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Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I. Effect of Inequality of Variance in the One-Way Classification
Open accessAbstract
This is the first of two papers describing a study of the effect of departures from assumptions, other than normality, on the null-distribution of the $F$-statistic in the analysis of variance. In this paper, certain theorems required in the study and concerning the distribution of quadratic forms in multi-normally distributed variables are first enunciated and simple approximations tested numerically. The results are then applied to determine the effect of group-to-group inequality of variance in the one-way classification. It appears that if the groups are equal, moderate inequality of variance does not seriously affect the test. However, with unequal groups, much larger discrepancies appear. In a second paper, similar methods are used to determine the effect of inequality of variance and serial correlation between errors in the two-way classification.
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Citations
Cited by
Glass, G. V., Peckham, P. D., & Sanders, J. R. (1972) · Review of Educational Research · doi:10.3102/00346543042003237 · Cited by 1,826
Social exclusion impairs self-regulation
Baumeister, R. F., DeWall, C. N., Ciarocco, N. J., & Twenge, J. M. (2005) · Journal of Personality and Social Psychology · doi:10.1037/0022-3514.88.4.589 · Cited by 1,401
An Extension of Box's Results on the Use of the $F$ Distribution in Multivariate Analysis
Geisser, S., & Greenhouse, S. W. (1958) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177706545 · Cited by 1,098
ROBPCA: A New Approach to Robust Principal Component Analysis
Hubert, M., Rousseeuw, P. J., & Vanden Branden, K. (2005) · Technometrics · doi:10.1198/004017004000000563 · Cited by 1,052
Consequences of violating the independence assumption in analysis of variance.
Kenny, D. A., & Judd, C. M. (1986) · Psychological Bulletin · doi:10.1037/0033-2909.99.3.422 · Cited by 616
Metadata
- Authors
- Box, G. E. P.
- Venue
- The Annals of Mathematical Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1954-06
- Volume
- 25
- Issue
- 2
- Pages
- 290-302
- ISSN
- 0003-4851 (ISSN-L)
- OpenAlex
- W2020737422
- Cited by
- 1,513
- References
- 0
- FWCI
- 10.18
- Type
- journal article
- Language
- en
- Open access
- bronze
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- CoChat. (2026). Citation check: Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I. Effect of Inequality of Variance in the One-Way Classification. https://app.cochat.ai/papers/10.1214/aoms/1177728786
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- Box, G. E. P. (1954). Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I. Effect of Inequality of Variance in the One-Way Classification. The Annals of Mathematical Statistics. https://doi.org/10.1214/aoms/1177728786
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