Analysis of Interaction in the Case of No Replication in a Two-Factor Experiment

Authors

  • Samyia Khalid Hasan

DOI:

https://doi.org/10.31272/jae.i141.1017

Keywords:

Parameter Estimates , Randomized Complete Block Design , Tukey's test , Mandel test , Classification, ANOVA table

Abstract

This research was concerned with the problem of interaction between effects in the data that can be arranged in two directions, which are called two-way classification models , in the absence of redundancy in the observations . The research was applied to a set of two -way classification data and used two methods to test the presence of interaction in the model , namely the Tukey test, which depends on one degree of freedom, and the Mandel test (a stack of lines) . The data included five levels of phosphorus and three levels of nitrogen in the wheat crop ; it can be seen in appendix A .

As a result , the Tukey and Mandel tests have a significant effect on nesting. The interaction effect had a clear and significant effect on the results of the analysis and the main effects tests . 

 

Downloads

Download data is not yet available.

References

Anderson, V.L. and Mclean, R.A. (1974) .Design of Experiments. Vol.5, Marcel Dekker, INC. New York.

Arnold, S. F. (1981).The Theory of Linear Models and Multivariate Analysis. New York: John Wily.

Bawrry, D. (1993) .Testing for additivity of a regression Function. Ann. Statist. 21,235-254. DOI: https://doi.org/10.1214/aos/1176349024

Cochran W.G.and Cox G.M., (1957).Experimental Designs. New York: Wiley. DOI: https://doi.org/10.1097/00010694-195711000-00018

Ghosh, M.N. and Sharma, Divakar,(1963) .Power of Tukey’s Test for Non-Additivity. Journal of the Royal Statistical Society, Ser.B, 25, No. 1, 213-219. DOI: https://doi.org/10.1111/j.2517-6161.1963.tb00503.x

Goodman, L. A., (1981).Association Models and Canonical Correlation in the Analysis of Cross-Classifications Having Ordered Categories. J.Amer.Statist. Assoc., 76,320-334. DOI: https://doi.org/10.1080/01621459.1981.10477651

Goodman, L. A. and Haberman, S.J. (1990) .Nonadditivity in Two-Way Analysis of Variance. J.Amer.Statist. Assoc., 85,139-145. DOI: https://doi.org/10.1080/01621459.1990.10475317

Graybill, F.A. (1961).An Introduction to Linear Statistical Models. Vol.1.New York:McGraw-Hill

Graybill, F.A. (1969).Introduction to Matrix With Applications in Statistics. Belmont, Calif.: Wadsworth Publishing Company.

Graybill, F.A. (1976). Theory and application of the linear model. Belmont, Calif.: Wadsworth Publishing Company.

Hasan. S., (2017).A comparison between Yates and Rubin's methods for estimating missing values in the Latin square design. Vol. 21, Issue 4 (31 Aug. 2017), pp.300-312, 13 p. Iraqi- Erbil...https://search.emarefa.net/detail/BIM-771034.

Hegemann, V., and Johnson, D. E. (1976a).On Analyzing Two-Way AOV Data with Interaction. Technometrics, 18,273-281. DOI: https://doi.org/10.1080/00401706.1976.10489447

Hegemann, V., and Johnson, D. E. (1976b).The Power of Two Tests for Nonadditivity. J.Amer.Statist. Assoc., 71,945-948. DOI: https://doi.org/10.1080/01621459.1976.10480974

Johnson, Dallas E. and Graybill, Franklin A., (1972b).An Analysis of a Two-Way Model with Interaction and No Replication. J.Amer. Statist. Assoc., 67,862-868. DOI: https://doi.org/10.1080/01621459.1972.10481307

Krishnaiah, P. R., and Yochmowitz, M. G. (1980).Inference on the Structure of Interaction in Two-Way Classification Model. In Hand-book of Statistics (Vol. 1), ed. P.R. Krishnaiah, Amsterdam: North-Holland, pp. 973-994. DOI: https://doi.org/10.1016/S0169-7161(80)80055-1

Li, C.C., (1964).Introduction to Experimental Statistics. McGraw-Hill Book Company, New York.

Mandel, J. (1961).Non-additivity in Two-Way Analysis of Variance. J. Amer. Statist. Assoc., 56, 878-888. DOI: https://doi.org/10.1080/01621459.1961.10482132

Mandel, J. (1969). Partitioning the interaction in analysis of variance. J. Res. Nat. Bur. Standards Sect. B., 73B, 309-328. DOI: https://doi.org/10.6028/jres.073B.031

Scheffe,H.(1959).The Analysis of Variance. John Wiley , New York.

Snee, R. D. (1982).Non-additivity in a Two-Way Classification: Is It Interaction or Nonhomogeneous Variance. J. Amer. Statis. Assoc., 77, 515-519. DOI: https://doi.org/10.1080/01621459.1982.10477840

Tukey,John W.,(1949).One Degree of Freedom for Non-Additivity. Biometrics, 5, 232-242. DOI: https://doi.org/10.2307/3001938

Tukey,John W.,(1955).Answer to Query 113. Biometrics 11,111-113. DOI: https://doi.org/10.2307/3001486

Tukey,John W.,(1962).The future of data analysis.Ann. Math. Statist. 33, 1-67. DOI: https://doi.org/10.1214/aoms/1177704711

Venables W. V.and Ripley B.D. (2002) .Statistics Complements to Modern Applied Statistics Withs.Fourth edition, Available from http/www.stats.ox.ac.uk/pub/Mass4/. DOI: https://doi.org/10.1007/978-0-387-21706-2

Ward, G. C. and Dick, I. D. (1952). Non-additivity in randomized block designs and balanced incomplete block designs .New Zealand Journal of Science and Technology 33, 430-436.

Downloads

Published

2026-01-09

How to Cite

Analysis of Interaction in the Case of No Replication in a Two-Factor Experiment. (2026). Journal of Administration and Economics, 48(141), 253-262. https://doi.org/10.31272/jae.i141.1017

Similar Articles

1-10 of 111

You may also start an advanced similarity search for this article.