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Non-Additivity in Two-Way Analysis of Variance
Abstract
In two-way classification analysis of variance situations there often exists a systematic type of row column interaction. A model is proposed in which the interaction is of the type Q i γ i where Q i is a parameter of the ith row, not necessarily associated with the main effect for rows, and γ j is the main effect for column j. The analysis of data according to this model is given, including estimation and tests of significance. The model is more general than that involved in Tukey's “one degree of freedom for non-additivity” and includes the latter as a special case. The relationship between the two methods is discussed. Applications of the method to different types of problems are mentioned and a numerical example is included.
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Cited by
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Atkinson, A. C., Cook, R. D., & Weisberg, S. (1983) · Biometrics · doi:10.2307/2531125 · Cited by 1,904
Group representations in probability and statistics
Diaconis, P. (1988) · doi:10.1214/lnms/1215467407 · Cited by 1,381
Some statistical aspects of partitioning genotype-environmental components of variability
Shukla, G. K. (1972) · Heredity · doi:10.1038/hdy.1972.87 · Cited by 1,077
Statistical Analyses of Multilocation Trials
Crossa, J. (1990) · Advances in Agronomy · doi:10.1016/s0065-2113(08)60818-4 · Cited by 640
Residuals and Influence in Regression.
Chatterjee, S., Cook, R. D., & Weisberg, S. (1984) · Journal of the American Statistical Association · doi:10.2307/2288741 · Cited by 622
Metadata
- Authors
- Mandel, J.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1961-12
- Volume
- 56
- Issue
- 296
- Pages
- 878-888
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W1982784691
- Cited by
- 267
- References
- 0
- FWCI
- 10.46
- Type
- journal article
- Language
- en
- Open access
- closed
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