無趨勢PBIB設計的建構和最佳化性質

Abstract

實驗設計中，我們假設在區塊中存在一趨勢效應(trend effect)。此趨勢效應影響觀察值，也影響我們對區塊效應(block effect)和處理效應(treatment effect)的估計。此種設計模式不同於一般的區塊設計模式，因此須將趨勢效應加人設計模式中。

Yeh and Bradley conjectured that every binary connected block design with blocks of size k and a constant replication numberr for each treatment can be converted to a linear trend-free design by permuting the positions of theatments within blocks if and only if r(k+1)≡0 (mod 2). Chai and Majumdar (1993) proved that any BIB design which satisfies r(k+1)≡0 (mod 2) is even can be converted to a linear trend-free design. In this thesis, we want to examine this conjecture is true or not for group-divisible designs (GD designs).