Cited by 649Statistical Methods and ApplicationsAdvanced Statistical Methods and ModelsPsychometric Methodologies and Testing

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On choosing a test statistic in multivariate analysis of variance

Olson, Chester L.·1976·Psychological Bulletin

DOI 10.1037/0033-2909.83.4.579

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“Moreover, Pillai’s trace criterion is said to be more powerful when effects are spread over dimensions (Olson, 1976, 1979; Tabachnick and Fidell, 2007), and more robust than other classic multivariate statistics especially when data are unbalanced (Olson, 1976, 1979; Tabachnick and Fidell, 2007).”
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“statistic, as recommended by Olson (1976). Gender did not qualify”
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“Here, we report Pillai’s criteria which is the most robust to violations of assumptions concerning homogeneity of the covariance matrix (Olson, 1976).”
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“The Pillai’s Trace criterion was therefore reported because it is considered robust to violations of this assumption (Olson, 1976).”
Background
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“08) with Pillai’s Trace (Olson 1976) equal to 0.”
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“Pillai’s trace criterion was always reported, as this is considered the most robust of significance tests (Olson, 1976).”
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Method
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“Therefore, we followed the suggestions of Olson (1976) and of Tabachnick and Fidell (1996) to use Pillai’s Trace instead of Wilk’s Lambda to evaluate the multivariate significance of the principal effects and interactions.”
Method
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“Pillai’s trace is the F-statistic that is reported for within-subject effects (time) (Olson 1976).”
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“The Pillai-Bartlett V criterion was used as it is more robust than Wilks’s U (Olson, 1976) and is appropriate for small or unequal sample sizes.”
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“This statistic has been recommended to multivariate tests because it is the least sensitive to violations of assumptions (Olson 1976).”
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“Therefore, in the main analysis Pillai’s Trace will be reported because it is the most robust against violations of assumptions (Olson, 1976).”
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“The Pillai-Trace statistics has been shown to be less sensitive to deviations from assumptions than other multivariate statistics (Johnson & Field 1993, Olson 1976).”
A WAIS longitudinal study of cognitive development during the life span from ages 50 to 70
Mortensen, E. L., & Kleven, M. (1993) · Developmental Neuropsychology · doi:10.1080/87565649109540548 · Cited by 38
On the Role of Fragmentary Knowledge in a Sequence Learning Task
Buchner, A., Steffens, M. C., & Rothkegel, R. (1998) · The Quarterly Journal of Experimental Psychology Section A · doi:10.1080/713755757 · Cited by 38
“The Pillai-Bartlett V was used as the test criterion, but F -approximations to V are reported (cf. Olson, 1976).”
Method
Effects of parenting styles, academic self-efficacy, and achievement motivation on the academic achievement of university students in Ethiopia
Gota, A. A. (2012) · Australasian Journal of Paramedicine · Cited by 37
Multivariate Analysis of Variance and Repeated Measures: A Practical Approach for Behavioural Scientists
Dawson-Saunders, B. K., Hand, D. J., & Taylor, C. C. (1990) · Journal of Educational Statistics · doi:10.2307/1165036 · Cited by 38
Testing Multivariable Covariance Structure and Means Hypotheses via Structural Equation Modeling
Raykov, T. (2001) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1207/s15328007sem0802_4 · Cited by 37
“…seems to be available on the robustness of MANOVA then, which provides clear practical guidance and in particular methodological alternatives (e.g., Algina & Coombs, 1996; Coombs, Algina, & Oltman, 1996; Keselman & Lix, 1997; Maxwell & Delaney, 1990; Olson, 1976; see also Cole et al., 1993).”
Background
Gender differences in psychological distress in adults with asthma
Tovt-Korshynska, M. I., Dew, M. A., Chopey, I. V., NIa, S., & Lemko, I. (2001) · Journal of Psychosomatic Research · doi:10.1016/s0022-3999(01)00254-9 · Cited by 37
“[42] Olson CL.”
Method
Longitudinal Effects of Pay Increase on Teachers? Job Satisfaction: A Motivational Perspective
Abd‐El‐Fattah, S. M. (2010) · Cited by 36
Multivariate Analysis of Variance
Morrison, D. F. (2005) · Encyclopedia of Biostatistics · doi:10.1002/0470011815.b2a13045 · Cited by 37
To CALL or not to CALL: empirical evidence from neuroscience
Hsu, L. (2020) · Computer Assisted Language Learning · doi:10.1080/09588221.2020.1750429 · Cited by 40
“According to Olson (1976), Roy ’ s largest root is a target that may suffer from Type I errors; therefore, it should be avoided.”
MethodInfluential
Analyzing Designed Experiments with Multiple Responses
Langsrud, Ø., J⊘rgensen, K., Ofstad, R., & Næs, T. (2007) · Journal of Applied Statistics · doi:10.1080/02664760701594246 · Cited by 36
In search of reliable persuasion effects: I. A computer-controlled procedure for studying persuasion.
Ronis, D. L., Baumgardner, M. H., Leippe, M. R., Cacioppo, J. T., & Greenwald, A. G. (1977) · Journal of Personality and Social Psychology · doi:10.1037/0022-3514.35.8.548 · Cited by 36
Increased stressor‐evoked cardiovascular reactivity is associated with reduced amygdala and hippocampus volume
Trotman, G. P., Gianaros, P. J., Zanten, J. V., Williams, S. E., & Ginty, A. T. (2018) · Psychophysiology · doi:10.1111/psyp.13277 · Cited by 35
“Pillai’s trace was reported as this is considered the most robust of the multivariate significance tests (Olson, 1976), and alpha level was set at p 0.05.”
Influential
Amplitudes of Pain-Related Evoked Potentials Are Useful to Detect Small Fiber Involvement in Painful Mixed Fiber Neuropathies in Addition to Quantitative Sensory Testing – An Electrophysiological Study
Hansen, N., Káhn, A.-K., Zeller, D., Katsarava, Z., Sommer, C., & Üçeyler, N. (2015) · Frontiers in Neurology · doi:10.3389/fneur.2015.00244 · Cited by 36
“Since the MPS examination may result in “zero,” we applied the Bartlett procedure (31, 32) and added a constant of 0.”
Method
Chronic pain: A multiple-setting comparison of patient characteristics
Holzman, A. D., Rudy, T. E., Gerber, K. E., Turk, D. C., Sanders, S. H., Zimmerman, J. L., & Kerns, R. D. (1985) · Journal of Behavioral Medicine · doi:10.1007/bf00848372 · Cited by 35
“The violation of this assumption can seriously distort the results and interpretation of a comparative treatment study since the statistical power is reduced when group covariances are unequal (cf., Olson, 1976; Stevens, 1980).”
Result
Exogenous Melatonin Application Induced Morpho-Physiological and Biochemical Regulations Conferring Salt Tolerance in Ranunculus asiaticus L.
Eisa, E. A., Honfi, P., Tilly-Mándy, A., & Mirmazloum, I. (2023) · Horticulturae · doi:10.3390/horticulturae9020228 · Cited by 36
Will Women Lead the Way? Differences in Demand for Corporate Social Responsibility Information for Investment Decisions
Nath, L., Holder‐Webb, L., & Cohen, J. (2012) · Journal of Business Ethics · doi:10.1007/s10551-012-1573-2 · Cited by 38
“Significance tests are based on Pillai’s statistic, because it is the most robust to potential violations of the assumptions about distributions for a MANCOVA, and provides thus is the most conservative measure of significance (Olson 1976).”
Minnows trust conspecifics more than themselves when faced with conflicting information about predation risk
Crane, A. L., & Ferrari, M. C. O. (2015) · Animal Behaviour · doi:10.1016/j.anbehav.2014.12.002 · Cited by 33
“Because MANOVA assumptions were not fully met, we used Pillai's trace because of its robustness to non-normality and covariance heterogeneity (Olson, 1976), which occurred for some treatment groups for some response variables.”
Method

Authors: Olson, C. L.
Affiliations: McGill University (CA)
Corresponding author: Olson, Chester L.
Venue: Psychological Bulletin
Publisher: American Psychological Association (APA)
Published: 1976-07
Volume: 83
Issue: 4
Pages: 579-586
ISSN: 0033-2909 (ISSN-L)
1939-1455
DOI: 10.1037/0033-2909.83.4.579
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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On choosing a test statistic in multivariate analysis of variance

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