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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
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“We examined the Pillai‐Bartlett trace statistic due to its robustness against violations of MANOVA assumptions and its high statistical power for dependent variables with a multidimensional structure (Olson, 1976).”
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“In order to compare vowel qualities, we compute Pillai scores , a measure which is often used in sociophonetics to assess whether two vowel types are distinct [25, 26, 27].”
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“Box’s M test was significant ( p = .003), and we therefore reported Pillai’s trace (Olson, 1976).”
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“appropriate test statistic for these data (Olson, 1976).”
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“While robustness has been studied (Schatzoff 1966; Olson 1974, 1976, 1979; Ito 1980; Davis 1982), these are done under the large sample framework, where p is fixed, and n is large.”
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“Pillai’s trace was additionally included given its reliability with relatively small sample sizes (Olson, 1976).”
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“In fact, there at least 10 different omnibus statistics available, and each tends to give unique results in certain situations (Olson, 1976, 1979; Stevens, 1979).”
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“It is hopeful to assume that univariate robustness will generalize to the multivariate case, but at this time empirical proof is in short supply (Davidson, 1972; Olson, 1976).”
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Method
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BackgroundMethod
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“as this test is the most robust to violations to assumptions (Olson, 1976).”
BackgroundMethod
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“Pillai’s Trace test results are generally more reliable even the violations of basic assumptions of MAOVA (Olson, 1976).”
Method
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References
PhD, D. J. D. (2021) · doi:10.1002/9781119578208.biblio
Randomized Designs: Ordinal Data, I
Berry, K. J., Mielke, P. W., & Johnston, J. E. (2016) · Springer eBooks · doi:10.1007/978-3-319-28770-6_5
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Introduction
Berry, K. J., Mielke, P. W., & Johnston, J. E. (2016) · Springer eBooks · doi:10.1007/978-3-319-28770-6_1
Randomized Block Designs: Nominal Data
Berry, K. J., Mielke, P. W., & Johnston, J. E. (2016) · Springer eBooks · doi:10.1007/978-3-319-28770-6_11
References
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Faculty Opinions recommendation of Insights into the genetic architecture of the human face.
Pettersson, U. (2021) · Faculty Opinions – Post-Publication Peer Review of the Biomedical Literature · doi:10.3410/f.739166760.793583082
A cross-modal effect of noise: the disappearance of the alarm reaction of a freshwater fishPreprint
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Denis, D. J. (2020) · doi:10.1002/9781119549963.refs
Communication deficits in babies with autism and Pervasive Developmental Disorder - not otherwise specified (PDD-NOS)
Horovitz, M. (2010) · Louisiana State University · doi:10.31390/gradschool_theses.850
“The Pillai-Bartlett test statistic was again used, due to its robustness to violations of assumptions, in the presence of equal sample sizes (Olson, 1976).”
Method
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“Kolmogorov-Smirnov tests, Box's M Test of Equality of Covariance Matricesa, Wilks' lambda (Olson, 1976; Stevens, 1979) was used to test the assumption of homogeneity of variances, and Bonferroni for the Post-hoc method were employed to ensure that all data were normal.”
The Proteus Effect in Fallout: Investigating Gender-Conforming Behaviours in VideogamesPreprint
Szolin, K., Kuss, D. J., Nuyens, F. M., & Griffiths, M. D. (2023) · SSRN Electronic Journal · doi:10.2139/ssrn.4496363
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From Scratch: A Didactic Example of Multivariate Regression in Python
Ashiabi, G. S. (2024) · The Quantitative Methods for Psychology · doi:10.20982/tqmp.20.2.p186
“Thus, Olson (1976) recommends Pillai’s trace for general use and Ate¸s et al. (2019) also suggested that Pillai’s trace gives more robust results in the case of homogeneous and heterogeneous variances.”
Method
Assessing the effectiveness of ticket promotional strategies in sports: A comparative analysis
Chen, K., Chen, S. S., Min, S. D., & Zhang, J. J. (2024) · Journal of Infrastructure Policy and Development · doi:10.24294/jipd9352
“It was speculated that unequal sample sizes between the two institutions were a major factor contributing to this violation.”
R. Darrell Bock Multivariate Statistical Methods in Behavioral Research. New York: McGraw-Hill, 1975. Pp. xiii + 623. $21.00.
Olson, C. L. (1976) · Psychometrika · doi:10.1017/s0033312300003549

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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