The Power of Four Tests in Two Way Models with Interaction and No Replication

Yıl 2012, Cilt: 25 Sayı: 3, 677 - 688, 19.07.2012

Hülya Olmus Semra Erbas

Öz

This article presents tests for the interaction in a two way table with one observation per cell. The conventional linear model theory cannot be used to check for the interaction when there is exactly one observation per cell (no replication) in two way ANOVA models. For this purpose, two different approaches are presented in the literature. The first of these approaches is to assume a specific functional form for the interaction terms.  The second approach is not to assume a specific functional form for the interaction terms. In this article, we present four additivity tests by proposed Tusell (1990), Boik (1993a), Piepho (1994), Kharrati-Kopaei and            Sadooghi-Alvandi (2007) for second approach. We compared their performance by means of simulation studies with respect to the power.

 

 

                Key Words:  Two-way ANOVA models,  fixed effects,  

                interaction,  no replication, power.    

Anahtar Kelimeler

Two-way ANOVA models, fixed effects, interaction, no replication, power

Kaynakça

• Aylin, A., Kurt, S., “Testing non-additivity (interaction) in two-way ANOVA tables with no replication”, Statistical Medical Research, 15: 63-85. (2006).
• Boik, R.J., “Testing additivity in two-way classifications with no replications: the locally best invariant test”, Journal Applied Statistics. 20(1): 41-55, (1993a).
• Boik, R. J., “A comparison of three invariant tests of additivity in two-way classifications with no replications”, Analysis,15: 411-424, (1993b). Statistics&Data
• Clinical and Laboratory Standards Institute (CLSI). “Methods for antimicrobial dilution and disk susceptibility testing of infrequently isolated or fastidious bacteria;approval guideline”, Document M45-A. Clinical and Laboratory Standards Institute, Wayne, P.A., (2008).
• Hegemann, V., Johnson, D.E., “The power of two tests for non-additivity”, Journal of the American Statistical Association, 71: 945-948, (1976).
• Johnson, D.E., Graybill, F.A., “An analysis two-way model with interaction and no Replication”, Journal of the American Statistical Association, 67: 862-868, (1972).
• Kharrati-Kopaei, M., Sadooghi-Alvandi, S.M., “A new method for testing interaction in unreplicated two-way analysis of variance”, Communications in Statistics-Theory and Methods, 36: 2787-2803, (2007).
• Kresh, H., “Statistical tables for multivariate analysis”, Springer Verlag, New York, (1975).
• Mandel, J., “Non-additivity in two-way analysis of variance”, Journal of the American Statistical Association, 56: 878-888, (1961).
• Mandel, J., “A new analysis of variance model for non-additivity”, Technometrics, 13: 1-18, (1971).
• Milliken, G.A., Rasmuson, D., “A heuristic technique for testing for the presence of interaction in nonreplicated factorial experiments”, Austral. Journal Statist., 19: 32-38, (1977).
• Piepho, H.P., ”Comment on shukla’s test for homogeneity calssification”, Journal of Animal Science, 70: 1644-1645, (1992a). in a two-way
• Piepho, H.P., “On the tests for interaction in a nonreplicated two-way layout”, Austral. J. Statist., 36 (3): 363-369, (1994).
• Rasch, D., Rusch, T., Simeckova, M., Kubinger, K.D., Moder, K., Simecek, P., “Tests of additivity in mixed and fixed effect two-way ANOVA models with single subclass numbers”, Statistical Papers, 50: 905-916, (2009). [15] Snee, R.D.,
• “Nonadditivity in a Two-way
• classification: Is it interaction or Nonhomogeneous
• Variance?”, Journal of American Statistical
• Association, 77( 379): 515-519, (1982).
• Speed, F.M., Speed, F.M., “An ad-hoc diagnostic tool foe checking for interaction in a nonreplicated experiment”, Communications Statistics Theory and Methods, 23 (54): 1364-1374, (1994).
• Tukey, J.W., “One degree of freedom for non- additivity”, Biometrics, 5: 232-242, (1949).
• Tusell, F., “Testing for interaction in two-way ANOVA tables with no replication”, Computational Statistics and Data Analysis, 10: 29-45, (1990).
• Yochmowitz, M.G., Cornell, R. G., “Stepwise tests for multiplicative components of interaction”, Technometrics, 20: 79-84, (1978).
• Yucel, N., Erdoğan, S., “Virulence properties and characterization of aeromonads isolated from foods of animal origin and enviromental sources”, Journal of Food Protection, 73(5): 855-860, (2010).