多層級試驗設計之評介

Abstract

試驗設計早期多用於農業上，但中後期至現代，工業上的應用漸多。在目前應用上，不管農業上或工業上，多朝向多層級設計(multi-stratum design)研究，即包含兩個或兩個以上的參試因子，利用巢式劃分(nesting)或跨越劃分(crossing)來決定試驗單位。多層級設計一般會符合簡單直交區集結構(simple orthogonal block structure)，巢式劃分與跨越劃分即為簡單直交區集結構基本的區集劃分方式。最簡單的巢式劃分為裂區設計(Split-plot designs)，而最簡單的跨越劃分為條區設計(Split-Block designs)。但目前的研究大多只是利用多層級設計的基本架構套用於實用中，並未去詳加探討層級的精確度比較，處理效應置放的問題。藉由Nelder提出的兩個重要函數，我們可以相當容易了解層級如何劃分，再藉由空白變方分析表(null analysis of variance)中變方成分(variance component)的計算，可以看出何者變異較大，即可將較重要的因子放置在變異較小的層級中。

Multi-stratum designs are often used with applications in various areas, such as agriculture, industry, social science, etc. The main purpose of such designs is to effectively arrange treatments or treatment combinations to experimental units. The partition of experimental units basically uses the two schemes nesting and crossing. So the multi-stratum designs usually contain at least two experimental factors. The simplest nesting design is the split plot design, and the simplest crossing design is the split block design. Most of the published studies only implement the basic framework of multi-stratum designs, but often do not discuss which stratum has higher precision or how to arrange treatments or treatment combinations into the stratum. By two basic functions corresponding to nesting and crossing, proposed by Nelder (1964), we show how to divide the stratum and construct the null analysis of variance. This would guide users to arrange the more important effects in the stratum with less variation.