<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The main estimation and hypothesis testing procedures are presented for experiments conducted in nested block designs of a certain type. It is shown that, under appropriate randomization, these experiments have the convenient orthogonal block structure. Due to this property, the analysis of experimental data can be performed in a comparatively simple way. Certain simplifying procedures are indicated. The main advantage of the presented methodology concerns the analysis of variance and related hypothesis testing procedures. Under the adopted approach one can perform these analytical methods directly, not by combining the results from analyses based on stratum submodels. The application of the presented theory is illustrated by three examples of real experiments in relevant nested block designs. The present paper is the second in the planned series concerning the analysis of experiments with orthogonal block structure.</p></abstract>

The main estimation and hypothesis testing procedures are presented for experiments conducted in nested block designs of a certain type. It is shown that, under appropriate randomization, these experiments have the convenient orthogonal block structure. Due to this property, the analysis of experimental data can be performed in a comparatively simple way. Certain simplifying procedures are indicated. The main advantage of the presented methodology concerns the analysis of variance and related hypothesis testing procedures. Under the adopted approach one can perform these analytical methods directly, not by combining the results from analyses based on stratum submodels. The application of the presented theory is illustrated by three examples of real experiments in relevant nested block designs. The present paper is the second in the planned series concerning the analysis of experiments with orthogonal block structure.

On a new approach to the analysis of variance for experiments with orthogonal block structure.

Department of Mathematical and Statistical Methods

Biometrical Letters

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

II. Experiments in nested block designs

The main estimation and hypothesis testing procedures are presented for experiments conducted in nested block designs of a certain type. It is shown that,...

On a new approach to the analysis of variance for experiments with orthogonal block structure.

Published Online: Dec 14, 2018

Page range: 147 - 178

DOI: https://doi.org/10.2478/bile-2018-0011

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

© 2018 Tadeusz Caliński et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On a new approach to the analysis of variance for experiments with orthogonal block structure.

Published Online: Dec 14, 2018

Page range: 147 - 178

DOI: https://doi.org/10.2478/bile-2018-0011

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

© 2018 Tadeusz Caliński et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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