以固定型模式及混合型模式分析各類型區集設計試驗資料之結果探討

Abstract

設置區集是進行試驗時很常見的做法，然而區集效應應該視為是逢機型或是固定型在早期的教科書中多是把區集效應視為固定型加以分析，但是這樣的想法對於推論上會有所限制，另外，傳統的公式都是利用代數的方式求解，這對於有缺值的資料而言非常不方便。 本研究將對於幾種常見的區集設計分別利用固定型模式與混合型模式加以分析，並且比較其中的差異。此外，本研究也稍加探討非均衡資料的情況。 結果發現，在均衡資料的情況之下，以傳統代數與矩陣代數分析固定型模式得到的結果會是一致的，這可以說明以矩陣代數分析所得到的結果是正確的，而且，利用矩陣代數的方法可以很容易的以混合型模式分析資料，而且對於有缺值的資料矩陣的運算方法也不會受到影響。 在比較固定型模式與混合型模式所分析的結果，很多的統計量都是不同的，因此，對於區集設驗的資料，就區集效應而言，仍然應該是為是逢機型的效應較為合適。

Blocking is commonly used in experiments as a local control method and to improve the efficiency. Block effects therefore should be regarded as ramdom rather than fixed. Unfortunately most textbooks on experimental designs treat block effects as fixed and the analysis formulae presented in the textbooks can only be used to handle the balanced data. Several commonly used block designs are analyzed as fixed model and mixed model separately and comparison of analysis results are made in this paper. We also compare the situations of balanced data and unbalanced data. Merits of general linear models by matrix formulae relative to traditional analysis by algebraic formulae are discussed, especially for mixed models and/or unbalanced data. Results indicate that many important statistics differ when cited data were analyzed assuming block effects as fixed and assuming block effects as random. For the purpose of making a logical statistical inference, block effects should be treated as random rather than fixed.