<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Summary The main estimation and hypothesis testing results are presented for experiments conducted in proper block designs. It is shown that, under appropriate randomization, these experiments have the convenient orthogonal block structure. Because of this, the analysis of experimental data can be performed in a comparatively simple way. Certain simplifying procedures are introduced. The main advantage of the presented methodology concerns the analysis of variance and related hypothesis testing procedures. Under the adopted approach one can perform them directly, not by combining results from intra-block and inter-block analyses. Application of the theory is illustrated by three examples of real experiments in proper block designs. This is the first of a projected series of papers concerning the analysis of experiments with orthogonal block structure.</p></abstract>

Summary The main estimation and hypothesis testing results are presented for experiments conducted in proper block designs. It is shown that, under appropriate randomization, these experiments have the convenient orthogonal block structure. Because of this, the analysis of experimental data can be performed in a comparatively simple way. Certain simplifying procedures are introduced. The main advantage of the presented methodology concerns the analysis of variance and related hypothesis testing procedures. Under the adopted approach one can perform them directly, not by combining results from intra-block and inter-block analyses. Application of the theory is illustrated by three examples of real experiments in proper block designs. This is the first of a projected series of papers concerning the analysis of experiments with orthogonal block structure.

On a New Approach to the Analysis of Variance for Experiments with Orthogonal Block Structure.

Biometrical Letters

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

I. Experiments in proper block designs

Summary The main estimation and hypothesis testing results are presented for experiments conducted in proper block designs. It is shown that, under appropriate...

On a New Approach to the Analysis of Variance for Experiments with Orthogonal Block Structure.

Published Online: Dec 13, 2017

Page range: 91 - 122

DOI: https://doi.org/10.1515/bile-2017-0006

Keywords
analysis of variance, estimation, hypothesis testing, orthogonal block structure, proper block designs, randomization-derived model

© by Tadeusz Calinski

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

On a New Approach to the Analysis of Variance for Experiments with Orthogonal Block Structure.

Published Online: Dec 13, 2017

Page range: 91 - 122

DOI: https://doi.org/10.1515/bile-2017-0006

Keywordsanalysis of variance, estimation, hypothesis testing, orthogonal block structure, proper block designs, randomization-derived model

© by Tadeusz Calinski

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
analysis of variance, estimation, hypothesis testing, orthogonal block structure, proper block designs, randomization-derived model