The DOI matches its Crossref record; 37 of the 37 references it cites were found in a registry or an index.
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]
Citations
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Robust Estimates, Residuals, and Outlier Detection with Multiresponse Data
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“Olson (1976) suggests using Pillai-Bartlett V as a measure of effect size for multivariate designs; we chose a value of .25 as our desired effect size for an F test.”
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“…test, p < .001); we proceeded given that our sample sizes were relatively balanced such that all groups were between a 1.5:1 and 2:1 ratio (Huberty & Olejnik, 2006) and used Pillai’s trace when interpreting our results (Olson, 1976; Tabachnick & Fidell, 2014) given that we had unequal group sizes.”
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Bergner, C. M. (2014) · doi:10.31274/etd-180810-3403
“Olson (1976; 1979) asserted that when the assumption of homogeneity of covariance matrices has been violated, researchers should use the Pillai-Bartlett statistic (Pillai’s trace) to evaluate multivariate significance rather than using Wilks’ lambda or the Hotelling-Lawley trace.”
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“Olson (1976) recommends Pillai's Trace as the most appropriate small sample statistic, so little confidence may be placed in the single significant test statistic, the Hotelling-Lawley Trace.”
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“Despite the significance of Box’s M, Pillai’s Trace was selected as the primary multi-variate test statistic, given its robustness to violations of MANOVA assumptions, including heterogeneity of covariance matrices and deviations from multivariate normality (Olson, 1976; Tabachnick & Fidell, 2013).”
Kamza, A. (2026) · Frontiers in Psychology · doi:10.3389/fpsyg.2026.1713752 · Cited by 1
“Given the balanced group sizes (22–25 per condition) and the superior robustness of Pillai’s Trace to violations of normality and homogeneity (Olson, 1976; Hair et al., 2022), Pillai’s V was selected as the omnibus MANOVA statistic.”
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“Therefore, Pillai ’ s Trace was used because of its relative robustness to covariance heterogeneity (Nimon, 2012; Olson, 1976).”
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“We used Pillai’s trace to test significance because it is robust to violations of MANOVA assumptions such as multivariate normality and homogeneity of variance (Olson 1976; Finch 2005).”
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“…of the homogeneity of covariance matrices ( p = 0.027), Pillai’s Trace was employed, as it is widely recommended for MANOVA due to its robustness and is particularly appropriate when this assumption is violated (Nimon, 2012; Olson, 1976) (recent research since 2022 on this issue appears limited).”
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“Pillai’s trace, a test statistic used in MANOVA ranging from 0 to 1, with values closer to 1 indicating stronger effects, is con - sidered the most robust of the multivariate measures, especially when MANOVA assumptions are violated (Olson 1976).”
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“Given the robustness of Pillai’s trace to deviations from normality, unequal group sizes, and minor violations of homogeneity of covariance matrices (Olson, 1976; Wilks, 1932; IBM Corp, 2023), we used Pillai’s trace as the multivariate test statistic (Tabachnick and Fidell, 2019; Pietrzak, 2020).”
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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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