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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Statistical principles in experimental design.
Winer, B. J. (1962) · McGraw-Hill Book Company · doi:10.1037/11774-000 · Cited by 27,137
An Introduction to Multivariate Statistical Analysis
Muirhead, R. J., & Anderson, T. W. (1986) · Journal of Business and Economic Statistics · doi:10.2307/1391399 · Cited by 9,179
The Analysis of Variance
Scheffé, H. (1960) · Soil Science · doi:10.1097/00010694-196006000-00016 · Cited by 5,625
Advanced Statistical Methods In Biometric Research
Rao, C. R. (1952) · Birchandra State Central Library,tripura · Cited by 1,953
Multivariate Data Analysis
(2008) · Springer eBooks · doi:10.1007/978-1-4020-5614-7_2260 · Cited by 1,924
An analysis of transformations (with discussion)
Box, G. E. P. (1964) · Journal of the Royal Statistical Society Series A (Statistics in Society) · Cited by 1,891
Applied Multivariate Analysis
Timm, N. H. (2004) · Springer eBooks · doi:10.1007/b98963 · Cited by 1,664
The Use of Transformations
Bartlett, M. S. (1947) · Biometrics · doi:10.2307/3001536 · Cited by 1,253
CERTAIN GENERALIZATIONS IN THE ANALYSIS OF VARIANCE
Wilks, S. S. (1932) · Biometrika · doi:10.1093/biomet/24.3-4.471 · Cited by 1,011
Robust Estimates, Residuals, and Outlier Detection with Multiresponse Data
Gnanadesikan, R., & Kettenring, J. R. (1972) · Biometrics · doi:10.2307/2528963 · Cited by 826

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“When the Box’s M result was statistically significant, we reported Pillai’s Trace, as recommended due to its robustness against this violation (Olson, 1976; Tabachnick & Fidell, 2014).”
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“This deficiency is very common in the published accounts of multivariate research in the behavioral sciences (Olson, 1976).”
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“Comprehensive multicollinearity tests yielded a mean VIF of 2.06, well below the threshold of ten, and none of the correlation coefficients exceeded 0.601, confirming no significant multicollinearity issues [58–67].”
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“from the Pillai-Bartlett trace test statistic recommended by Olson (1976) because of its superior robustness.”
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“As suggested by Olson [52], Pillai’s trace is recommended for general use as one or more of these assumptions being violated (residuals normality, equal variance–covariance matrices of each group of residuals, independence of observations) tends to be the most robust test statistic.”
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“To prevent the loss of data points during this transformation, a ﬁ xed value of 0.1 was added to each value to avoid recording zeroes, as described before [34].”
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“Pillai’s trace is a multivariate measure of association to ensure maximum protection against finding a statistical significance when there is none (Olson, 1976).”
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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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