Abstract
The additive main effects multiplicative interaction model is frequently used in the analysis of multilocation trials. In the analysis of such data it is of interest to decide how many of the multiplicative interaction terms are significant. Several tests for this task are available, all of which assume that errors are normally distributed with a common variance. This paper investigates the robustness of several tests (Gollob, F GH1, FGH2, FR)to departures from these assumptions. It is concluded that, because of its better robustness, the F Rtest is preferable. If the other tests are to be used, preliminary tests for the validity of assumptions should be performed.
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References
Cohen AC (1967) Estimation in mixtures of two normal distributions. Technometrics 9:15–28
Cornelius PL (1980) Functions approximating Mandel's tables for the means and standard deviations of the first three roots of a Wishart matrix. Technometrics 22:613–616
Cornelius PL (1993) Statistical tests and retention of terms in the additive main effects and multiplicative interaction model for cultivar trials. Crop Sci 33:1186–1193
Cornelius PL, Seyedsadr M, Crossa J (1992) Using the shifted multiplicative model to search for “separability” in crop cultivar trials. Theor Appl Genet 84:161–172
Gauch HG (1988) Model selection and validation for yield trials with interaction. Biometrics 44:705–715
Gauch HG (1992) Statistical analysis of regional yield trials. AMMI analysis of factorial designs. Elsevier, New York
Gauch HG, Zobel RW (1988) Predictive and postdictive success of statistical analyses of yield trials. Theor Appl Genet 76:1–10
Gollob HF (1968) A statistical model which combines features of factor analytic and analysis of variance techniques. Psychometrika 33:73–155
Goodman LA, Haberman SJ (1990) The analysis of nonadditivity in two-way analysis of variance. J Am Stat Assoc 85:139–145
Johnson NL, Kotz S (1970) Continuous univariate distributions 1. Wiley, New York
Mandel J (1969) The partitioning of interaction in analysis of variance. J Res Int Bur Stand Sect B 73:309–328
Mandel J (1971) A new analysis of variance model for nonadditive data. Technometrics 13:1–8
Piepho HP (1992) Vergleichende Untersuchungen der statistischen Eigenschaften verschiedener Stabilitätsmaße mit Anwendungen auf Hafer, Winterraps, Ackerbohnen sowie Futterund Zuckerrüben. Doctoral Thesis (unpublished), Kiel
Piepho HP (1994) Best Linear Unbiased Prediction (BLUP) for regional yield trials: a comparison to additive main effects and multiplicative interaction (AMMI) analysis. Theor Appl Genet 89:647–654
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Communicated by A. R. Hallauer
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Piepho, H.P. Robustness of statistical tests for multiplicative terms in the additive main effects and multiplicative interaction model for cultivar trials. Theoret. Appl. Genetics 90, 438–443 (1995). https://doi.org/10.1007/BF00221987
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DOI: https://doi.org/10.1007/BF00221987