080/03637758709390242 · Cited by 20
Maurissen, J. P. J., Shankar, M. R., & Mattsson, J. L. (2000) · Neurotoxicology and Teratology · doi:10.1016/s0892-0362(99)00062-8 · Cited by 20
“Olson compared several multivariate indices and recommended the Pillai trace statistics as the most robust index of the MANOVA tests [22,23].”
MethodThe Possible Trajectory of Relationship Satisfaction Across the Longevity of a Romantic Partnership
Meyer, D. D., Robinson, B. A., Cohn, A., Gildenblatt, L., & Barkley, S. (2016) · The Family Journal · doi:10.1177/1066480716670141 · Cited by 19
“For its robustness, the Pillai–Bartlett trace was chosen as our multivariate test statistic (Olson, 1976).”
MethodSzabó, Z. R., Ravert, H. T., Gözükara, I., Geckle, W. J., Seki, C., Sostre, S., Peller, P. J., Monsein, L. H., Natarajan, T. K., Links, J. M., et al. (1993) · Synapse · doi:10.1002/syn.890150403 · Cited by 19
Retention of learned predator recognition in embryonic and juvenile rainbow trout
Horn, M. E., Ferrari, M. C. O., & Chivers, D. P. (2019) · Behavioral Ecology · doi:10.1093/beheco/arz116 · Cited by 19
Sierra, E. M., Pérez, M. N., Rivera, F. F., & Seijo, D. (2020) · Anales de Psicología · doi:10.6018/analesps.428631 · Cited by 19
Geographically Weighted Regression Modeling for Multiple Outcomes
Chen, V. Y.-J., Yang, T., & Jian, H.-L. (2022) · Annals of the American Association of Geographers · doi:10.1080/24694452.2021.1985955 · Cited by 19
Implications of Mainstream Classrooms for Adolescents with Spina Bifida
Lord, J., Varzos, N., Behrman, B., Wicks, J., & Wicks, D. (1990) · Developmental Medicine & Child Neurology · doi:10.1111/j.1469-8749.1990.tb08463.x · Cited by 19
“First, the Pillai criterion was used to assess the multivariate results, since this criterion has been shown to be robust when sample sizes are small (Olsen 1976).”
MethodWinter Time-Activity Budgets of Diving Ducks on Eastern Texas Reservoirs
Crook, S. L., Conway, W. C., Mason, C. D., & Kraai, K. J. (2009) · Waterbirds · doi:10.1675/063.032.0408 · Cited by 19
“…lacking for greater than two dependent variables (Johnson and Wichern 1988: 146), normality does not affect the MANOVA test criterion (i.e. Wilks’ lambda) (Olson 1976), and MANOVA is robust to heterogeneity in dispersion matrices (i.e. variance-covariance matrix) (Ito and Schull 1964; Ito 1969).”
BackgroundHypothesis Testing in Multivariate Linear Models with Randomly Missing Data
Barton, C. N., & Cramer, E. (1989) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610918908812796 · Cited by 19
THE HETEROGENEITY OF AMAZONIAN TREEFALL GAPS AND BIRD COMMUNITY COMPOSITION
Banks‐Leite, C., & Cintra, R. J. (2008) · Cited by 19
An investigation of biasing factors in the attributions of subordinates and their supervisors
Huber, V. L., Podsakoff, P. M., & Todor, W. D. (1986) · Journal of Business Research · doi:10.1016/0148-2963(86)90058-5 · Cited by 19
Effects of aging, organicity, alcoholism, and functional psychopathology on WAIS subtest profiles.
Overall, J. E., Hoffmann, N. G., & Levin, H. S. (1978) · Journal of Consulting and Clinical Psychology · doi:10.1037//0022-006x.46.6.1315 · Cited by 19
Kabib, A. R., & Harwell, M. R. (1989) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610918908812791 · Cited by 19
Quinton, M. L., Clarke, F. J., Parry, B. J., & Cumming, J. (2021) · Journal of Community Psychology · doi:10.1002/jcop.22517 · Cited by 18
The Differential Impact of Screen Time on Children’s Wellbeing
Belton, S., Issartel, J., Behan, S., Goss, H. R., & Peers, C. (2021) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph18179143 · Cited by 50
“Both outliers were assessed for data entry and measurement errors and deemed genuinely unusual values [45]; neither were removed from the analysis.”
BackgroundThe aftermath of childhood suicide: Influences on the perception of the parent
Calhoun, L. G., Selby, J. W., & Faulstich, M. E. (1982) · Journal of Community Psychology · doi:10.1002/1520-6629(198207)10:3 · Cited by 18
Some Properties of Two Measures of Multivariate Association
van den Burg, W., & Lewis, C. (1988) · Psychometrika · doi:10.1007/bf02294197 · Cited by 18
“A last point to be made in favor of multivariate R 2 and p2 as multivariate coefficients of association is that both R 2 (i.e., Wilks' A) and p2 (i.e., V) appear to compare favorably to other test statistics, in view of their power and robustness ( Olson, 1976, 1979; Stevens, 1979).”
ANOVA versus Regression Analysis of ATI Designs: An Empirical Investigation
Thompson, B. (1986) · Educational and Psychological Measurement · doi:10.1177/001316448604600411 · Cited by 18
Both Gender and Agonistic Experience Affect Perceived Pain during the Cold Pressor Test
Diotaiuti, P., Corrado, S., Mancone, S., Palombo, M., Rodio, A., Falese, L., Langiano, E., Siqueira, T. C., & Andrade, A. (2022) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph19042336 · Cited by 17
“As the number of participants in the group was balanced, in order to determine the interaction between the variables, Pillai’s criterion was used instead of Wilks’ Lambda, as it is more robust to unequal covariance matrices [54].”
MethodAttentional enhancement for positive and negative tones at an early stage of auditory processing
Folyi, T., Liesefeld, H. R., & Wentura, D. (2015) · Biological Psychology · doi:10.1016/j.biopsycho.2015.12.001 · Cited by 17
Rohde, J., Hofmann, T., Voigt, B., Rose, M., & Obbarius, A. (2019) · Frontiers in Psychology · doi:10.3389/fpsyg.2019.02326 · Cited by 17
Destrezas cognitivas en menores infractores, de protección y normalizados: un estudio de contraste
Sierra, E. M., Novo, M., Rivera, F. F., & Fernández, R. A. (2020) · Revista Latinoamericana de Psicología · doi:10.14349/rlp.2020.v52.16 · Cited by 17
Comparing PETTLEP imagery against observation imagery on vividness and ease of movement imagery
Anuar, N. A., Williams, S. E., & Cumming, J. (2016) · International Journal of Sport and Exercise Psychology · doi:10.1080/1612197x.2016.1177104 · Cited by 17
“For the main analyses, when repeated measures MANOVAs were run, the Pillai’s trace value was reported as it is the most robust for the multivariate significance test (Olson, 1976).”
Method
Metadata
- Authors
- Olson, C. L.
- Affiliations
- McGill University (CA)
- Corresponding author
- Olson, Chester L.
- Venue
- Psychological Bulletin
- Published
- 1976-07
- Volume
- 83
- Issue
- 4
- Pages
- 579-586
- ISSN
- 0033-2909 (ISSN-L)
- 1939-1455
- OpenAlex
- W2059439688
- Cited by
- 649
- References
- 37
- Citations by year
- 2026: 31 · 2025: 18 · 2024: 20 · 2023: 19 · 2022: 12 · 2021: 17 · 2020: 18 · 2019: 17 · 2018: 20 · 2017: 13 · 2016: 37 · 2015: 21 · 2014: 20 · 2013: 7 · 2012: 19
- FWCI
- 16.37
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Psychological Bulletin (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Keywords
- multivariate analysis of variance, hypothesis testing
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