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Analysis of a Lattice Design for the Farm Experiment
PAIK, UHN BOONG 忠南大學校 1962 論文集 Vol.2 No.-
Lattice 計劃에 依한 實驗結果를 直交排列表에 依하여 分析하는 要領을 說明한 것이다. 直交排列表의 여러가지 利用法의 大要는 이미 忠南大學校 論文集 第 1 輯에서 說明한 바 있다. PartⅢ에서 說明하는 方法은 Simple Lattice, Triple Lattice 또는 Balanced Lattice의 어느 경우에 있어서나 適用되는 方法이다. 直交排列表와 카-드의 作成法은 增山元三郎著 "實驗計劃法" 岩波全書, 1956에 자세히 說明되어 있으나 여기서의 分析上의 利用法의 要領은 筆者에 依한 것이다. Snedecor 氏는 이를 利用할 수 있는 計算機를 가지고 있는가 라고 묻고있지만 몬로 電氣計算機 한臺도 없음이 遺感이다. 여기에 私信의 一部를 公開한 點에 대하여 Snedecor 氏에게 깊이 謝過하는 바이며 資料의 公開를 快諾하여주신 農事院作物第一科長 崔鉉玉先生에게 感謝하는 바이다.
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백운붕 高麗大學校統計硏究所 1991 應用統計 Vol.6 No.-
This is a review paepr for the book entitled Quality Through Design by N. Logo-thetis and H.P. Wynn. N.Logothetis is Senior Consultant, British Telecom and H.P.Wynn is Professor of Statistics, City University, London England The authors state in their preface as follows: "Our approach has been two-fold. First, we hope to have laid bare the (Taguchi's) methods, 'warts and all', with enough real examples to give a feel for applications. Second, we have drawn on methods available in statistics which, together with special Taguchi methodo-logy and philosophy, should form the backbone of a post-Taguchi methodology in off-line quality improvement."
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백운붕 高麗大學校統計硏究所 1992 應用統計 Vol.7 No.-
임상실험에서 교차실험계획의 기본형식은 실험대상 각 자가 두가지 이상의 약물실험에 이용된다는 것이다. 이중에서 가장 간단한 형식의 것이 두 처리(two-treatment) 두 시기 (two-period) 교차실험계획이다. 이러한 두 처리 두 시기 교차실험계획으로 Grizzle (1965)의 방법이 표준적인 접근방법으로 알려져 있다. 그러나 Grizzle의 방법에는 수용하기 어려운 오류가 있음이 지적되고있다. 본 논문에서는 SAS/GLM을 이용하여 Grizzle의 논문에서 인용하고 있는 예에 대해서 다각도로 검토하고, 일반적인 2×2-실험 (2×2-trial)에 대한 비판을 소개하고, 바람직한 교차실험계획을 제시할 것이다. The standard, classical approch to the analysis of the two-period change-over (or crossover) design was originally proposed by Grizzle (1995). In this design, however, potentially important effects are aliased (sequence group, residual and treatment-by-period interaction). Unless we make assumptions about two of these we are not entitled to draw conclusions about any of them. This strict and rather formal criticism of the design, however, has not precluded its use in practice; indeed, its widespread use indicates at least a moderately successful record. Grizzle's approach is based on standard linear model theoey with slight modification. In this paper, we review the Grizzle's methods utilizing SAS/GLM and a critical review of the 2×2 trial is presented.
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白雲鶴 忠南大學校 1963 論文集 Vol.3 No.-
In most plans, especially in the farm experiments, it is necessary to use block of six or fewer experimental units. Such a design as the Table ⑴ may be suitable in the sense of reducing of the size of block. This may be called a “Augmented 2^3 factorial Design,” or may be called a “Fractional Replication of the Factorial Experiments with Block of 6 Units.” Let the i th one of the v treatments be replicated r_i times in the b incomplete blocks of size n._i_h. Let the yield of the ijh th observation be expressed by the equation ⑴, where i=1,2,…v=number of treatments: j=1,2,…r=number of complete blocks; h=1,2,…b=number of incomplete blocks in the j th complete block; n_i_j_h=1 if i th treatment occurs in the h th incomplete block of the jth complete block and zero otherwise. Intrablock Analysis The least square estimates of effects for the linear model 1 are obtained by minimizing the residual sum of squares and equating to zero each of the partial derivatives of the above residual sum of spuares with respect to μ, T_i, p_j and β_j_h results in the normal equations ⑵. In matrix notation in the augmented 2^3 factorial design, the v+1 equations from ⑶ plus the equation ∑T^_i=0 is the equation ⑷. The solutions for T^_g is obtained such as expression ⑸. The solutions for the p_i and β_j_h must be obtained jointly since they are not orthogonal. From the equation ⑺ solutions for p^_j+β^_j_h are obtained such as expression ⑻. Recovery of Interblock Information The sum of squares to be minimized is the expression ⑾, where the true weights are w=σ_e^2 and w´=mean of w´_j_h, w_j_h=1/(σ_e^2+n_j_hσ_β^2)From the resulting normal equations, I obtained w=1/E_e, w'=2.7/6E_b - 3.3E_e from the Table ⑴. Analysis for Repetitions of the Design In this case, the block ss contains two components. One (component b) is the component that is present even when there are no repetitions (E_b), and the other one (component a) is a new component. The sum of squares for the component a is obtained by same method of the lattice design (see Table 3). Factorial Analysis (with adjusted data) We can obtain the Table ⑷ of three 3×3 table from the Table ⑴. And, from these we can calculate the main effects of N, P, k and two factor interactions with the method for fitting constants. But, if interaction becomes obvious, different coefficients must be calculated for each component in each effect. But, it is a bit tedious. I think, the following approximate method would have several advantage, including a familiar form of calulation. ⑴. We can test the main effect (say N)only for standards as a 2_3 factorial design, and test the same effect for the new treatments in the second and third replication. ⑵. We can test the main effect of N for the first replication as a 3×2^2 factorial design.
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백운붕 高麗大學校統計硏究所 1990 應用統計 Vol.5 No.1
SAS/GLM can be used for intrablock analysis (ordinary least squares method) of incomplete block designs. GLM procedure, however, cannot be used for interblock analysis. Paik(1986) showed that the best linear combined intra-and inter-block estimators of the treatment effects are equivalent to the generalized least squares(GLS) estimators. In this paper, a SAS/IML program for OLS and GLS estimators of the treatment effects of incomplete block designs is presented. Numerical examples are included.
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