Measure of overall regression sum of squares of symmetric randomized complete block design with a lost observation

  • Authors

    • Kittiwat Sirikasemsuk
    2018-03-08
    https://doi.org/10.14419/ijet.v7i2.3.9967
  • Design of Experiment, Randomized Complete Block Design, Lost Observation, Overall Regression Sum of Squares

  • Abstract

    A randomized complete block design (RCBD) is useful for analyzing a treatment variable and one block variable under the condition where experimental units are limited. The RCBD is assumed that there is no interaction between the treatment variable and the block variable. This paper considered the symmetric randomized complete block design (SRCBD) with t treatments and t blocks, when a lost value occurs in the experiments. For the analysis of variance for the unbalanced data, the ready-made formulae were not provided in the past. The SRCBD with a lost value was analyzed by means of the fundamental underlying linear regression model in order to determine the reliable mathematical formulae for the fitted parameters and the overall regression sum of squares of experimental data. It is noted that all possible parameters are considered in the overall regression sum of squares which will be helpful for the analysis of variance through the exact approach (the model comparison approach) at a later stage.

  • References

    1. [1] Montgomery DC (2008), Design and Analysis of Experiments, 5thedn.John Wiley & Sons.

      [2] Mead R, Gilmour SG, & Mead A (2012), Statistical Principles for the Design of Experiments: Applications to Real Experiments, Vol. 36,Cambridge University Press.

      [3] Kelechi AC (2012), Symmetric and unsymmetric balanced incomplete block designs: a comparative analysis.International Journal of Statistics and Applications 2, pp. 33-39.

      [4] Manivannan S, Arumugam R, Sudharsan NM, &Prasanna DS (2010), Taguchi based linear regression modeling of flat plate heat sink.Journal of Engineering and Applied Sciences 5, pp. 36-44.

      [5] Ngo MT, Hoang V, & Hoang VS (2017), Optimization cutting fluids and parameters for minimizing cutting force in fly-hobbing.Journal of Engineering and Applied Sciences 12, pp. 5212-5218.

      [6] Youden WJ (1937), Use of incomplete block replications in estimating tobacco-mosaic virus.Contributions from Boyce Thompson Institute 9, pp. 41-48.

      [7] Yates F (1936), Incomplete randomized blocks.Annals of Eugenics7, pp. 121-140.

      [8] Ai M, Li K, Liu S, & Lin DK (2013), Balanced incomplete latin square designs.Journal of Statistical Planning and Inference143, pp. 1575-1582.

      [9] Allan FE & Wishart J (1930), A method of estimating the yield of a missing plot in field experimental work.Journal of Agricultural Science20, pp. 399-406.

      [10] Little RJA & Rubin DB (2002), Statistical Analysis with Missing Data, 2ndedn.John Wiley & Sons, New York.

      [11] Baird HR &Kramer CY (1960), Analysis of variance of a balanced incomplete block design with missing observations.Journal of the Royal Statistical Society: Series C9, pp. 189-198.

      [12] Coons I (1957), The analysis of covariance as a missing plot technique. Biometrics13, pp. 387-405.

      [13] Cochran WG (1957), Analysis of covariance: its nature and uses.Biometrics13, pp. 261-281.

      [14] Wilkinson GN (1958), Estimation of missing values for the analysis of incomplete data. Biometrics 14, pp. 257-286.

      [15] Bartlett MS (1937), Some examples of statistical methods of research in agriculture and applied biology.Journal of the Royal Statistical Society 4, pp. 137-183.

      [16] Ogbonnaya CE&Uzochukwu EC (2016), Estimation of missing data in analysis of covariance: a least-squares approach.Communications in Statistics - Theory and Methods45, pp. 1902-1909.

      [17] Sirikasemsuk K (2016), One missing value problem in latin square design of any order: regression sum of squares. Proceedings of the .Joint 8th International Conference on Soft Computing and Intelligent Systems and 17th International Symposium on Advanced Intelligent Systems (SCIS&ISIS), pp. 142-147.

      [18] Sirikasemsuk K&Leerojanaprapa K (2017), One missing value problem in latin square design of any order: exact analysis of variance.Cogent Engineering4, pp. 1411222.

      [19] SirikasemsukK &Leerojanaprapa K (2017), Analysis of two-missing-observation 4x4 latin squares using the exact approach.Advances in Intelligent Systems and Computing 566, P. Meesad P, Sunantha S, Unger H, Eds. Springer, pp. 69–81.

      [20] Rencher AC &Schaalje GB (2008), Linear Models in Statistics, 2ndedn. John Wiley & Sons.

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  • How to Cite

    Sirikasemsuk, K. (2018). Measure of overall regression sum of squares of symmetric randomized complete block design with a lost observation. International Journal of Engineering & Technology, 7(2.3), 50-53. https://doi.org/10.14419/ijet.v7i2.3.9967

    Received date: 2018-03-08

    Accepted date: 2018-03-08

    Published date: 2018-03-08