On a new approach to the analysis of variance for experiments with orthogonal block structure. III. Experiments in row-column designs

Abstract

SummaryThe main estimation and hypothesis testing procedures are presented for experiments conducted in row-column designs of a certain desirable 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. Relevant 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 results from analyses based on some stratum submodels. Practical application of the presented theory is illustrated by four examples of real experiments in the relevant row-column designs. The present paper is the third in the projected series of publications concerning the analysis of experiments with orthogonal block structure.

On a new approach to the analysis of variance for experiments with orthogonal block structure. IV. Experiments in split-plot designs

“…as can be shown (see Appendix 1 in Caliński and Siatkowski, 2018). The equality (12) indicates that H 0 in (10) is consistent; see formula (3.2.8) in Rao (1971).…”

“…as follows from Theorem 3.2 in Rao (1971). Note, however, that the sums of squares in (13) can equivalently be written (see Appendix 2 in Caliński and Siatkowski, 2018) as…”

“…Thus, it has been decided to publish a series of papers focused on practical applications of the new approach to the analysis of experiments with the OBS property. The first (Caliński and Siatkowski, 2017) is devoted to experiments conducted in proper block designs. The second (Caliński and Siatkowski, 2018) is devoted to experiments in nested block designs.…”

“…The second (Caliński and Siatkowski, 2018) is devoted to experiments in nested block designs. The third (Caliński, Łacka and Siatkowski, 2019) concerns experiments in row-column designs. In each of these papers the subject is confined to experiments with the desirable OBS property.…”

“…But note that this concerns nested block designs also. At this point it may be interesting to note that Example 1 in Caliński and Siatkowski (2018) illustrates a split-plot design considered by Brzeskwiniewicz (1994).…”